@article{pasmann_variansyah_kelley_mcclarren_2024, title={Mitigating Spatial Error in the Iterative Quasi-Monte Carlo (iQMC) Method for Neutron Transport Simulations with Linear Discontinuous Source Tilting and Effective Scattering and Fission Rate Tallies}, volume={5}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2024.2332007}, abstractNote={The iterative Quasi–Monte Carlo (iQMC) method is a recently proposed method for neutron transport simulations. iQMC can be viewed as a hybrid between deterministic iterative techniques, Monte Carlo simulation, and Quasi–Monte Carlo techniques. iQMC holds several algorithmic characteristics that make it desirable for high-performance computing environments, including an O(N−1) convergence scheme, a ray-tracing transport sweep, and a highly parallelizable nature similar to analog Monte Carlo. While there are many potential advantages of using iQMC, there are also inherent disadvantages, namely, the spatial discretization error introduced from the use of a mesh across the domain.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Pasmann, Samuel and Variansyah, Ilham and Kelley, C. T. and McClarren, Ryan G.}, year={2024}, month={May} }
 @article{pasmann_variansyah_kelley_mcclarren_2023, title={A Quasi-Monte Carlo Method With Krylov Linear Solvers for Multigroup Neutron Transport Simulations}, volume={1}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2022.2143704}, abstractNote={Abstract In this work we investigate replacing standard quadrature techniques used in deterministic linear solvers with a fixed-seed Quasi–Monte Carlo (QMC) calculation to obtain more accurate and efficient solutions to the neutron transport equation (NTE). QMC is the use of low-discrepancy sequences to sample the phase-space in place of pseudorandom number generators used by traditional Monte Carlo (MC). QMC techniques decrease the variance in the stochastic transport sweep and therefore increase the accuracy of the iterative method. Historically, QMC has largely been ignored by the particle transport community because it breaks the Markovian assumption needed to model scattering in analog MC particle simulations. However, by using iterative methods the NTE can be modeled as a pure-absorption problem. This removes the need to explicitly model particle scattering and provides an application well suited for QMC. To obtain solutions we experimented with three separate iterative solvers: the standard Source Iteration (SI) Solver and two linear Krylov Solvers, i.e., the Generalized Minimal RESidual method (GMRES) and the BiConjugate Gradient STABilized method (BiCGSTAB). The resulting hybrid iterative-QMC solver was assessed on three slab geometry problems of one dimension. In each sample problem the Krylov Solvers achieve convergence with far fewer iterations (up to eight times) than the SI Solver. Regardless of the linear solver used, the hybrid method achieved an approximate convergence rate of as compared to the expected of traditional MC simulation across all test problems.}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Pasmann, Sam and Variansyah, Ilham and Kelley, C. T. and McClarren, Ryan}, year={2023}, month={Jan} }
 @article{kwon_curtin_morrow_kelley_jakubikova_2023, title={Adaptive basis sets for practical quantum computing}, volume={4}, ISSN={["1097-461X"]}, url={https://doi.org/10.1002/qua.27123}, DOI={10.1002/qua.27123}, abstractNote={Abstract}, journal={INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY}, author={Kwon, Hyuk-Yong and Curtin, Gregory M. M. and Morrow, Zachary and Kelley, C. T. and Jakubikova, Elena}, year={2023}, month={Apr} }
 @article{kelley_2022, title={Newton's Method in Mixed Precision}, volume={64}, ISSN={["1095-7200"]}, url={https://doi.org/10.1137/20M1342902}, DOI={10.1137/20M1342902}, abstractNote={. We investigate the use of reduced precision arithmetic to solve the linear equation for the Newton step. If one 3 neglects the backward error in the linear solve, then well-known convergence theory implies that using single precision in the 4 linear solve has very little negative e(cid:11)ect on the nonlinear convergence rate. 5 However, if one considers the e(cid:11)ects of backward error, then the usual textbook estimates are very pessimistic and even the 6 state-of-the-art estimates using probabilistic rounding analysis do not fully conform to experiments. We report on experiments 7 with a speci(cid:12)c example. We store and factor Jacobians in double, single, and half precision. In the single precision case we 8 observe that the convergence rates for the nonlinear iteration do not degrade as the dimension increases and that the nonlinear 9 iteration statistics are essentially identical to the double precision computation. In half precision we see that the nonlinear 10 convergence rates, while poor, do not degrade as the dimension increases. 11 Audience. This paper is intended for students who have completed or are taking an entry-level graduate course in 12 numerical analysis and for faculty who teach numerical analysis. The important ideas in the paper are O notation, (cid:13)oating 13 point precision, backward error in linear solvers, and Newton’s method.}, number={1}, journal={SIAM REVIEW}, author={Kelley, C. T.}, year={2022}, month={Mar}, pages={191–211} }
 @article{bian_chen_kelley_2021, title={ANDERSON ACCELERATION FOR A CLASS OF NONSMOOTH FIXED-POINT PROBLEMS}, volume={43}, ISSN={["1095-7197"]}, url={https://doi.org/10.1137/20M132938X}, DOI={10.1137/20M132938X}, abstractNote={We prove convergence of Anderson acceleration for a class of nonsmooth fixed-point problems for which the nonlinearities can be split into a smooth contractive part and a nonsmooth part which has a...}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Bian, Wei and Chen, Xiaojun and Kelley, C. T.}, year={2021}, pages={S1–S20} }
 @article{morrow_kwon_kelley_jakubikova_2021, title={Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation}, volume={17}, ISSN={["1549-9626"]}, url={https://doi.org/10.1021/acs.jctc.1c00569}, DOI={10.1021/acs.jctc.1c00569}, abstractNote={The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.}, number={9}, journal={JOURNAL OF CHEMICAL THEORY AND COMPUTATION}, publisher={American Chemical Society (ACS)}, author={Morrow, Zachary and Kwon, Hyuk-Yong and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Sep}, pages={5673–5683} }
 @article{kwon_morrow_kelley_jakubikova_2021, title={Interpolation Methods for Molecular Potential Energy Surface Construction}, volume={125}, ISSN={["1520-5215"]}, url={https://doi.org/10.1021/acs.jpca.1c06812}, DOI={10.1021/acs.jpca.1c06812}, abstractNote={The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.}, number={45}, journal={JOURNAL OF PHYSICAL CHEMISTRY A}, publisher={American Chemical Society (ACS)}, author={Kwon, Hyuk-Yong and Morrow, Zachary and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Nov}, pages={9725–9735} }
 @article{morrow_kwon_kelley_jakubikova_2021, title={Reduced-dimensional surface hopping with offline-online computations}, volume={8}, ISSN={["1463-9084"]}, url={https://doi.org/10.1039/D1CP03446D}, DOI={10.1039/D1CP03446D}, abstractNote={We simulate the photodissociation of azomethane with a fewest-switches surface hopping method on reduced-dimensional potential energy surfaces constructed with sparse grid interpolation.}, journal={PHYSICAL CHEMISTRY CHEMICAL PHYSICS}, publisher={Royal Society of Chemistry (RSC)}, author={Morrow, Zachary and Kwon, Hyuk-Yong and Kelley, C. T. and Jakubikova, Elena}, year={2021}, month={Aug} }
 @article{kelley_bernholc_briggs_hamilton_lin_yang_2020, title={Mesh independence of the generalized Davidson algorithm}, volume={409}, url={https://doi.org/10.1016/j.jcp.2020.109322}, DOI={10.1016/j.jcp.2020.109322}, abstractNote={We give conditions under which the generalized Davidson algorithm for eigenvalue computations is mesh-independent. In this case mesh-independence means that the iteration statistics (residual norms, convergence rates, for example) of a sequence of discretizations of a problem in a Banach space converge the statistics for the infinite-dimensional problem. We illustrate the result with several numerical examples.}, journal={Journal of Computational Physics}, publisher={Elsevier BV}, author={Kelley, C.T. and Bernholc, J. and Briggs, E.L. and Hamilton, Steven and Lin, Lin and Yang, Chao}, year={2020}, month={May}, pages={109322} }
 @article{morrow_liu_kelley_jakubikova_2019, title={Approximating Periodic Potential Energy Surfaces with Sparse Trigonometric Interpolation}, volume={123}, ISSN={1520-6106 1520-5207}, url={http://dx.doi.org/10.1021/acs.jpcb.9b08210}, DOI={10.1021/acs.jpcb.9b08210}, abstractNote={The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in computational chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as local minima, maxima, and transition states. Construction of full-dimensional PESs for molecules with more than ten atoms is computationally expensive and often not feasible. Previous work in our group used sparse interpolation with polynomial basis functions to construct a surrogate reduced-dimensional PESs along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. However, polynomial interpolation does not preserve the periodicity of the PES gradient with respect to angular components of geometry, such as torsion angles, which can lead to nonphysical phenomena. In this work, we construct a surrogate PES using trigonometric basis functions, for a system where the selected reaction coordinates all correspond to the torsion angles, resulting in a periodically repeating PES. We find that a trigonometric interpolation basis not only guarantees periodicity of the gradient, but also results in slightly lower approximation error than polynomial interpolation.}, number={45}, journal={The Journal of Physical Chemistry B}, publisher={American Chemical Society (ACS)}, author={Morrow, Zack and Liu, Chang and Kelley, C. T. and Jakubikova, Elena}, year={2019}, month={Oct}, pages={9677–9684} }
 @article{chen_kelley_2019, title={Convergence of the EDIIS Algorithm for Nonlinear Equations}, volume={41}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/18M1171084}, DOI={10.1137/18M1171084}, abstractNote={The Energy Direct Inversion on the Iterative Subspace (EDIIS) algorithm was designed to globalize Anderson acceleration, a method for improving the performance of fixed point iteration. The motivat...}, number={1}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Chen, Xiaojun and Kelley, C. T.}, year={2019}, month={Jan}, pages={A365–A379} }
 @article{liu_kelley_jakubikova_2019, title={Molecular Dynamics Simulations on Relaxed Reduced-Dimensional Potential Energy Surfaces}, volume={123}, ISSN={1089-5639 1520-5215}, url={http://dx.doi.org/10.1021/acs.jpca.9b02298}, DOI={10.1021/acs.jpca.9b02298}, abstractNote={Molecular dynamics (MD) simulations with full-dimensional potential energy surfaces (PESs) obtained from high-level ab initio calculations are frequently used to model reaction dynamics of small molecules (i.e., molecules with up to 10 atoms). Construction of full-dimensional PESs for larger molecules is, however, not feasible since the number of ab initio calculations required grows rapidly with the increase of dimension. Only a small number of coordinates are often essential for describing the reactivity of even very large systems, and reduced-dimensional PESs with these coordinates can be built for reaction dynamics studies. While analytical methods based on transition-state theory framework are well established for analyzing the reduced-dimensional PESs, MD simulation algorithms capable of generating trajectories on such surfaces are more rare. In this work, we present a new MD implementation that utilizes the relaxed reduced-dimensional PES for standard microcanonical (NVE) and canonical (NVT) MD simulations. The method is applied to the pyramidal inversion of a NH3 molecule. The results from the MD simulations on a reduced, three-dimensional PES are validated against the ab initio MD simulations, as well as MD simulations on full-dimensional PES and experimental data.}, number={21}, journal={The Journal of Physical Chemistry A}, publisher={American Chemical Society (ACS)}, author={Liu, Chang and Kelley, C. T. and Jakubikova, Elena}, year={2019}, month={Apr}, pages={4543–4554} }
 @article{ellis_evans_hamilton_kelley_pandya_2019, title={Optimization of processor allocation for domain decomposed Monte Carlo calculations}, volume={87}, ISSN={0167-8191}, url={http://dx.doi.org/10.1016/j.parco.2019.06.001}, DOI={10.1016/j.parco.2019.06.001}, abstractNote={Load imbalance plagues domain decomposed Monte Carlo calculations when sources are not uniform. Parallel efficiency for domain decomposed Monte Carlo transport calculations improves through a nonuniform allocation of processors over subdomains. We optimize the allocation with runtime diagnostics collected during a calibration step, then complete the full calculation. The diagnostic-based approach is compared to implicit filtering, an optimization algorithm for bound constrained noisy optimization problems. We consider both forward and hybrid radiation transport calculations to measure performance.}, journal={Parallel Computing}, publisher={Elsevier BV}, author={Ellis, J. Austin and Evans, Thomas M. and Hamilton, Steven P. and Kelley, C.T. and Pandya, Tara M.}, year={2019}, month={Sep}, pages={77–86} }
 @article{chen_kelley_xu_zhang_2018, title={A Smoothing Direct Search  Method for Monte Carlo-Based Bound Constrained Composite Nonsmooth Optimization}, volume={40}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/17M1116714}, DOI={10.1137/17M1116714}, abstractNote={We propose and analyze a smoothing direct search algorithm for finding a minimizer of a nonsmooth nonconvex function over a box constraint set, where the objective function values cannot be compute...}, number={4}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Chen, Xiaojun and Kelley, C. T. and Xu, Fengmin and Zhang, Zaikun}, year={2018}, month={Jan}, pages={A2174–A2199} }
 @article{weigand_schultz_giffen_farthing_crockett_kelley_gray_miller_2018, title={Modeling Nondilute Species Transport Using the Thermodynamically Constrained Averaging Theory}, volume={54}, ISSN={0043-1397}, url={http://dx.doi.org/10.1029/2017WR022471}, DOI={10.1029/2017WR022471}, abstractNote={Abstract}, number={9}, journal={Water Resources Research}, publisher={American Geophysical Union (AGU)}, author={Weigand, T. M. and Schultz, P. B. and Giffen, D. H. and Farthing, M. W. and Crockett, A. and Kelley, C. T. and Gray, W. G. and Miller, C. T.}, year={2018}, month={Sep}, pages={6656–6682} }
 @article{kelley_2018, title={Numerical methods for nonlinear equations}, volume={27}, ISSN={0962-4929 1474-0508}, url={http://dx.doi.org/10.1017/S0962492917000113}, DOI={10.1017/s0962492917000113}, abstractNote={This article is about numerical methods for the solution of nonlinear equations. We consider both the fixed-point form $\mathbf{x}=\mathbf{G}(\mathbf{x})$ and the equations form $\mathbf{F}(\mathbf{x})=0$ and explain why both versions are necessary to understand the solvers. We include the classical methods to make the presentation complete and discuss less familiar topics such as Anderson acceleration, semi-smooth Newton’s method, and pseudo-arclength and pseudo-transient continuation methods.}, journal={Acta Numerica}, publisher={Cambridge University Press (CUP)}, author={Kelley, C. T.}, year={2018}, month={May}, pages={207–287} }
 @inbook{terlaky_anjos_ahmed_2017, place={Philadelphia}, title={Implicit Filtering and Hidden Constraints}, DOI={10.1137/1.9781611974683.ch38}, abstractNote={38.1 ▪ IntroductionA hidden constraint, a yes-no constraint [409], or a virtual constraint [498] in an optimization problem is one without an explicit representation as an equality or inequality. In many cases, one detects constraint violation if the objective function fails to return a value. At other times, the constraint is tested by a separate computation but only returns a flag for failure or success. Our view is that if one cannot quantify the degree of infeasibility, then the constraints are hidden from the optimization.}, booktitle={Advances and Trends in Optimization with Engineering Applications}, publisher={SIAM}, year={2017}, pages={507–508} }
 @inbook{kelley_2017, place={Philadelphia}, title={Implicit filtering and hidden constraints, in Advances and Trends in Optimization with Engineering Applications}, volume={24}, booktitle={MOS-SIAM Series on Optimization}, publisher={SIAM}, author={Kelley, C.T.}, editor={Terlaky, T. and Anjos, M. and Ahmed, S.Editors}, year={2017}, pages={507–518} }
 @article{toth_ellis_evans_hamilton_kelley_pawlowski_slattery_2017, title={Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations}, volume={39}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/16M1080677}, DOI={10.1137/16m1080677}, abstractNote={We analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.}, number={5}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Toth, Alex and Ellis, J. Austin and Evans, Tom and Hamilton, Steven and Kelley, C. T. and Pawlowski, Roger and Slattery, Stuart}, year={2017}, month={Jan}, pages={S47–S65} }
 @article{wyers_morton_sollner_kelley_franzon_2016, title={A Generally Applicable Calibration Algorithm for Digitally Reconfigurable Self-Healing RFICs}, volume={24}, ISSN={1063-8210 1557-9999}, url={http://dx.doi.org/10.1109/TVLSI.2015.2424211}, DOI={10.1109/tvlsi.2015.2424211}, abstractNote={A generally applicable calibration technique for digitally reconfigurable self-healing radio frequency integrated circuits based on a hybrid of the Nelder-Mead and Hooke-Jeeves direct search algorithms is presented. The proposed algorithm is applied to the multiobjective problem of gain error and phase error minimization for a self-healing phase rotator test case. For the 8-D phase rotator calibration problem, we show that the proposed hybrid Nelder-Mead and Hooke-Jeeves calibration algorithm is capable of reducing the gain error and phase error of the phase rotator output to less than a maximum of 0.5 dB and 2°, respectively, relative to the chosen gain and phase targets. A 3-GHz self-healing phase rotator test chip was fabricated in a 45-nm silicon-on-insulator CMOS process, and the measured data were obtained to validate the performance of the proposed calibration algorithm.}, number={3}, journal={IEEE Transactions on Very Large Scale Integration (VLSI) Systems}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Wyers, Eric J. and Morton, Matthew A. and Sollner, T. C. L. Gerhard and Kelley, C. T. and Franzon, Paul D.}, year={2016}, month={Mar}, pages={1151–1164} }
 @article{hamilton_berrill_clarno_pawlowski_toth_kelley_evans_philip_2016, title={An assessment of coupling algorithms for nuclear reactor core physics simulations}, volume={311}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2016.02.012}, abstractNote={This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss–Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton–Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Numerical simulations demonstrating the efficiency of JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Hamilton, Steven and Berrill, Mark and Clarno, Kevin and Pawlowski, Roger and Toth, Alex and Kelley, C. T. and Evans, Thomas and Philip, Bobby}, year={2016}, month={Apr}, pages={241–257} }
 @article{nance_kelley_2015, title={A Sparse Interpolation Algorithm for Dynamical Simulations in Computational Chemistry}, volume={37}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/140965284}, DOI={10.1137/140965284}, abstractNote={In this paper we present a new implementation of Smolyak's sparse grid interpolation algorithm designed for dynamical simulations. The implementation is motivated by an application to quantum chemistry where the goal is to simulate photo-induced molecular transformations. A molecule conforms to a geometry that minimizes its potential energy, and many molecules have multiple potential energy minima. These geometries correspond to local minima of the molecule's potential energy surface, and one can simulate how a molecule transitions from one geometry to another by following the steepest descent path, or reaction path, on potential energy surfaces. Molecular vibrations and thermal fluctuations cause randomness in dynamics, so one must follow several paths simultaneously to more accurately simulate possible reaction paths. Current algorithms for reaction path following are too computationally burdensome for molecules of moderate size, but Smolyak's interpolation algorithm offers a cheap surrogate for potenti...}, number={5}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Nance, J. and Kelley, C. T.}, year={2015}, month={Jan}, pages={S137–S156} }
 @inproceedings{toth_kelley_slattery_hamilton_clarno_pawlowski_2015, title={Analysis of Anderson acceleration on a simplified neutronics/thermal hydraulics system}, booktitle={Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method}, author={Toth, A. and Kelley, C.T. and Slattery, S. and Hamilton, S. and Clarno, K. and Pawlowski, R.}, year={2015} }
 @article{toth_kelley_2015, title={Convergence Analysis for Anderson Acceleration}, volume={53}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/130919398}, DOI={10.1137/130919398}, abstractNote={Anderson($m$) is a method for acceleration of fixed point iteration which stores m+1 prior evaluations of the fixed point map and computes the new iteration as a linear combination of those evaluations. Anderson(0) is fixed point iteration. In this paper we show that Anderson($m$) is locally r-linearly convergent if the fixed point map is a contraction and the coefficients in the linear combination remain bounded. Without assumptions on the coefficients, we prove q-linear convergence of Anderson(1) and, in the case of linear problems, Anderson($m$). We observe that the optimization problem for the coefficients can be formulated and solved in nonstandard ways and report on numerical experiments which illustrate the ideas.}, number={2}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Toth, Alex and Kelley, C. T.}, year={2015}, month={Jan}, pages={805–819} }
 @article{nance_bowman_mukherjee_kelley_jakubikova_2015, title={Insights into the Spin-State Transitions in [Fe(tpy)2]2+: Importance of the Terpyridine Rocking Motion}, volume={54}, ISSN={0020-1669 1520-510X}, url={http://dx.doi.org/10.1021/acs.inorgchem.5b01747}, DOI={10.1021/acs.inorgchem.5b01747}, abstractNote={Iron(II) polypyridine complexes have the potential for numerous applications on a global scale, such as sensitizers, sensors, and molecular memory. The excited-state properties of these systems, particularly the intersystem crossing (ISC) rates, are sensitive to the choice of ligands and can be significantly altered depending on the coordination environment. We employ density functional theory and Smolyak's sparse grid interpolation algorithm to construct potential energy surfaces (PESs) for the photophysically relevant states ((1)A, (3,5)MC, and (1,3)MLCT) of the [Fe(tpy)2](2+) (tpy = 2,2':6',2"-terpyridine) complex, with the goal of obtaining a deeper understanding of the ground- and excited-state electronic structure of this system. The three dimensions that define our adiabatic PESs consist of equatorial and axial metal-ligand bond length distortions and a terpyridine ligand "rocking angle", which has not previously been investigated. The intersection crossing seams and minimum energy crossing points (MECPs) between surfaces are also determined. Overall, we find that the PESs of all electronic excited states investigated are characterized by low-energy valleys along the tpy rocking-angle coordinate. This results in the presence of large low-energy areas around the MECPs on the intersection seams of different electronic states and indicates that inclusion of this third coordinate is crucial for an adequate description of the PESs and surface crossing seams of the [Fe(tpy)2](2+) complex. Finally, we suggest that tuning the energetics of the tpy ligand rocking motion could provide a way to control the ISC process in this complex.}, number={23}, journal={Inorganic Chemistry}, publisher={American Chemical Society (ACS)}, author={Nance, James and Bowman, David N. and Mukherjee, Sriparna and Kelley, C. T. and Jakubikova, Elena}, year={2015}, month={Nov}, pages={11259–11268} }
 @article{willert_chen_kelley_2015, title={Newton's Method for Monte Carlo--Based Residuals}, volume={53}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/130905691}, DOI={10.1137/130905691}, abstractNote={We analyze the behavior of inexact Newton methods for problems where the nonlinear residual, Jacobian, and Jacobian-vector products are the outputs of Monte Carlo simulations. We propose algorithms which account for the randomness in the iteration, develop theory for the behavior of these algorithms, and illustrate the results with an example from neutronics.}, number={4}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Willert, Jeffrey and Chen, Xiaojun and Kelley, C. T.}, year={2015}, month={Jan}, pages={1738–1757} }
 @article{chen_kelley_2015, title={Optimization with Hidden Constraints and Embedded Monte Carlo Computations}, journal={Optimization and Engineering}, author={Chen, X and Kelley, C. T.}, year={2015} }
 @article{chen_kelley_2015, title={Optimization with hidden constraints and embedded Monte Carlo computations}, volume={17}, ISSN={1389-4420 1573-2924}, url={http://dx.doi.org/10.1007/s11081-015-9302-1}, DOI={10.1007/s11081-015-9302-1}, abstractNote={In this paper we explore the convergence properties of deterministic direct search methods when the objective function contains a stochastic or Monte Carlo simulation. We present new results for the case where the objective is only defined on a set with certain minimal regularity properties. We present two numerical examples to illustrate the ideas.}, number={1}, journal={Optimization and Engineering}, publisher={Springer Science and Business Media LLC}, author={Chen, Xiaojun and Kelley, C. T.}, year={2015}, month={Dec}, pages={157–175} }
 @article{willert_kelley_knoll_park_2014, title={A Hybrid Deterministic/Monte Carlo Method for Solving the k-Eigenvalue Problem with a Comparison to Analog Monte Carlo Solutions}, volume={43}, ISSN={2332-4309 2332-4325}, url={http://dx.doi.org/10.1080/00411450.2014.910225}, DOI={10.1080/00411450.2014.910225}, abstractNote={In this article we present a hybrid deterministic/Monte Carlo algorithm for computing the dominant eigenvalue/eigenvector pair for the neutron transport k-eigenvalue problem in multiple space dimensions. We begin by deriving the Nonlinear Diffusion Acceleration method (Knoll, Park, and Newman, 2011; Park, Knoll, and Newman, 2012) for the k-eigenvalue problem. We demonstrate that we can adapt the algorithm to utilize a Monte Carlo simulation in place of a deterministic transport sweep. We then show that the new hybrid method can be used to solve a two-group, two dimensional eigenvalue problem. The hybrid method is competitive with analog Monte Carlo in terms of number of particle flights required to compute the eigenvalue; however it produces a much less noisy eigenvector and fission source distribution. Furthermore, we show that we can reduce the error induced by the discretization of the low-order system by appropriate refinement of the mesh.}, number={1-7}, journal={Journal of Computational and Theoretical Transport}, publisher={Informa UK Limited}, author={Willert, J. and Kelley, C. T. and Knoll, D. A. and Park, H.}, year={2014}, month={Aug}, pages={50–67} }
 @article{eslinger_winton_ballard_howington_fregosi_ward_kelley_2014, title={Estimating Sampling Distributions of Apparent Thermal Diffusivity for Partially Saturated Soils}, journal={IEEE Trans. Geosci. Remote Sensing}, author={Eslinger, O J and Winton, C and Ballard, J R and Howington, Stacy E and Fregosi, Anna and Ward, K and Kelley, C T}, year={2014}, pages={15} }
 @article{hu_smith_willert_kelley_2014, title={HDMR applied to the 1-D, Single Speed Neutron Transport k-Eigenvalue Problem}, volume={177}, journal={Nuclear Science and Engineering}, author={Hu, Z. and Smith, R. and Willert, J. and Kelley, C.T.}, year={2014}, pages={1–11} }
 @article{hu_smith_willert_kelley_2014, title={High-Dimensional Model Representations for the Neutron Transport Equation}, volume={177}, ISSN={["1943-748X"]}, DOI={10.13182/nse13-52}, abstractNote={Abstract The Boltzmann transport equation is used to model the neutron flux in a nuclear reactor. The solution of the transport equation is the neutron flux, which depends on a large number of material cross sections that can be on the order of thousands. These cross sections describe various types of possible interactions between neutrons, such as fission, capture, and scattering. The cross sections are measured experimentally and therefore have associated uncertainties. It is thus necessary to quantify how the uncertainty of the cross-section values is propagated through the model for the neutron flux. High-dimensional model representations (HDMRs) can be employed to systematically quantify input-output relations. It can, however, be computationally prohibitive to construct a surrogate model using the HDMR framework for a model that has thousands of parameters. In this paper, we introduce an algorithm that utilizes the New Morris Method to first reduce the parameter space to include only the significant individual and pairwise effects and then construct a surrogate model using a Cut-HDMR expansion within the reduced space. A unified index is introduced to facilitate the comparison of the significance of the model parameters. The accuracy and efficiency of the surrogate model is demonstrated using a one-dimensional neutron transport equation.}, number={3}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Hu, Zhengzheng and Smith, Ralph C. and Willert, Jeffrey and Kelley, C. T.}, year={2014}, month={Jul}, pages={350–360} }
 @article{nance_jakubikova_kelley_2014, title={Reaction Path Following with Sparse Interpolation}, volume={10}, ISSN={1549-9618 1549-9626}, url={http://dx.doi.org/10.1021/ct5004669}, DOI={10.1021/ct5004669}, abstractNote={Computing the potential energy of an N-atom molecule is an expensive optimization process of 3N - 6 molecular coordinates, so following reaction pathways as a function of all 3N - 6 coordinates is unfeasible for large molecules. In this paper, we present a method that isolates d < 3N - 6 molecular coordinates and continuously follows reaction paths on d-dimensional potential energy surfaces approximated by a Smolyak's sparse grid interpolation algorithm.1 Compared to dense grids, sparse grids efficiently improve the ratio of invested storage and computing time to approximation accuracy and thus allow one to increase the number of coordinates d in molecular reaction path following simulations. Furthermore, evaluation of the interpolant is much less expensive than the evaluation of the actual energy function, so our technique offers a computationally efficient way to simulate reaction paths on ground and excited state potential energy surfaces. To demonstrate the capabilities of our method, we present simulation results for the isomerization of 2-butene with two, three, and six degrees of freedom.}, number={8}, journal={Journal of Chemical Theory and Computation}, publisher={American Chemical Society (ACS)}, author={Nance, James and Jakubikova, Elena and Kelley, C. T.}, year={2014}, month={Jul}, pages={2942–2949} }
 @article{aoi_kelley_novak_olufsen_2014, title={Sparse interpolatory reduced-order models for simulation of light-induced molecular transformations}, volume={29}, DOI={10.3182/20090812-3-DK-2006.0088}, abstractNote={Abstract This study presents an analysis of a cerebral autoregulation (CA) model developed by Ursino and Lodi Ursino and Lodi (1997). We have used this model to analyze non-invasive measurements of cerebral blood flow velocity (CBFV) and arterial blood pressure obtained during postural change from sitting to standing for a healthy young subject. This paper includes a sensitivity analysis, ranking model parameters from the most to the least sensitive, and an analysis (using a methodology called subset selection) that allows identification of correlations among model parameters. Finally, we estimated patient specific parameters using the Levenberg-Marquardt optimization method minimizing the least square errors between computed and measured values of CBFV.}, number={2}, journal={Optimization Methods and Software}, publisher={Elsevier BV}, author={Aoi, M C and Kelley, Carl and Novak, V and Olufsen, M S}, year={2014}, pages={264–273} }
 @article{wyers_steer_kelley_franzon_2013, title={A Bounded and Discretized Nelder-Mead Algorithm Suitable for RFIC Calibration}, volume={60}, ISSN={["1558-0806"]}, DOI={10.1109/tcsi.2012.2230496}, abstractNote={This paper describes a calibration technique for noisy and nonconvex circuit responses based on the Nelder-Mead direct search algorithm. As Nelder-Mead is intended for unconstrained optimization problems, we present an implementation of the algorithm which is suitable for bounded and discretized RFIC calibration problems. We apply the proposed algorithm to the problem of spurious tone reduction via VCO control line ripple minimization for a PLL operating at a frequency of 12 GHz. For this nonconvex calibration test case, we show that a gradient descent-based algorithm has difficulty in reducing the VCO control line ripple, while the proposed algorithm reduces the relative power of the first harmonic reference spurs by at least 10 dBc and effectively enables design complexity reduction in the supporting analog calibration circuitry.}, number={7}, journal={IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS}, author={Wyers, Eric J. and Steer, Michael B. and Kelley, C. T. and Franzon, Paul D.}, year={2013}, month={Jul}, pages={1787–1799} }
 @inproceedings{willert_kelley_knoll_park_2013, title={A Hybrid Approach to the Neutron Transport k-Eigenvalue Problem using NDA-based Algorithms}, booktitle={Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering}, author={Willert, J. and Kelley, C.T. and Knoll, D.A. and Park, H.K.}, year={2013}, pages={1934–1941} }
 @inproceedings{costolanski_kelley_howell_salinger_2013, title={An Efficient Parallel Solution to the Wigner-Poisson Equations}, volume={45}, booktitle={High Performance Computing Symposium (HPC 2013), Simulation Series Vol. 45, Society for Modeling & Simulation International}, publisher={Curran Associates Inc.}, author={Costolanski, A.S. and Kelley, C.T. and Howell, G.W. and Salinger, A.G.}, editor={Liu, F.Editor}, year={2013}, month={Apr}, pages={773–780} }
 @inproceedings{willert_kelley_2013, title={Efficient Solutions to the NDA-NCA Low-Order Eigenvalue Problem}, booktitle={Proceedings of International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering}, author={Willert, J. and Kelley, C.T.}, year={2013}, pages={2725–2735} }
 @article{kelley_liao_2013, title={Explicit Pseudo-Transient Continuation}, volume={9}, number={1}, journal={Pacific J. Opt.}, author={Kelley, C T and Liao, Li-Zhi}, year={2013}, pages={77–91} }
 @article{kelley_liao_2013, title={Explicit pseudo-transient continuation}, volume={9}, number={1}, journal={Pacific Journal of Optimization}, author={Kelley, C. T. and Liao, L. Z.}, year={2013}, pages={77–91} }
 @article{willert_kelley_knoll_park_2013, title={HYBRID DETERMINISTIC/MONTE CARLO NEUTRONICS}, volume={35}, ISSN={["1095-7197"]}, DOI={10.1137/120880021}, abstractNote={In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm.}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Willert, Jeffrey and Kelley, C. T. and Knoll, D. A. and Park, H.}, year={2013}, pages={S62–S83} }
 @article{willert_kelley_knoll_park_2013, title={Hybrid Deterministic/Monte Carlo Neutronics}, volume={35}, DOI={http://dx.doi.org/10.1137/120880021}, abstractNote={In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton--Krylov iteration for the low-order problem. We couple the Monte Carlo solution with the low-order problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobian-vector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm.}, number={5}, journal={SIAM J. Sci. Comp.}, author={Willert, Jeff and Kelley, C T and Knoll, D A and Park, H K}, year={2013}, pages={S62–S83} }
 @inproceedings{briggs_hodak_rose_lu_kelley_bernholc_2013, place={Denver CO}, title={Mechanism of Drug Action on Alzheimer's Disease Protein}, booktitle={Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis}, publisher={IEEE Computer Society Press}, author={Briggs, E. and Hodak, M and Rose, F and Lu, W and Kelley, C.T. and Bernholc, J}, year={2013} }
 @article{miller_dawson_farthing_hou_huang_kees_kelley_langtangen_2013, title={Numerical simulation of water resources problems: Models, methods, and trends}, volume={51}, ISSN={["1872-9657"]}, DOI={10.1016/j.advwatres.2012.05.008}, abstractNote={Mechanistic modeling of water resources systems is a broad field with abundant challenges. We consider classes of model formulations that are considered routine, the focus of current work, and the foundation of foreseeable work over the coming decade. These model formulations are used to assess the current and evolving state of solution algorithms, discretization methods, nonlinear and linear algebraic solution methods, computational environments, and hardware trends and implications. The goal of this work is to provide guidance to enable modelers of water resources systems to make sensible choices when developing solution methods based upon the current state of knowledge and to focus future collaborative work among water resources scientists, applied mathematicians, and computational scientists on productive areas.}, journal={ADVANCES IN WATER RESOURCES}, author={Miller, Cass T. and Dawson, Clint N. and Farthing, Matthew W. and Hou, Thomas Y. and Huang, Jingfang and Kees, Christopher E. and Kelley, C. T. and Langtangen, Hans Petter}, year={2013}, month={Jan}, pages={405–437} }
 @article{ellwein_pope_xie_batzel_kelley_olufsen_2013, title={Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia}, volume={241}, ISSN={0025-5564}, url={http://dx.doi.org/10.1016/j.mbs.2012.09.003}, DOI={10.1016/j.mbs.2012.09.003}, abstractNote={This study develops a lumped cardiovascular–respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO2 partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO2 reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO2 induced challenges. It is difficult to characterize cerebral CO2 reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO2 reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO2 and O2) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO2 partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.}, number={1}, journal={Mathematical Biosciences}, publisher={Elsevier BV}, author={Ellwein, L.M. and Pope, S.R. and Xie, A. and Batzel, J.J. and Kelley, C.T. and Olufsen, M.S.}, year={2013}, month={Jan}, pages={56–74} }
 @article{willert_kelley_knoll_park_2013, title={Scalable Hybrid Deterministic/Monte Carlo Neutronics Simulations in Two Space Dimensions}, DOI={10.1109/dcabes.2013.8}, abstractNote={In this paper we discuss a parallel hybrid deterministic/Monte Carlo (MC) method for the solution of the neutron transport equation in two space dimensions. The algorithm uses an NDA formulation of the transport equation, with a MC solver for the high-order equation. The scalability arises from the concentration of work in the MC phase of the algorithm, while the overall run-time is a consequence of the deterministic phase.}, journal={2013 12TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING & SCIENCE (DCABES)}, author={Willert, Jeffrey and Kelley, C. T. and Knoll, D. A. and Park, H.}, year={2013}, pages={7–10} }
 @article{kavouras_georgakis_kelley_siettos_kevrekidis_2013, title={Steady states for chemical process plants: A legacy code, time-stepping approach}, volume={59}, ISSN={["0001-1541"]}, DOI={10.1002/aic.14199}, abstractNote={Given a legacy dynamic simulator of a chemical process plant, we construct a computational procedure that can be “wrapped around” the simulator to compute its steady states (both stable and unstable) and their dependence on input parameters. We apply this approach to the Tennessee Eastman (TE) challenge problem presented by Downs and Vogel, who also provided a FORTRAN process model. Using the FORTRAN simulator as a black‐box input‐output map, we enable it to systematically converge to isolated solutions and study their stability and parametric dependence within the equation‐free framework. The presence of neutrally stable modes in TE problem (due to so‐called inventories), their interplay with the problem formulation and the convergence of the solution procedure is explored and rationalized. Interestingly, our time‐stepper formulation can automatically take advantage of separation of time scales, when present, to enhance computational convergence. The approach enables legacy dynamic simulators to calculate several dynamic problem characteristics useful for controller design and/or process optimization. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3308–3321, 2013}, number={9}, journal={AICHE JOURNAL}, author={Kavouras, Andreas and Georgakis, Christos and Kelley, C. T. and Siettos, Constantinos and Kevrekidis, Ioannis G.}, year={2013}, month={Sep}, pages={3308–3321} }
 @article{benner_embree_lehoucq_kelley_2012, title={A Mathematical Biography of {Danny C. Sorensen}}, volume={436}, journal={LAA}, author={Benner, Peter and Embree, Mark and Lehoucq, Richard B and Kelley, C T}, year={2012}, pages={2717–2724} }
 @article{benner_embree_lehoucq_kelley_2012, title={A mathematical biography of Danny C. Sorensen Preface}, volume={436}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2012.01.031}, abstractNote={On the occasion of his 65th birthday, we briefly recount Dan Sorensen’s profound contributions to optimization, numerical linear algebra, and model order reduction for dynamical systems.}, number={8}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Benner, Peter and Embree, Mark and Lehoucq, Richard B. and Kelley, C. T.}, year={2012}, month={Apr}, pages={2717–2724} }
 @article{willert_kelley_knoll_dong_ravishankar_sathre_sullivan_taitano_2012, title={Hybrid Deterministic/Monte Carlo Neutronics using GPU Accelerators}, DOI={10.1109/dcabes.2012.37}, abstractNote={In this paper we discuss a GPU implementation of a hybrid deterministic/Monte Carlo method for the solution of the neutron transport equation. The key feature is using GPUs to perform a Monte Carlo transport sweep as part of the evaluation of the nonlinear residual and Jacobian-vector product. We describe the algorithm and present some preliminary numerical results which illustrate the effectiveness of the GPU Monte Carlo sweeps.}, journal={2012 11TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING & SCIENCE (DCABES)}, author={Willert, Jeff and Kelley, C. T. and Knoll, D. A. and Dong, Han and Ravishankar, Mahesh and Sathre, Paul and Sullivan, Michael and Taitano, William}, year={2012}, pages={43–47} }
 @inproceedings{willert_kelley_knoll_dong_ravishankar_sathre_sullivan_taitano_2012, place={Los Alamitos, CA}, title={Hybrid Deterministic/Monte Carlo Neutronics using GPU Accelerators}, booktitle={2012 International Symposium on Distributed Computing and Applications to Business, Engineering and Science}, publisher={IEEE}, author={Willert, Jeff and Kelley, C T and Knoll, D A and Dong, H and Ravishankar, M and Sathre, P and Sullivan, M and Taitano, W}, editor={Guo, Qingping and Douglas, CraigEditors}, year={2012}, pages={43–47} }
 @article{winton_kelley_eslinger_hensley_hines_2012, title={Inexact Levenberg-Marquardt with Reduced Order Models}, journal={Water Resources Research}, author={Winton, C and Kelley, C T and Eslinger, O J and Hensley, J and Hines, A}, year={2012} }
 @article{kelley_tuminaro_2012, title={Research Spotlights: New Opportunities for SIAM Review Authors}, journal={SIAM News}, author={Kelley, C T and Tuminaro, Ray}, year={2012} }
 @article{mokrauer_kelley_bykhovski_2012, title={Simulations of Light-Induced Molecular Transformations in Multiple Dimensions with Incremental Sparse Surrogates}, volume={6}, ISSN={1748-3018 1748-3026}, url={http://dx.doi.org/10.1260/1748-3018.6.4.577}, DOI={10.1260/1748-3018.6.4.577}, abstractNote={ Simulations of light-induced molecular conformational transformations have traditionally been limited to a single degree of freedom because of the complexity of potential energy calculations. We propose a method of simulation that incrementally builds a surrogate for the potential energy function by computing gridpoints in parallel. We incorporate Smolyak's algorithm for sparse interpolation as the energy surrogates since it keeps the number of gridpoints at a manageable number. Our multi-dimensional algorithm is applied to the molecule 2-butene whose transition path is well known. }, number={4}, journal={Journal of Algorithms & Computational Technology}, publisher={SAGE Publications}, author={Mokrauer, David and Kelley, C. T. and Bykhovski, Alexei}, year={2012}, month={Dec}, pages={577–592} }
 @article{mokrauer_kelley_bykhovski_2012, title={Simulations of Light-Induced Molecular Transformations in Multiple Dimensions with Incremental Sparse Surrogates}, volume={6}, number={4}, journal={J. Algorithms Comp Tech}, author={Mokrauer, David and Kelley, C T and Bykhovski, Alexei}, year={2012}, pages={577–592} }
 @article{mokrauer_kelley_2012, title={Sparse interpolatory reduced-order models for simulation of light-induced molecular transformations}, volume={29}, url={http://www.tandfonline.com/doi/abs/10.1080/10556788.2012.693928}, DOI={10.1080/10556788.2012.693928}, abstractNote={We describe a method for using interpolatory models to accurately and efficiently simulate molecular excitation and relaxation. We use sparse interpolation for efficiency and local error estimation and control for robustness and accuracy.}, number={2}, journal={Optimization Methods and Software}, author={Mokrauer, David and Kelley, Carl}, year={2012}, month={Jul}, pages={1–10} }
 @article{winton_pettway_kelley_howington_eslinger_2011, title={Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow}, volume={34}, ISSN={["1872-9657"]}, DOI={10.1016/j.advwatres.2011.09.007}, abstractNote={We develop a new Proper Orthogonal Decomposition (POD) reduced order model for saturated groundwater flow, and apply that model to an inverse problem for the hydraulic conductivity field. We use sensitivities as the POD basis. We compare the output when the optimizer uses the reduced order model against results obtained with a full PDE based model. The solutions generated using the POD reduced model are comparable in residual norm to the solutions formed using only the full-scale model. The material parameters are similarly comparable. The time to solution when using the reduced model is reduced by at least an order of magnitude, as are the number of calls to the full model.}, number={12}, journal={ADVANCES IN WATER RESOURCES}, author={Winton, Corey and Pettway, Jackie and Kelley, C. T. and Howington, Stacy and Eslinger, Owen J.}, year={2011}, month={Dec}, pages={1519–1526} }
 @inproceedings{wyers_steer_kelley_franzon_2011, title={Application of a Modified Nelder-Mead Algorithm for calibrating RF Analog Integrated Circuits}, booktitle={Proceedings GOMACTech'11}, author={Wyers, E.J. and Steer, M.B. and Kelley, C.T. and Franzon, P.D.}, year={2011}, pages={545–548} }
 @article{mokrauer_kelley_bykhovski_2011, title={Efficient Parallel Computation of Molecular Potential Energy Surfaces for the Study of Light-Induced Transition Dynamics in Multiple Coordinates}, volume={10}, ISSN={["1941-0085"]}, DOI={10.1109/tnano.2010.2058862}, abstractNote={The conformational dynamics of molecules that arise due to light-induced transitions are critically important in many biochemical reactions, and therefore dictate the functionality of many types of biological sensors. Therefore, researchers of biological science and biological-inspired technology often need to prescribe the molecular geometry of the stable states and the associated transition trajectories that occur as a result of external excitation, e.g., light-induced transitions from the ground state to the excited states. The traditional approach to study this type of phenomenology is to limit the number of varying molecular coordinates to one or a few due to the considerable computational expense of the required physically modeling required for generating an accurate physical model for analysis. While the conformational dynamics for some types of simple molecules (e.g., retinal) are known to be adequately described by one or few numbers of molecular coordinates, light-induced transitions in arbitrarily complex molecules can be expected to involve the influence of multiple coordinates, and their influence can be expected to vary as a function of time. The research reported here will address the development of parallel computational algorithms that allow for the highly efficient study of molecular conformational dynamics over multiple numbers of multidimensional energy surfaces. Here, the goal is the development of a simulation tool that is capable of: constructing physically accurate multidimensional potential energy surfaces (i.e., from first-principle physical modeling codes); deriving the natural trajectories to local minima within individual surfaces; and that allows for dynamics human interfacing for specifying the transition between energy surfaces and the number of coordinates to be used for the optimization within a particular energy surface. As will be illustrated, this type of physics-based simulation tool will allow researchers to efficiently explore the light-induced conformation dynamics associated with complex biomolecules, and therefore, be a useful tool for the design of biological-sensing processes in the future.}, number={1}, journal={IEEE TRANSACTIONS ON NANOTECHNOLOGY}, author={Mokrauer, David and Kelley, C. T. and Bykhovski, Alexei}, year={2011}, month={Jan}, pages={70–74} }
 @article{kelley_qi_tong_yin_2011, title={FINDING A STABLE SOLUTION OF A SYSTEM OF NONLINEAR EQUATIONS ARISING FROM DYNAMIC SYSTEMS}, volume={7}, ISSN={["1553-166X"]}, DOI={10.3934/jimo.2011.7.497}, abstractNote={This paper presents new methods for finding dynamically stable solutions of systems of nonlinear equations. The concepts of stability functions and the so-called stable solutions are defined. Based on those new concepts, two models of stable solutions and three stability functions are proposed. These stability functions are semismooth. Smoothing technology is applied to such stability functions. Smoothing Newton methods are proposed to solve the stable solution models. Convergence properties of these methods are studied. We report on numerical examples which illustrate the utility of the new approach.}, number={2}, journal={JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION}, author={Kelley, Carl T. and Qi, Liqun and Tong, Xiaojiao and Yin, Hongxia}, year={2011}, month={May}, pages={497–521} }
 @article{kelley_qi_tong_yin_2011, title={Finding A Stable Solution of A System of Nonlinear Equations}, volume={7}, journal={J. Indus. Manag. Opt.}, author={Kelley, C T and Qi, L and Tong, X and Yin, H}, year={2011}, pages={497–521} }
 @misc{kelley_2011, title={Implicit Filtering}, ISBN={9781611971897 9781611971903}, url={http://dx.doi.org/10.1137/1.9781611971903}, DOI={10.1137/1.9781611971903}, abstractNote={Implicit filtering is a way to solve bound-constrained optimization problems for which derivative information is not available. Unlike methods that use interpolation to reconstruct the function and its higher derivatives, implicit filtering builds upon coordinate search and then interpolates to get an approximation of the gradient. The author describes the algorithm, its convergence theory, and a new MATLAB implementation, and includes three case studies. This book is unique in that it is the only one in the area of derivative-free or sampling methods and is accompanied by publicly available software. It is also designed as a software manual and as a reference for implicit filtering - one can approach the book as a consumer of the software, as a student, or as a researcher in sampling and derivative-free methods. The book includes a chapter on convergence theory that is both accessible to students and an overview of recent results on optimization of noisy functions, including results that depend on non-smooth analysis and results on the handling of constraints. Implicit filtering is used in applications in electrical, civil, and mechanical engineering. Audience: This book is intended for students who want to learn about this technology, scientists and engineers who would like to apply the methods to real-world problems, and specialists who will use the ideas and the software from this book in their own research. Contents: Preface; How to Get the Software; Chapter 1 Introduction; Chapter 2 Getting Started with imfil.m; Chapter 3 Notation and Preliminaries; Chapter 4 Implicit Filtering Algorithm; Chapter 5 Convergence Theory; Chapter 6 Using imfil.m; Chapter 7 Advanced Options; Chapter 8 Harmonic Oscillator; Chapter 9 Hydraulic Capture Problem; Chapter 10 Water Resources Policy; Bibliography; Index.}, publisher={Society for Industrial and Applied Mathematics}, author={Kelley, C. T.}, year={2011}, month={Jan} }
 @book{kelley_2011, place={Philadelphia}, title={Implicit Filtering}, number={23}, publisher={SIAM}, author={Kelley, C T}, year={2011} }
 @article{ipsen_kelley_pope_2011, title={Nonlinear Least Squares Problems and Subset Selection}, volume={49}, journal={SIAM J. Numer. Anal.}, author={Ipsen, I C F and Kelley, C T and Pope, S R}, year={2011}, pages={1244–1266} }
 @article{ellwein_pope_xie_batzel_kelley_olufsen_2011, title={Patient specific modeling of cardiovascular and respiratory dynamics during hypercapnia}, volume={241}, number={1}, journal={Mathematical Biosciences}, author={Ellwein, L M and Pope, S R and Xie, A and Batzel, J and Kelley, C T and Olufsen, M S}, year={2011}, pages={56–74} }
 @article{ipsen_kelley_pope_2011, title={RANK-DEFICIENT NONLINEAR LEAST SQUARES PROBLEMS AND SUBSET SELECTION}, volume={49}, ISSN={["0036-1429"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79960422161&partnerID=MN8TOARS}, DOI={10.1137/090780882}, abstractNote={We examine the local convergence of the Levenberg-Marquardt method for the solution of nonlinear least squares problems that are rank-deficient and have nonzero residual. We show that replacing the Jacobian by a truncated singular value decomposition can be numerically unstable. We recommend instead the use of subset selection. We corroborate our recommendations by perturbation analyses and numerical experiments.}, number={3}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Ipsen, I. C. F. and Kelley, C. T. and Pope, S. R.}, year={2011}, pages={1244–1266} }
 @article{kelley_2011, title={Users' Guide for imfil}, author={Kelley, C T}, year={2011} }
 @article{costolanski_kelley_2010, title={Efficient Solution of the Wigner-Poisson Equation for Modeling Resonant Tunneling Diodes}, volume={9}, DOI={10.1109/tnano.2010.2053214}, abstractNote={A more efficient and accurate discretization of the Wigner-Poisson model for double barrier resonant tunneling diodes is presented. This new implementation uses nonuniform grids and higher order numerical methods to improve the accuracy of the solutions at a significantly lower computational cost. Using the new implementation, devices with short and long contact regions are analyzed as well as the effect of a correlation length parameter that defines the degree of nonlocality effects. The results show that devices with longer contact regions reduce numerical inconsistencies present when modeling shorter devices, and that longer correlation lengths generally improve the correspondence of the numerical solutions with those typically expected from experimental measurement. These new numerical simulation tools will enable researchers to successfully apply the Wigner-Poisson model to describe electron transport in nanoscale semiconductor tunneling devices. More specifically, the computationally more efficient numerical algorithms presented will be shown to allow for the quantum-based studies of resonant tunneling devices useful as sources and detectors at very high frequencies (e.g., THz regime). These types of devices are very important for use in sensors and sensing systems where very long wavelength characterization capabilities are important (e.g., interrogation of chemical and biological systems) as well as an array of other electronics applications.}, number={6}, journal={IEEE Transactions on Nanotechnology}, author={Costolanski, Anne S and Kelley, C T}, year={2010}, pages={708–715} }
 @inproceedings{mokrauer_kelley_bykhovski_2010, place={Los Alamitos, CA}, title={Parallel Computation of Surrogate Models for Potential Energy Surfaces}, booktitle={2010 International Symposium on Distributed Computing and Applications to Business, Engineering and Science}, publisher={IEEE}, author={Mokrauer, David and Kelley, C T and Bykhovski, Alexei}, editor={Qingping, Quo and Yucheng, GuoEditors}, year={2010}, pages={1–4} }
 @article{kelley_ipsen_pope_2010, title={Rank-Deficient and Ill-Conditioned Nonlinear Least Squares Problems}, author={Kelley, C T and Ipsen, I C F and Pope, S R}, year={2010} }
 @article{fukushima_kelley_qi_sun_ye_2010, title={Special issue in Memory of Alexander Rubinov}, volume={6}, number={2}, journal={Pacific Journal of Optimization}, author={Fukushima, M. and Kelley, C. T. and Qi, L. Q. and Sun, J. and Ye, Y. Y.}, year={2010} }
 @inproceedings{kelley_winton_eslinger_pettway_2009, title={Calibration of Ground Water Models with {POD}}, booktitle={Numerical Techniques for Optimization Problems with PDE constraints}, author={Kelley, C T and Winton, C and Eslinger, O J and Pettway, J}, editor={Heinkenschloss, M and Hoppe, R H W and Schultz, VEditors}, year={2009}, pages={47–49} }
 @article{luo_kelley_liao_tam_2009, title={Combining Trust-Region Techniques and Rosenbrock Methods to Compute Stationary Points}, volume={140}, ISSN={["1573-2878"]}, DOI={10.1007/s10957-008-9469-0}, abstractNote={Rosenbrock methods are popular for solving a stiff initial-value problem of ordinary differential equations. One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with other implicit methods such as backward difference formulas or implicit Runge–Kutta methods. In this article, we introduce a trust-region technique to select the time steps of a second-order Rosenbrock method for a special initial-value problem, namely, a gradient system obtained from an unconstrained optimization problem. The technique is different from the local error approach. Both local and global convergence properties of the new method for solving an equilibrium point of the gradient system are addressed. Finally, some promising numerical results are also presented.}, number={2}, journal={JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS}, author={Luo, X. -L. and Kelley, C. T. and Liao, L. -Z. and Tam, H. W.}, year={2009}, month={Feb}, pages={265–286} }
 @article{luo_kelley_liao_tam_2009, title={Combining Trust-Region Techniques and {R}osenbrock Methods for Gradient Systems}, volume={140}, journal={J. Optim. Theory Appl.}, author={Luo, X-L and Kelley, C T and Liao, L-Z. and Tam, H-W}, year={2009}, pages={265–286} }
 @article{finkel_kelley_2009, title={Convergence Analysis of Sampling Methods for Perturbed {L}ipschitz Functions}, volume={5}, number={2}, journal={Pacific J. Opt.}, author={Finkel, D E and Kelley, C T}, year={2009}, pages={339–350} }
 @article{pope_ellwein_zapata_novak_kelley_olufsen_2009, title={ESTIMATION AND IDENTIFICATION OF PARAMETERS IN A LUMPED CEREBROVASCULAR MODEL}, volume={6}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2009.6.93}, abstractNote={This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.}, number={1}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Pope, Scott R. and Ellwein, Laura M. and Zapata, Cheryl L. and Novak, Vera and Kelley, C. T. and Olufsen, Mette S.}, year={2009}, month={Jan}, pages={93–115} }
 @article{kirsch_characklis_dillard_kelley_2009, title={More efficient optimization of long-term water supply portfolios}, volume={45}, ISSN={["0043-1397"]}, DOI={10.1029/2008wr007018}, abstractNote={The use of temporary transfers, such as options and leases, has grown as utilities attempt to meet increases in demand while reducing dependence on the expansion of costly infrastructure capacity (e.g., reservoirs). Earlier work has been done to construct optimal portfolios comprising firm capacity and transfers, using decision rules that determine the timing and volume of transfers. However, such work has only focused on the short‐term (e.g., 1‐year scenarios), which limits the utility of these planning efforts. Developing multiyear portfolios can lead to the exploration of a wider range of alternatives but also increases the computational burden. This work utilizes a coupled hydrologic‐economic model to simulate the long‐term performance of a city's water supply portfolio. This stochastic model is linked with an optimization search algorithm that is designed to handle the high‐frequency, low‐amplitude noise inherent in many simulations, particularly those involving expected values. This noise is detrimental to the accuracy and precision of the optimized solution and has traditionally been controlled by investing greater computational effort in the simulation. However, the increased computational effort can be substantial. This work describes the integration of a variance reduction technique (control variate method) within the simulation/optimization as a means of more efficiently identifying minimum cost portfolios. Random variation in model output (i.e., noise) is moderated using knowledge of random variations in stochastic input variables (e.g., reservoir inflows, demand), thereby reducing the computing time by 50% or more. Using these efficiency gains, water supply portfolios are evaluated over a 10‐year period in order to assess their ability to reduce costs and adapt to demand growth, while still meeting reliability goals. As a part of the evaluation, several multiyear option contract structures are explored and compared.}, journal={WATER RESOURCES RESEARCH}, author={Kirsch, Brian R. and Characklis, Gregory W. and Dillard, Karen E. M. and Kelley, C. T.}, year={2009}, month={Mar} }
 @article{gee_kelley_lehoucq_2009, title={Pseudo-transient continuation for nonlinear transient elasticity}, volume={78}, ISSN={["1097-0207"]}, DOI={10.1002/nme.2527}, abstractNote={Abstract}, number={10}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING}, author={Gee, Michael W. and Kelley, C. T. and Lehoucq, R. B.}, year={2009}, month={Jun}, pages={1209–1219} }
 @article{fowler_reese_kees_dennis_kelley_miller_audet_booker_couture_darwin_et al._2008, title={A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Problems}, volume={31}, DOI={10.1016/j.advwatres.2008.10.010}, journal={Advances in Water Resources}, author={Fowler, K R and Reese, J P and Kees, C E and Dennis, J E and Kelley, C T and Miller, C T and Audet, Charles and Booker, A J and Couture, Gilles and Darwin, Robert W and et al.}, year={2008}, pages={743–757} }
 @article{zhang_kelley_liao_2008, title={A continuous {N}ewton-type method for unconstrained optimization}, volume={4}, number={2}, journal={Pacific Journal of Optimization}, author={Zhang, L-H. and Kelley, C T and Liao, L.-Z.}, year={2008}, pages={259–277} }
 @article{fowler_reese_kees_dennis_kelley_miller_audet_booker_couture_darwin_et al._2008, title={Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems}, volume={31}, ISSN={["1872-9657"]}, DOI={10.1016/j.advwatres.2008.01.010}, abstractNote={Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.}, number={5}, journal={ADVANCES IN WATER RESOURCES}, author={Fowler, K. R. and Reese, J. P. and Kees, C. E. and Dennis, J. E., Jr. and Kelley, C. T. and Miller, C. T. and Audet, C. and Booker, A. J. and Couture, G. and Darwin, R. W. and et al.}, year={2008}, month={May}, pages={743–757} }
 @article{pope_ellwein_zapata_novak_kelley_olufsen_2008, title={Estimation and identification of parameters in a lumped cerebrovascular model}, volume={6}, journal={Math. Biosci. Eng.}, author={Pope, S R and Ellwein, L M and Zapata, C I and Novak, V and Kelley, C T and Olufsen, M S}, year={2008}, pages={93–115} }
 @article{kelley_liao_qi_chu_reese_winton_2008, title={PROJECTED PSEUDOTRANSIENT CONTINUATION}, volume={46}, ISSN={["1095-7170"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-55349118529&partnerID=MN8TOARS}, DOI={10.1137/07069866X}, abstractNote={We propose and analyze a pseudotransient continuation algorithm for dynamics on subsets of $R^N$. Examples include certain flows on manifolds and the dynamic formulation of bound-constrained optimization problems. The method gets its global convergence properties from the dynamics and inherits its local convergence properties from any fast locally convergent iteration.}, number={6}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Kelley, C. T. and Liao, Li-Zhi and Qi, Liqun and Chu, Moody T. and Reese, J. P. and Winton, C.}, year={2008}, pages={3071–3083} }
 @article{kelley_liao_qi_chu_reese_winton_2008, title={Projected Pseudo-Transient Continuation}, volume={46}, number={6}, journal={SIAM J. Numer. Anal.}, author={Kelley, C T and Liao, L-Z. and Qi, L and Chu, M T and Reese, J P and Winton, C}, year={2008}, pages={3071–3083} }
 @article{marucho_kelley_pettitt_2008, title={Solutions of the optimized closure integral equation theory: Heteronuclear polyatomic fluids}, volume={4}, ISSN={["1549-9626"]}, DOI={10.1021/ct700202h}, abstractNote={Recently, we developed a thermodynamically optimized integral equation method which has been successfully tested on both simple and homonuclear diatomic Lennard-Jones fluids [J. Chem. Phys. 2007, 126, 124107]. The systematic evaluation of correlation functions required by the optimization of the chemical potential has shown a clear need for more efficient algorithms to solve these integral equations. In the present paper we introduce a high-performance algorithm which is found to be faster and more efficient than the direct Picard iteration. Here we have utilized this to solve the aforementioned optimized theory for molecules more complex than those considered previously. We analyzed representative models for heteronuclear diatomic and triatomic polar molecular fluids. We include results for several modified SPC-like models for water, obtaining site-site correlation functions in good agreement with simulation data.}, number={3}, journal={JOURNAL OF CHEMICAL THEORY AND COMPUTATION}, author={Marucho, M. and Kelley, C. T. and Pettitt, B. Montgomery}, year={2008}, month={Mar}, pages={385–396} }
 @article{a case study in using local {i/o} and {gpfs} to improve simulation scalability_2007, journal={8th LCI International Conference on High-Performance Clustered Computing}, year={2007} }
 @article{lasater_kelley_salinger_woolard_recine_zhao_2007, title={Analysis of A Scalable Preconditioner for the Wigner-Poisson Equation}, volume={37}, journal={International Journal of Pure and Applied Mathematics}, author={Lasater, M.S. and Kelley, C.T. and Salinger, A. and Woolard, D.L. and Recine, G. and Zhao, P.}, year={2007}, pages={247–270} }
 @article{dickson_kelley_ipsen_kevrekidis_2007, title={Condition estimates for pseudo-arclength continuation}, volume={45}, ISSN={["1095-7170"]}, DOI={10.1137/060654384}, abstractNote={We bound the condition number of the Jacobian in pseudo-arclength continuation problems, and we quantify the effect of this condition number on the linear system solution in a Newton-GMRES solve. Pseudo-arclength continuation solves parameter dependent nonlinear equations $G(u,\lambda) = 0$ by introducing a new parameter $s$, which approximates arclength, and viewing the vector $x = (u,\lambda)$ as a function of $s$. In this way simple fold singularities can be computed directly by solving a larger system $F(x,s) = 0$ by simple continuation in the new parameter $s$. It is known that the Jacobian $F_x$ of $F$ with respect to $x=(u,\lambda)$ is nonsingular if the path contains only regular points and simple fold singularities. We introduce a new characterization of simple folds in terms of the singular value decomposition, and we use it to derive a new bound for the norm of $F_x^{-1}$. We also show that the convergence rate of GMRES in a Newton step for $F(x,s)=0$ is essentially the same as that of the original problem $G(u,\lambda)=0$. In particular, we prove that the bounds on the degrees of the minimal polynomials of the Jacobians $F_x$ and $G_u$ differ by at most 2. We illustrate the effectiveness of our bounds with an example from radiative transfer theory.}, number={1}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Dickson, K. I. and Kelley, C. T. and Ipsen, I. C. F. and Kevrekidis, I. G.}, year={2007}, pages={263–276} }
 @article{finkel_kelley_2007, title={Convergence Analysis of the {DIRECT} Algorithm}, author={Finkel, D E and Kelley, C T}, year={2007} }
 @article{finkel_kelley_2006, title={Additive scaling and the DIRECT algorithm}, volume={36}, ISSN={["0925-5001"]}, DOI={10.1007/s10898-006-9029-9}, number={4}, journal={JOURNAL OF GLOBAL OPTIMIZATION}, author={Finkel, D. E. and Kelley, C. T.}, year={2006}, month={Dec}, pages={597–608} }
 @article{characklis_kirsch_ramsey_dillard_kelley_2006, title={Developing portfolios of water supply transfers}, volume={42}, ISSN={["1944-7973"]}, DOI={10.1029/2005wr004424}, abstractNote={Most cities rely on firm water supply capacity to meet demand, but increasing scarcity and supply costs are encouraging greater use of temporary transfers (e.g., spot leases, options). This raises questions regarding how best to coordinate the use of these transfers in meeting cost and reliability objectives. This paper combines a hydrologic–water market simulation with an optimization approach to identify portfolios of permanent rights, options, and leases that minimize the expected costs of meeting a city's annual demand with a specified reliability. Spot market prices are linked to hydrologic conditions and described by monthly lease price distributions which are used to price options via a risk‐neutral approach. Monthly choices regarding when and how much water to acquire through temporary transfers are made on the basis of anticipatory decision rules related to the ratio of expected supply to expected demand. The simulation is linked with an algorithm that uses an implicit filtering search method designed for solution surfaces that exhibit high‐frequency, low‐amplitude noise. This simulation‐optimization approach is applied to a region that currently supports an active water market, with results suggesting that temporary transfers can reduce expected water supply costs substantially, while still maintaining high reliability. Also evaluated are trade‐offs between expected costs and cost variability that occur with variation in a portfolio's distribution of rights, options, and leases.}, number={5}, journal={WATER RESOURCES RESEARCH}, author={Characklis, GW and Kirsch, BR and Ramsey, J and Dillard, KEM and Kelley, CT}, year={2006}, month={May} }
 @article{kelley_sorensen_reese_winton_2006, title={Model Reduction for Nonlinear Least Squares}, author={Kelley, C T and Sorensen, D and Reese, J P and Winton, C}, year={2006} }
 @inproceedings{kees_farthing_howington_jenkins_kelley_2006, title={Nonlinear multilevel iterative methods for multiscale models of air/water flow in porous media}, booktitle={Proceedings of Computational Methods in Water Resources XVI}, author={Kees, C E and Farthing, M W and Howington, S E and Jenkins, E W and Kelley, C T}, year={2006}, pages={Paper number 256, 8 pages} }
 @article{lasater_kelley_salinger_woolard_zhao_2006, title={Parallel Parameter Study of the {Wigner-Poisson} Equations for {RTDs}}, volume={51}, journal={Computers and Mathematics with Applications}, author={Lasater, M S and Kelley, C T and Salinger, A and Woolard, D L and Zhao, P}, year={2006}, pages={1677–1688} }
 @article{lasater_kelley_salinger_woolard_zhao_2006, title={Parallel parameter study of the Wigner-Poisson equations for RTDs}, volume={51}, ISSN={["1873-7668"]}, DOI={10.1016/j.camwa.2006.05.006}, abstractNote={We will discuss a parametric study of the solution of the Wigner-Poisson equations for resonant tunneling diodes. These structures exhibit self-sustaining oscillations in certain operating regimes. We will describe the engineering consequences of our study and how it is a significant advance from some previous work, which used much coarser grids. We use LOCA and other packages in the Trilinos framework from Sandia National Laboratory to enable efficient parallelization of the solution methods and to perform bifurcation analysis of this model. We report on the parallel efficiency and scalability of our implementation.}, number={11}, journal={COMPUTERS & MATHEMATICS WITH APPLICATIONS}, author={Lasater, M. S. and Kelley, C. T. and Salinger, A. G. and Woolard, D. L. and Zhao, P.}, year={2006}, month={Jun}, pages={1677–1688} }
 @article{kelley_sorensen_reese_winton_2006, title={Reduced order models for nonlinear least squares problems}, author={Kelley, C T and Sorensen, D and Reese, J P and Winton, C}, year={2006} }
 @inproceedings{lasater_kelley_salinger_zhao_woolard_2006, title={Simulating Nanoscale Devices}, volume={16}, booktitle={International Journal of High Speed Electronics and Systems}, publisher={World Scientific}, author={Lasater, M S and Kelley, C T and Salinger, A and Zhao, P and Woolard, D L}, editor={Iwai, H and Nishi, Y and Shur, M S and Wong, HEditors}, year={2006}, pages={677–690} }
 @inproceedings{reese_long_kelley_miller_gray_2006, title={Simulating Non-{D}arcy Flow through Porous Media using {S}undance}, booktitle={Proceedings of Computational Methods in Water Resources XVI}, author={Reese, J P and Long, Kevin and Kelley, C T and Miller, C T and Gray, W G}, year={2006}, pages={Paper number 148, 8 pages} }
 @article{qiao_erban_kelley_kevrekidis_2006, title={Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations}, volume={125}, ISSN={["1089-7690"]}, DOI={10.1063/1.2372492}, abstractNote={Spatially distributed problems are often approximately modeled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g., concentrations). The derivation of accurate such PDEs starting from finer scale, atomistic models, and using suitable averaging is often a challenging task; approximate PDEs are typically obtained through mathematical closure procedures (e.g., mean field approximations). In this paper, we show how such approximate macroscopic PDEs can be exploited in constructing preconditioners to accelerate stochastic computations for spatially distributed particle-based process models. We illustrate how such preconditioning can improve the convergence of equation-free coarse-grained methods based on coarse timesteppers. Our model problem is a stochastic reaction-diffusion model capable of exhibiting Turing instabilities.}, number={20}, journal={JOURNAL OF CHEMICAL PHYSICS}, author={Qiao, Liang and Erban, Radek and Kelley, C. T. and Kevrekidis, Ioannis G.}, year={2006}, month={Nov} }
 @article{characklis_kirsch_ramsey_dillard_kelley_2006, place={Chapel Hill, NC}, title={Using Water Transfers to Manage Supply Risk}, journal={Proceedings of Symposium on Safe Drinking Water: Where Science Meets Policy}, author={Characklis, G W and Kirsch, B R and Ramsey, J and Dillard, K E M and Kelley, C T}, year={2006} }
 @article{lasater_recine_kelley_woolard_zhao_2006, title={{SETraNS} Manual: Simulation of Electronic Transport in Nanoscale Structures}, author={Lasater, M S and Recine, Greg and Kelley, C T and Woolard, D L and Zhao, P}, year={2006} }
 @book{federov_chuev_kelley_pettitt_2005, title={Multilevel wavelet solver for the Ornstein-Zernike equation}, number={CRSC-TR05-07}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Federov, M V and Chuev, G N and Kelley, C T and Pettitt, B Montgomery}, year={2005}, month={Jan} }
 @article{fowler_kelley_2005, title={Pseudo-transient Continuation for Nonsmooth Nonlinear Equations}, volume={43}, DOI={10.1137/s0036142903431298}, abstractNote={Pseudo-transient continuation is a Newton-like iterative method for computing steady-state solutions of differential equations in cases where the initial data are far from a steady state. The iteration mimics a temporal integration scheme, with the time step being increased as steady state is approached. The iteration is an inexact Newton iteration in the terminal phase. 
In this paper we show how steady-state solutions to certain ordinary and differential algebraic equations with nonsmooth dynamics can be computed with the method of pseudo-transient continuation. An example of such a case is a discretized PDE with a Lipschitz continuous, but nondifferentiable, constitutive relation as part of the nonlinearity. In this case we can approximate a generalized derivative with a difference quotient. 
The existing theory for pseudo-transient continuation requires Lipschitz continuity of the Jacobian. Newton-like methods for nonsmooth equations have been globalized by trust-region methods, smooth approximations, and splitting methods in the past, but these approaches are not designed to find steady-state solutions of time-dependent problems. The method in this paper synthesizes the ideas from nonsmooth calculus and the method of pseudo-transient continuation.}, number={4}, journal={SIAM J. Numer. Anal.}, author={Fowler, K R and Kelley, C T}, year={2005}, pages={1385–1406} }
 @inproceedings{zhao_woolard_lasater_kelley_2005, title={Terahertz-Frequency Quantum Oscillator Operating in the Positive Differential Resistance Region}, volume={5790}, booktitle={Proceedings of SPIE Defense and Security Symposium 2005: Terahertz for Military & Security Application III, paper number 5790-34}, author={Zhao, P and Woolard, D L and Lasater, M S and Kelley, C T}, year={2005}, pages={289–300} }
 @article{kelley_pettitt_2004, title={A Fast Algorithm for the {Ornstein-Zernike} Equations}, volume={197}, journal={J. Comp. Phys.}, author={Kelley, C T and Pettitt, B Montgomery}, year={2004}, pages={491–591} }
 @inproceedings{fowler_kelley_kees_miller_2004, place={Amsterdam}, title={A Hydraulic Capture Application for Optimal Remeidation Design}, booktitle={Proceedings of Computational Methods in Water Resources XV}, publisher={Elsevier}, author={Fowler, K R and Kelley, C T and Kees, C E and Miller, C T}, editor={Miller, C T and Farthing, M. W. and Gray, W G and Pinter, G FEditors}, year={2004}, pages={1149–1158} }
 @article{kelley_pettitt_2004, title={A fast solver for the Ornstein-Zernike equations}, volume={197}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2003.12.006}, abstractNote={In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein–Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson–Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Kelley, CT and Pettitt, BM}, year={2004}, month={Jul}, pages={491–501} }
 @inproceedings{lasater_kelley_salinger_woolard_zhao_2004, title={Enhancement of Numerical Computations of the {W}igner-{P}oisson Equations for Application to the Simulation of {TH}z-Frequency {RTD} Oscillators}, booktitle={Proceedings of SPIE: Chemical and Biological Standoff Detection II Volume 5584, paper number 07}, author={Lasater, M S and Kelley, C T and Salinger, A and Woolard, D L and Zhao, P}, editor={Jensen, J O and Theriault, J-MEditors}, year={2004}, pages={42–51} }
 @article{conn_kelley_scheinberg_vicente_2004, title={Implicit Filtering Revisited}, author={Conn, A R and Kelley, C T and Scheinberg, K and Vicente, L N}, year={2004} }
 @inproceedings{lasater_kelley_salinger_woolard_zhao_2004, place={Wuhan, China}, title={Parallel Solution of the {Wigner-Poisson} Equations for {RTDs}}, booktitle={2004 International Symposium on Distributed Computing and Applications to Business, Engineering and Science}, publisher={Hubei Science and Technology Press}, author={Lasater, M S and Kelley, C T and Salinger, A and Woolard, D L and Zhao, P}, editor={Qingping, QuoEditor}, year={2004}, pages={672–676} }
 @inproceedings{kelley_fowler_kees_2004, place={Amsterdam}, title={Simulation of Nondifferentiable Models for Groundwater Flow and Transport}, booktitle={Proceedings of Computational Methods in Water Resources XV}, publisher={Elsevier}, author={Kelley, C T and Fowler, K R and Kees, C E}, editor={Miller, C T and Farthing, M. W. and Gray, W G and Pinter, G FEditors}, year={2004}, pages={939–952} }
 @article{fowler_kelley_miller_kees_darwin_reese_farthing_reed_2004, title={Solution of a well-field design problem with implicit filtering}, volume={5}, ISSN={["1573-2924"]}, DOI={10.1023/B:OPTE.0000033375.33183.e7}, abstractNote={Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.}, number={2}, journal={OPTIMIZATION AND ENGINEERING}, author={Fowler, KR and Kelley, CT and Miller, CT and Kees, CE and Darwin, RW and Reese, JP and Farthing, MW and Reed, MSC}, year={2004}, month={Jun}, pages={207–234} }
 @article{kanney_miller_kelley_2003, title={Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems}, volume={26}, ISSN={["1872-9657"]}, DOI={10.1016/S0309-1708(02)00162-8}, abstractNote={Numerical solutions to nonlinear reactive solute transport problems (NRTPs) are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the ISO approach for solving NRTPs. We show that under certain assumptions regarding smoothness, the convergence rate of the ISO algorithm applied NRTPs is O(Δt2). We demonstrate that the theoretical convergence rate can be achieved in practice if the numerical solution of the transport and reaction steps are carried out with sufficient accuracy. We also show that accurate estimation of the lagged operator in each step is crucial to obtaining the theoretical convergence rate.}, number={3}, journal={ADVANCES IN WATER RESOURCES}, author={Kanney, JF and Miller, CT and Kelley, CT}, year={2003}, month={Mar}, pages={247–261} }
 @article{farthing_kees_coffey_kelley_miller_2003, title={Efficient steady-state solution techniques for variably saturated groundwater flow}, volume={26}, ISSN={["0309-1708"]}, DOI={10.1016/S0309-1708(03)00076-9}, abstractNote={We consider the simulation of steady-state variably saturated groundwater flow using Richards’ equation (RE). The difficulties associated with solving RE numerically are well known. Most discretization approaches for RE lead to nonlinear systems that are large and difficult to solve. The solution of nonlinear systems for steady-state problems can be particularly challenging, since a good initial guess for the steady-state solution is often hard to obtain, and the resulting linear systems may be poorly scaled. Common approaches like Picard iteration or variations of Newton’s method have their advantages but perform poorly with standard globalization techniques under certain conditions. Pseudo-transient continuation has been used in computational fluid dynamics for some time to obtain steady-state solutions for problems in which Newton’s method with standard line-search strategies fails. Here, we examine the use of pseudo-transient continuation as well as Newton’s method combined with standard globalization techniques for steady-state problems in heterogeneous domains. We investigate the methods’ performance with direct and preconditioned Krylov iterative linear solvers. We then make recommendations for robust and efficient approaches to obtain steady-state solutions for RE under a range of conditions.}, number={8}, journal={ADVANCES IN WATER RESOURCES}, author={Farthing, MW and Kees, CE and Coffey, TS and Kelley, CT and Miller, CT}, year={2003}, month={Aug}, pages={833–849} }
 @article{mayer_kelley_miller_2003, title={Electronic Supplement to ``{O}ptimal Design for Problems Involving Flow and Transport Phenomena in Saturated Subsurface Systems''}, author={Mayer, A S and Kelley, C T and Miller, C T}, year={2003} }
 @article{coffey_mcmullan_kelley_mcrae_2003, title={Globally Convergent Algorithms for Nonsmooth Nonlinear Equations in Computational Fluid Dynamics}, volume={152}, journal={J. Comp. Appl. Math.}, author={Coffey, T S and McMullan, R J and Kelley, C T and McRae, D S}, year={2003}, pages={69–81} }
 @article{coffey_mcmullan_kelley_mcrae_2003, title={Globally convergent algorithms for nonsmooth nonlinear equations in computational fluid dynamics}, volume={152}, ISSN={["0377-0427"]}, DOI={10.1016/S0377-0427(02)00697-0}, abstractNote={In this paper we report on a computational study in which a nonsmooth discretization of the Euler equations for flow in a nozzle is solved with splitting method which is in turn globalized with the method of pseudo-transient continuation.}, number={1-2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Coffey, T and McMullan, RJ and Kelley, CT and McRae, DS}, year={2003}, month={Mar}, pages={69–81} }
 @book{kelley_2003, place={Dordrecht}, title={Implicit filtering and nonlinear least squares problems}, number={CRSC-TR01-17}, journal={System Modeling and Optimization XX}, institution={Kluwer Academic Publishers}, author={Kelley, C T}, editor={Sachs, E W and Tichatschke, REditors}, year={2003}, month={Jul}, pages={71–90} }
 @inproceedings{kelley_2003, place={Dordrecht}, title={Implicit filtering and nonlinear least squares problems}, booktitle={System Modeling and Optimization XX}, publisher={Kluwer Academic Publishers}, author={Kelley, C T}, editor={Sachs, E W and Tichatschke, REditors}, year={2003}, pages={71–90} }
 @inproceedings{lasater_kelley_zhao_woolard_2003, title={Numerical Tools for the Study of Instabilities within the Positive-Differential-Resistance Regions of Tunnelling Devices}, number={CRSC-TR03-23}, booktitle={Proceedings of 2003 3nd IEEE Conference on Nanotechnology, San Francisco, CA, August 12--14, 2003}, publisher={IEEE}, author={Lasater, M S and Kelley, C T and Zhao, P and Woolard, D L}, year={2003}, pages={390–393} }
 @article{coffey_kelley_keyes_2003, title={Pseudotransient continuation and differential-algebraic equations}, volume={25}, ISSN={["1095-7197"]}, DOI={10.1137/S106482750241044X}, abstractNote={Pseudotransient continuation is a practical technique for globalizing the computation of steady-state solutions of nonlinear differential equations. The technique employs adaptive time-stepping to integrate an initial value problem derived from an underlying ODE or PDE boundary value problem until sufficient accuracy in the desired steady-state root is achieved to switch over to Newton's method and gain a rapid asymptotic convergence. The existing theory for pseudotransient continuation includes a global convergence result for differential equations written in semidiscretized method-of-lines form. However, many problems are better formulated or can only sensibly be formulated as differential-algebraic equations (DAEs). These include systems in which some of the equations represent algebraic constraints, perhaps arising from the spatial discretization of a PDE constraint. 
Multirate systems, in particular, are often formulated as differential-algebraic systems to suppress fast time scales (acoustics, gravity waves, Alfven waves, near equilibrium chemical oscillations, etc.) that are irrelevant on the dynamical time scales of interest. In this paper we present a global convergence result for pseudotransient continuation applied to DAEs of index 1, and we illustrate it with numerical experiments on model incompressible flow and reacting flow problems, in which a constraint is employed to step over acoustic waves.}, number={2}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Coffey, TS and Kelley, CT and Keyes, DE}, year={2003}, pages={553–569} }
 @book{kelley_2003, place={Philadelphia}, title={Solving Nonlinear Equations with Newton's Method}, number={1}, publisher={SIAM}, author={Kelley, C T}, year={2003} }
 @article{kelley_sachs_2003, title={Truncated Newton methods for optimization with inaccurate functions and gradients}, volume={116}, ISSN={["0022-3239"]}, DOI={10.1023/A:1022110219090}, abstractNote={We consider unconstrained minimization problems that have functions and gradients given by black box codes with error control. We discuss several modifications of the Steihaug truncated Newton method that can improve performance for such problems. We illustrate the ideas with two examples.}, number={1}, journal={JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS}, author={Kelley, CT and Sachs, EW}, year={2003}, month={Jan}, pages={83–98} }
 @article{kees_miller_jenkins_kelley_2003, title={Versatile two-level Schwarz preconditioners for multiphase flow}, volume={7}, ISSN={["1420-0597"]}, DOI={10.1023/A:1023514922877}, number={2}, journal={COMPUTATIONAL GEOSCIENCES}, author={Kees, CE and Miller, CT and Jenkins, EW and Kelley, CT}, year={2003}, pages={91–114} }
 @book{miller_farthing_kees_kelley_2002, title={Higher Order, Locally Conservative, Temporal Integration Methods for Multiphase Flow in Porous Media}, number={CRSC-TR02-02}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Miller, C T and Farthing, M W and Kees, C E and Kelley, C T}, year={2002}, month={Feb} }
 @inproceedings{miller_farthing_kees_kelley_2002, place={Amsterdam}, title={Higher Order, Locally Conservative, Temporal Integration Methods for Multiphase Flow in Porous Media}, booktitle={Computational Methods in Water Resources XIV, Vol. 1}, publisher={Elsevier}, author={Miller, C T and Farthing, M W and Kees, C E and Kelley, C T}, editor={Hassanizadeh, S Majid and Schotting, Ruud J and Gray, W G and Pinder, G FEditors}, year={2002}, pages={249–256} }
 @inproceedings{kavanagh_kelley_berger_hallberg_howington_2002, place={Amsterdam}, title={Nonsmooth Nonlinearities and Temporal Integration of {R}ichards' Equation}, booktitle={Computational Methods in Water Resources XIV, Vol. 2}, publisher={Elsevier}, author={Kavanagh, K R and Kelley, C T and Berger, R C and Hallberg, J P and Howington, Stacy E}, editor={Hassanizadeh, S Majid and Schotting, Ruud J and Gray, W G and Pinder, G FEditors}, year={2002}, pages={947–954} }
 @article{mayer_kelley_miller_2002, title={Optimal Design for Problems Involving Flow and Transport Phenomena in Saturated Subsurface Systems}, volume={12}, journal={Advances in Water Resources}, author={Mayer, A S and Kelley, C T and Miller, C T}, year={2002}, pages={1233–1256} }
 @misc{mayer_kelley_miller_2002, title={Optimal design for problems involving flow and transport phenomena in saturated subsurface systems}, volume={25}, ISSN={["1872-9657"]}, DOI={10.1016/S0309-1708(02)00054-4}, abstractNote={Estimation problems arise routinely in subsurface hydrology for applications that range from water resources management to water quality protection to subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state of the art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods exist to solve the most challenging applications in subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches.}, number={8-12}, journal={ADVANCES IN WATER RESOURCES}, author={Mayer, AS and Kelley, CT and Miller, CT}, year={2002}, pages={1233–1256} }
 @inproceedings{kelley_woolard_zhao_kerr_lasater_2002, title={Parallel-Platform Based Numerical Simulation of Instabilities in Nanoscale Tunneling Devices}, booktitle={Proceedings of 2002 2nd IEEE Conference on Nanotechnology, Washington DC, August 26-28, 2002}, publisher={IEEE}, author={Kelley, C T and Woolard, D L and Zhao, P and Kerr, M and Lasater, M S}, year={2002}, pages={417–421} }
 @book{coffey_kelley_keyes_2002, title={Pseudo-Transient Continuation and Differential-Algebraic Equations}, volume={25}, number={CRSC-TR02-18}, journal={SIAM J. Sci. Comp.}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Coffey, T and Kelley, C T and Keyes, D E}, year={2002}, month={Jul}, pages={553–569} }
 @article{battermann_gablonsky_patrick_kelley_coffey_kavanagh_miller_2002, title={Solution of A Groundwater Control Problem with Implicit Filtering}, volume={3}, journal={Optimization and Engineering}, author={Battermann, A and Gablonsky, J M and Patrick, A and Kelley, C T and Coffey, T and Kavanagh, K and Miller, C T}, year={2002}, pages={189–199} }
 @article{gablonsky_kelley_2001, title={A locally-biased form of the DIRECT algorithm}, volume={21}, ISSN={["0925-5001"]}, DOI={10.1023/A:1017930332101}, number={1}, journal={JOURNAL OF GLOBAL OPTIMIZATION}, author={Gablonsky, JM and Kelley, CT}, year={2001}, month={Sep}, pages={27–37} }
 @article{carter_gablonsky_patrick_kelley_eslinger_2001, title={Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization}, volume={2}, journal={Optimization and Engineering}, author={Carter, R. and Gablonsky, J.M. and Patrick, A. and Kelley, C.T. and Eslinger, O.J.}, year={2001}, pages={139–157} }
 @article{jenkins_kelley_miller_kees_2001, title={An Aggregation-based Domain Decomposition Preconditioner for Groundwater Flow}, volume={23}, journal={SIAM J. Sci. Comp.}, author={Jenkins, E W and Kelley, C T and Miller, C T and Kees, C E}, year={2001}, pages={430–441} }
 @article{jenkins_kees_kelley_miller_2001, title={An aggregation-based domain decomposition preconditioner for groundwater flow}, volume={23}, ISSN={["1095-7197"]}, DOI={10.1137/S1064827500372274}, abstractNote={We consider theoretical and computational issues associated with an aggregation-based domain decomposition preconditioner applied to a Bi-CGSTAB iterative solver used to solve both Laplace's equation and an important nonlinear model from hydrology used to simulate unsaturated flow, Richards' equation. Theoretical results for Laplace's equation provide estimates of the condition number and the rate of convergence for a two-level Schwarz domain decomposition preconditioner. Computational results for Laplace's equation and Richards' equation show excellent scalability, although no theory is yet available to support the results for the difficult nonlinear problem.}, number={2}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Jenkins, EW and Kees, CE and Kelley, CT and Miller, CT}, year={2001}, month={Aug}, pages={430–441} }
 @inproceedings{kelley_2001, place={Dordrecht}, title={Nonlinear Equations: Contraction-Mapping Principle}, booktitle={Encyclopedia of Optimization}, publisher={Kluwer}, author={Kelley, C T}, editor={Floudas, C A and Pardalos, P MEditors}, year={2001}, pages={two pages} }
 @article{gremaud_kelley_royal_coffey_2001, title={On a powder consolidation problem}, volume={62}, DOI={10.1137/s0036139900368479}, abstractNote={The problem of the consolidation of an aerated fine powder under gravity is considered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure is that of a coupled system for three unknowns, pressure, stress, and height of the powder in the (axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE, and an integral equation determining a free boundary corresponding to the height of the powder. Existence and uniqueness of a solution is established. A numerical method based on a formulation of the semidiscretized problem as an index 1 DAE is proposed and implemented. The feasibility of the approach is illustrated by computational results.}, number={1}, journal={SIAM J. Appl. Math.}, author={Gremaud, P A and Kelley, C T and Royal, T A and Coffey, K A}, year={2001}, pages={1–20} }
 @book{mayer_kelley_miller_2001, title={Optimal Design for Problems Involving Flow and Transport Phenomena in Saturated Subsurface Systems}, number={CRSC-TR01-33}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Mayer, A S and Kelley, C T and Miller, C T}, year={2001}, month={Dec} }
 @inproceedings{jenkins_berger_hallberg_howington_kelley_schmidt_stagg_tocci_2000, title={A Two-Level Aggregation-Based {Newton-Krylov-Schwarz} Method for Hydrology}, booktitle={Parallel Computational Fluid Dynamics 1999}, publisher={North Holland}, author={Jenkins, E W and Berger, R C and Hallberg, J P and Howington, Stacy E and Kelley, C T and Schmidt, Joseph H and Stagg, Alan and Tocci, M D}, editor={Keyes, D E and Ecer, A and Periaux, J and Satofuka, NEditors}, year={2000}, pages={257–264} }
 @inproceedings{kelley_2000, place={Dordrecht}, title={Broyden Method}, booktitle={Encyclopedia of Mathematics: Supplement II}, publisher={Kluwer}, author={Kelley, C T}, editor={Hazenwinkel, MEditor}, year={2000}, pages={96–98} }
 @article{ferng_kelley_2000, title={Mesh Independence of Matrix-Free Methods for Path Following}, volume={21}, journal={SIAM J. Sci. Comp.}, author={Ferng, W R and Kelley, C T}, year={2000}, pages={1835–1850} }
 @article{ferng_kelley_2000, title={Mesh independence of matrix-free methods for path following}, volume={21}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827598339360}, abstractNote={In this paper we consider a matrix-free path following algorithm for nonlinear parameter-dependent compact fixed point problems. We show that if these problems are discretized so that certain collective compactness and strong convergence properties hold, then this algorithm can follow smooth folds and capture simple bifurcations in a mesh-independent way.}, number={5}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ferng, WR and Kelley, CT}, year={2000}, month={May}, pages={1835–1850} }
 @article{choi_eslinger_kelley_david_etheridge_2000, title={Optimization of Automotive Valve Train Components with Implict Filtering}, volume={1}, journal={Optimization and Engineering}, author={Choi, T.D. and Eslinger, O.J. and Kelley, C.T. and David, J.W. and Etheridge, M.}, year={2000}, pages={9–28} }
 @article{choi_kelley_2000, title={Superlinear convergence and implicit filtering}, volume={10}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623499354096}, abstractNote={In this paper we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. In this way we give insight into the observations of good performance in practice of quasi-Newton methods when they are coupled with implicit filtering. We also report on numerical experiments that show how an implementation of implicit filtering that exploits these new results can improve the performance of the algorithm.}, number={4}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Choi, TD and Kelley, CT}, year={2000}, month={Jun}, pages={1149–1162} }
 @book{miller_williams_kelley_2000, title={Transformation Approaches for Simulating Flow in Variably Saturated Porous Media}, volume={36}, journal={Water Resources Research}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Miller, C T and Williams, G A and Kelley, C T}, year={2000}, month={Jan}, pages={923–934} }
 @article{williams_miller_kelley_2000, title={Transformation approaches for simulating flow in variably saturated porous media}, volume={36}, ISSN={["0043-1397"]}, DOI={10.1029/1999WR900349}, abstractNote={Sharp fronts with rapid changes in fluid saturations over short distance and timescales often exist in multiphase flow in subsurface systems. Such highly nonlinear problems are notoriously difficult to solve, and standard solution approaches are often inefficient and unreliable. We summarize four existing and one new transformation method (IT2) for solving Richards'; equation within a common framework and compare performance for a range of medium properties and simulation conditions. The new IT2 transform is defined as a linear combination of volumetric water fraction of the aqueous phase and integrated hydraulic conductivity terms. We show that transformation methods can significantly improve solution efficiency and robustness compared to standard solution approaches; optimal transformation parameters depend upon auxiliary conditions, medium properties, and spatial and temporal discretization and are difficult to evaluate a priori; and IT2 compares favorably with existing transforms.}, number={4}, journal={WATER RESOURCES RESEARCH}, author={Williams, GA and Miller, CT and Kelley, CT}, year={2000}, month={Apr}, pages={923–934} }
 @inproceedings{kelley_2000, place={Dordrecht}, title={{Broyden-Fletcher-Goldfarb-Shanno} Method}, booktitle={Encyclopedia of Mathematics: Supplement II}, publisher={Kluwer}, author={Kelley, C T}, editor={Hazenwinkel, MEditor}, year={2000}, pages={95–96} }
 @inproceedings{howington_berger_hallberg_peters_stagg_jenkins_kelley_1999, place={Monterrey, CA}, title={A Model to Simulate the Interaction between Groundwater and Surface Water}, number={CRSC-TR99-27}, booktitle={Proceedings of the High Performance Computing Users' Group Meeting}, author={Howington, S E and Berger, R C and Hallberg, J P and Peters, J F and Stagg, A K and Jenkins, E W and Kelley, C T}, year={1999}, month={Aug} }
 @article{banoczi_kelley_1999, title={A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations in two space dimensions}, volume={20}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827597322756}, abstractNote={In this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer in two space dimensions. This extends our previous work in one space dimension. We formulate the equations as a compact fixed point problem with the temperature as the unknown. The fixed point map requires both a Poisson solve and a transport solve for its evaluation. As a solver for both the transport problem and the full system we apply the Atkinson--Brakhage algorithm, using Newton-GMRES as the solver on the coarse mesh. We compare our solver choices with Newton-GMRES. Under modest stability and convergence assumptions on the transport solver, we prove convergence of the multilevel method for the complete system.}, number={4}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Banoczi, JM and Kelley, CT}, year={1999}, pages={1214–1228} }
 @article{kelley_sachs_1999, title={A trust region method for parabolic boundary control problems}, volume={9}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623496308965}, abstractNote={In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. For the computation of a trust region step we propose an iterative scheme which is a projected form of the Steihaug trust region conjugate gradient method. To ensure the good local convergence properties in the terminal phase, a smoothing step at each iteration is added. This step and the projection require the modification of the standard trust region algorithm and its convergence proof. The algorithm has sup-norm convergence in the terminal phase and L2 convergence in the global phase. The results are illustrated for a parabolic boundary control problem.}, number={4}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Kelley, CT and Sachs, EW}, year={1999}, pages={1064–1081} }
 @article{kelley_1999, title={Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition}, volume={10}, ISSN={["1095-7189"]}, DOI={10.1137/S1052623497315203}, abstractNote={The Nelder--Mead algorithm can stagnate and converge to a nonoptimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for all iterations, will guarantee convergence of the Nelder--Mead iteration to a stationary point if the objective function is smooth and the diameters of the Nelder--Mead simplices converge to zero. Failure of this condition is an indicator of potential stagnation. As a remedy we propose a new step, which we call an oriented restart, that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point. We also give results that apply when the objective function is a low-amplitude perturbation of a smooth function. We illustrate our results with some numerical examples.}, number={1}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Kelley, CT}, year={1999}, month={Nov}, pages={43–55} }
 @article{choi_kelley_1999, title={Estimates for the Nash-Sofer preconditioner for the reduced Hessian for some elliptic variational inequalities}, volume={9}, ISSN={["1052-6234"]}, DOI={10.1137/S1052623497323364}, abstractNote={The purpose of this paper is to present a class of examples to show how the quality of the Nash--Sofer preconditioner can be directly estimated. This class of examples includes certain discretized elliptic variational inequalities. We use sparsity and locality properties of discretizations of elliptic operators and smoothing properties of their inverses to estimate the quality of the preconditioner. One consequence of our results is that if the Hessian is the five-point discretization of a certain type of strongly elliptic operator with homogeneous Dirichlet boundary conditions on an $n \times n$ mesh and the preconditioner is a fast Poisson solver for that discretization, then the condition number of the reduced Hessian can be lowered from O(n2) to O(n ln(n)). We illustrate these theoretical results with calculations.}, number={2}, journal={SIAM JOURNAL ON OPTIMIZATION}, author={Choi, TD and Kelley, CT}, year={1999}, month={Apr}, pages={327–341} }
 @book{choi_eslinger_gilmore_patrick_kelley_gablonsky_1999, title={IFFCO: Implicit Filtering for Constrained Optimization, Version 2}, number={CRSC-TR99-23}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Choi, T D and Eslinger, O J and Gilmore, P and Patrick, A and Kelley, C T and Gablonsky, J M}, year={1999}, month={Jul} }
 @book{kelley_1999, place={Philadelphia}, title={Iterative Methods for Optimization}, ISBN={0898714338}, DOI={10.1137/1.9781611970920}, abstractNote={This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke& Jeeves, implicit filtering, MDS, and Nelder& Mead schemes in a unified way.}, number={18}, publisher={SIAM}, author={Kelley, C T}, year={1999} }
 @book{jenkins_berger_hallberg_howington_kelley_schmidt_stagg_tocci_1999, title={{Newton-Krylov-Schwarz} Methods for {R}ichards' Equation}, number={CRSC-TR99-32}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Jenkins, E W and Berger, R C and Hallberg, J P and Howington, Stacy E and Kelley, C T and Schmidt, Joseph H and Stagg, Alan and Tocci, M D}, year={1999}, month={Oct} }
 @article{banoczi_kelley_1998, title={A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations}, volume={19}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827596302965}, abstractNote={In this paper we describe and analyze a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer. This system of equations for radiative intensity and temperature can be formulated as a compact fixed point problem in temperature alone with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We obtain an efficient evaluation of the fixed point map by coupling a finite element diffusion solver with a fast transport solver developed by the second author. As a solver we apply a modification of the Atkinson--Brakhage method, with Newton--GMRES as the coarse mesh solver, to the full nonlinear system. We compare our discretization/solver pair with Newton--GMRES and the classical Atkinson--Brakhage algorithm.}, number={1}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Banoczi, JM and Kelley, CT}, year={1998}, month={Jan}, pages={266–279} }
 @article{kelley_keyes_1998, title={Convergence analysis of pseudo-transient continuation}, volume={35}, ISSN={["0036-1429"]}, DOI={10.1137/S0036142996304796}, abstractNote={Pseudo-transient continuation ($\Psi$tc) is a well-known and physically motivated technique for computation of steady state solutions of time-dependent partial differential equations. Standard globalization strategies such as line search or trust region methods often stagnate at local minima. \ptc succeeds in many of these cases by taking advantage of the underlying PDE structure of the problem. Though widely employed, the convergence of \ptc is rarely discussed. In this paper we prove convergence for a generic form of \ptc and illustrate it with two practical strategies.}, number={2}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Kelley, CT and Keyes, DE}, year={1998}, month={Apr}, pages={508–523} }
 @inproceedings{miller_williams_kelley_1998, title={Efficient and robust numerical modeling of variably saturated flow in layered porous media}, volume={1}, booktitle={XII Conference on Computational Methods in Water Resources, Crete, Greece}, author={Miller, C T and Williams, G A and Kelley, C T}, editor={Burganos, V N and Karatzas, G P and Payatakes, A C and Brebbia, C A and Gray, W G and Pinder, G FEditors}, year={1998}, pages={151–158} }
 @article{tocci_kelley_miller_kees_1998, title={Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions}, volume={2}, ISSN={["1420-0597"]}, DOI={10.1023/A:1011562522244}, number={4}, journal={COMPUTATIONAL GEOSCIENCES}, author={Tocci, MD and Kelley, CT and Miller, CT and Kees, CE}, year={1998}, pages={291–309} }
 @article{kelley_sachs_1998, title={Local convergence of the symmetric rank-one iteration}, volume={9}, ISSN={["0926-6003"]}, DOI={10.1023/A:1018330119731}, number={1}, journal={COMPUTATIONAL OPTIMIZATION AND APPLICATIONS}, author={Kelley, CT and Sachs, EW}, year={1998}, month={Jan}, pages={43–63} }
 @inproceedings{kelley_1998, title={New Analysis of the {N}elder-{M}ead Algorithm}, booktitle={Proceedings of the 29th Symposium on the Interface}, author={Kelley, C T}, editor={Scott, D WEditor}, year={1998}, pages={407} }
 @book{choi_eslinger_kelley_david_etheridge_1998, title={Optimization of Automotive Valve Train Components with Implicit Filtering}, volume={1}, journal={Optimization and Engineering}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={Choi, T D and Eslinger, O J and Kelley, C T and David, J W and Etheridge, M}, year={1998}, month={Dec}, pages={9–28} }
 @article{miller_williams_kelley_tocci_1998, title={Robust Solution of {R}ichards' Equation for Non-Uniform Porous Media}, volume={34}, journal={Water Resources Research}, author={Miller, C T and Williams, G A and Kelley, C T and Tocci, M D}, year={1998}, pages={2599–2610} }
 @article{miller_williams_kelley_tocci_1998, title={Robust solution of Richards' equation for nonuniform porous media}, volume={34}, ISSN={["0043-1397"]}, DOI={10.1029/98WR01673}, abstractNote={Capillary pressure–saturation‐relative permeability relations described using the van Genuchten [1980] and Mualem [1976] models for nonuniform porous media lead to numerical convergence difficulties when used with Richards' equation for certain auxiliary conditions. These difficulties arise because of discontinuities in the derivative of specific moisture capacity and relative permeability as a function of capillary pressure. Convergence difficulties are illustrated using standard numerical approaches to simulate such problems. We investigate constitutive relations, interblock permeability, nonlinear algebraic system approximation methods, and two time integration approaches. An integral permeability approach approximated by Hermite polynomials is recommended and shown to be robust and economical for a set of test problems, which correspond to sand, loam, and clay loam media.}, number={10}, journal={WATER RESOURCES RESEARCH}, author={Miller, CT and Williams, GA and Kelley, CT and Tocci, MD}, year={1998}, month={Oct}, pages={2599–2610} }
 @article{kelley_miller_tocci_1998, title={Termination of Newton/Chord iterations and the method of lines}, volume={19}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827596303582}, abstractNote={Many ordinary differential equation (ODE) and differential algebraic equation (DAE) codes terminate the nonlinear iteration for the corrector equation when the difference between successive iterates (the step) is sufficiently small. This termination criterion avoids the expense of evaluating the nonlinear residual at the final iterate. Similarly, Jacobian information is not usually computed at every time step but only when certain tests indicate that the cost of a new Jacobian is justified by the improved performance in the nonlinear iteration. In this paper, we show how an out-of-date Jacobian coupled with moderate ill conditioning can lead to premature termination of the corrector iteration and suggest ways in which this situation can be detected and remedied. As an example, we consider the method of lines (MOL) solution of Richards' equation (RE), which models flow through variably saturated porous media. When the solution to this problem has a sharp moving front, and the Jacobian is even slightly ill conditioned, the corrector iteration used in many integrators can terminate prematurely, leading to incorrect results. While this problem can be solved by tightening the tolerances for the solvers used in the temporal integration, it is more efficient to modify the termination criteria of the nonlinear solver and/or recompute the Jacobian more frequently. Of these two, recomputation of the Jacobian is the more important. We propose a criterion based on an estimate of the norm of the time derivative of the Jacobian for recomputation of the Jacobian and a second criterion based on a condition estimate for tightening of the termination criteria of the nonlinear solver.}, number={1}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Kelley, CT and Miller, CT and Tocci, MD}, year={1998}, month={Jan}, pages={280–290} }
 @inproceedings{bortz_kelley_1998, title={The Simplex Gradient and Noisy Optimization Problems}, volume={24}, booktitle={Computational Methods in Optimal Design and Control}, publisher={Birkh{ä}user, Boston}, author={Bortz, D M and Kelley, C T}, editor={Borggaard, J T and Burns, J and Cliff, E and Schreck, SEditors}, year={1998}, pages={77–90} }
 @article{tocci_kelley_miller_1997, title={Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines}, volume={20}, ISSN={["0309-1708"]}, DOI={10.1016/S0309-1708(96)00008-5}, abstractNote={The pressure-head form of Richards' equation (RE) is difficult to solve accurately using standard time integration methods. For example, mass balance errors grow as the integration progresses unless very small time steps are taken. Further, RE may be solved for many problems more economically and robustly with variable-size time steps rather than with a constant time-step size, but variable step-size methods applied to date have relied upon empirical approaches to control step size, which do not explicitly control temporal truncation error of the solution. We show how a differential algebrain equation implementation of the method of lines can give solutions to RE that are accurate, have good mass balance properties, explicitly control temporal truncation error, and are more economical than standard approaches for a wide range of solution accuracy. We detail changes to a standard integrator, DASPK, that improves efficiency for the test problems considered, and we advocate the use of this approach for both RE and other problems involving subsurface flow and transport phenomena.}, number={1}, journal={ADVANCES IN WATER RESOURCES}, author={Tocci, MD and Kelley, CT and Miller, CT}, year={1997}, month={Feb}, pages={1–14} }
 @book{david_cheng_choi_kelley_gablonsky_1997, title={Optimal Design of High Speed Mechanical Systems}, number={CRSC-TR97-18}, institution={North Carolina State University, Center for Research in Scientific Computation}, author={David, J W and Cheng, C Y and Choi, T D and Kelley, C T and Gablonsky, J}, year={1997}, month={Jul} }
 @inproceedings{campbell_kelley_yeomans_1996, title={Consistent Initial Conditions for Unstructured Higher Index {DAE}s: A Computational Study}, booktitle={Proceedings of Conference on Computational Engineering in Systems Applications (CESA'96), Lille, France}, author={Campbell, S L and Kelley, C T and Yeomans, K D}, year={1996}, pages={416–421} }
 @article{campbell_ipsen_kelley_meyer_xue_1996, title={Convergence Estimates for Solution of Integral Equations with GMRES}, volume={8}, ISSN={0897-3962}, url={http://dx.doi.org/10.1216/jiea/1181075914}, DOI={10.1216/jiea/1181075914}, abstractNote={In this paper we derive convergence estimates for the iterative solution of nonsymmetric linear systems by GMRES. We work in the context of strongly convergent-collectively compact sequences of approximations to linear compact xed point problems. Our estimates are intended to explain the observations that the performance of GMRES is independent of the discretization if the resolution of the discretization is su ciently good. Our bounds are independent of the right hand side of the equation, re ect the r-superlinear convergence of GMRES in the in nite dimensional setting, and also allow for more than one implementation of the discrete scalar product. Our results are motivated by quadrature rule approximation to second-kind Fredholm integral equations.}, number={1}, journal={Journal of Integral Equations and Applications}, publisher={Rocky Mountain Mathematics Consortium}, author={Campbell, S.L. and Ipsen, I.C.F. and Kelley, C.T. and Meyer, C.D. and Xue, Z.Q.}, year={1996}, month={Mar}, pages={19–34} }
 @article{kelley_1996, title={Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations}, volume={25}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411459608204839}, DOI={10.1080/00411459608204839}, abstractNote={Abstract We prove an existence and uniqueness results for a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. Our approach uses two different formulations of the system as a compact fixed-point problem. One formulation, which has been used in numerical work, is used for uniqueness and a new one is used for the existence proof.}, number={2}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1996}, month={Mar}, pages={249–260} }
 @article{kelley_xue_1996, title={GMRES and Integral Operators}, volume={17}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/0917015}, DOI={10.1137/0917015}, abstractNote={In this paper we show how the properties of integral operators and their approximations are reflected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates by an implicit application of Nystrom interpolation, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden’s method. We present an example to illustrate the ideas.}, number={1}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Xue, Z. Q.}, year={1996}, month={Jan}, pages={217–226} }
 @article{campbell_ipsen_kelley_meyer_1996, title={GMRES and the minimal polynomial}, volume={36}, ISSN={0006-3835 1572-9125}, url={http://dx.doi.org/10.1007/bf01733786}, DOI={10.1007/bf01733786}, abstractNote={We present a qualitative model for the convergence behaviour of the Generalised Minimal Residual (GMRES) method for solving nonsingular systems of linear equationsAx =b in finite and infinite dimensional spaces. One application of our methods is the solution of discretised infinite dimensional problems, such as integral equations, where the constants in the asymptotic bounds are independent of the mesh size. Our model provides simple, general bounds that explain the convergence of GMRES as follows: If the eigenvalues ofA consist of a single cluster plus outliers then the convergence factor is bounded by the cluster radius, while the asymptotic error constant reflects the non-normality ofA and the distance of the outliers from the cluster. If the eigenvalues ofA consist of several close clusters, then GMRES treats the clusters as a single big cluster, and the convergence factor is the radius of this big cluster. We exhibit matrices for which these bounds are tight. Our bounds also lead to a simpler proof of existing r-superlinear convergence results in Hilbert space.}, number={4}, journal={BIT Numerical Mathematics}, publisher={Springer Science and Business Media LLC}, author={Campbell, S. L. and Ipsen, I. C. F. and Kelley, C. T. and Meyer, C. D.}, year={1996}, month={Dec}, pages={664–675} }
 @article{david_kelley_cheng_1996, place={Washington, D. C.}, title={Use of an Implicit Filtering Algorithm for Mechanical System Parameter Identification}, journal={1996 SAE International Congress and Exposition Conference Proceedings, Modeling of CI and SI Engines}, publisher={Society of Automotive Engineers}, author={David, J W and Kelley, C T and Cheng, C Y}, year={1996}, pages={189–194} }
 @article{kelley_1995, title={A Fast Multilevel Algorithm for Integral Equations}, volume={32}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0732021}, DOI={10.1137/0732021}, abstractNote={We show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly converge. From this norm convergent formulation a two-level approximate inverse can be constructed whose evaluation requires no fine mesh evaluations of the integral operator. The resulting multilevel algorithm, therefore, is roughly half as costly as the Atkinson–Brakhage iteration. The algorithm is applicable to both linear and nonlinear equations.}, number={2}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T.}, year={1995}, month={Apr}, pages={501–513} }
 @article{gilmore_kelley_1995, title={An Implicit Filtering Algorithm for Optimization of Functions with Many Local Minima}, volume={5}, ISSN={1052-6234 1095-7189}, url={http://dx.doi.org/10.1137/0805015}, DOI={10.1137/0805015}, abstractNote={In this paper we describe and analyze an algorithm for certain box constrained optimization problems that may have several local minima. A paradigm for these problems is one in which the function to be minimized is the sum of a simple function, such as a convex quadratic, and high frequency, low amplitude terms that cause local minima away from the global minimum of the simple function. Our method is gradient based and therefore the performance can be improved by use of quasi-Newton methods.}, number={2}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Gilmore, P. and Kelley, C. T.}, year={1995}, month={May}, pages={269–285} }
 @inproceedings{gilmore_kelley_miller_williams_1995, title={Implicit Filtering and Optimal Design Problems: Proceedings of the Workshop on Optimal Design and Control, {B}lacksburg {VA}, {A}pril 8--9, 1994}, volume={19}, booktitle={Optimal Design and Control}, publisher={Birkh{ä}user, Boston}, author={Gilmore, P and Kelley, C T and Miller, C T and Williams, G A}, editor={Borggaard, J and Burkhardt, J and Gunzburger, M and Peterson, JEditors}, year={1995}, pages={159–176} }
 @article{ito_kelley_sachs_1995, title={Inexact primal-dual interior point iteration for linear programs in function spaces}, volume={4}, ISSN={0926-6003 1573-2894}, url={http://dx.doi.org/10.1007/bf01300870}, DOI={10.1007/bf01300870}, number={3}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Ito, S. and Kelley, C. T. and Sachs, E. W.}, year={1995}, month={Jul}, pages={189–201} }
 @book{kelley_1995, place={Philadelphia}, title={Iterative Methods for Linear and Nonlinear Equations}, number={16}, publisher={SIAM}, author={Kelley, C T}, year={1995} }
 @article{kelley_1995, title={Multilevel source iteration accelerators for the linear transport equation in slab geometry}, volume={24}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411459508206021}, DOI={10.1080/00411459508206021}, abstractNote={Abstract In this paper we show how classical error estimates for various discretizations of the source iteration map in slab geometry can be used to construct accurate approximate inverses in the context of fast multilevel methods. For discretizations that give strongly convergent collectively compact sequences of approximate source iteration maps, the Atkinson-Brakhage approximate inverse can be applied. For discretizations that give rise to norm convergent sequences, a more direct approach can be used. Our implementation of these ideas, based on use of GMRES iteration to solve the coarse mesh problems, gives the solution to an accuracy of fine mesh truncation error at a cost proportional to that of an evaluation of the fine mesh source iteration map. These methods require only the source iteration map and are hence easier to adapt to multiprocessor computers than methods that require solution of diffusion equations. We illustrate our results with a report on numerical experiments with both strongly and ...}, number={4-5}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1995}, month={Apr}, pages={679–707} }
 @article{kelley_sachs_1995, title={Solution of Optimal Control Problems by a Pointwise Projected Newton Method}, volume={33}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/s0363012993249900}, DOI={10.1137/s0363012993249900}, abstractNote={In the context of optimal control of ordinary differential equations, we prove local superlinear convergence and constraint identification results for an extension of the projected Newton method of Bertsekas. The estimates are also valid for discretized versions of the method-problem pair.}, number={6}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1995}, month={Nov}, pages={1731–1757} }
 @inproceedings{miller_kelley_1994, title={A comparison of strongly convergent solution schemes for sharp front infiltration problems}, booktitle={Computational Methods in Water Resources X, Vol. 1}, publisher={Kluwer Academic Publishers}, author={Miller, C T and Kelley, C T}, editor={Peters, A and Wittum, G and Herrling, B and Meissner, U and Brebbia, C A and Gray, W G and Pinder, G FEditors}, year={1994}, pages={325–332} }
 @inproceedings{kelley_1994, place={Boston}, title={Identification of the Support of Nonsmoothness}, booktitle={Large Scale Optimization: State of the Art}, publisher={Kluwer Academic Publishers B.V.}, author={Kelley, C T}, editor={Hager, W W and Hearn, D W and Pardalos, P MEditors}, year={1994}, pages={192–205} }
 @article{kelley_sachs_1994, title={Multilevel Algorithms for Constrained Compact Fixed Point Problems}, volume={15}, ISSN={1064-8275 1095-7197}, url={http://dx.doi.org/10.1137/0915042}, DOI={10.1137/0915042}, abstractNote={In this paper the authors extend the multilevel algorithm of Atkinson and Brakhage for compact fixed point problems and the projected Newton method of Bertsekas to create a fast multilevel algorithm for parabolic boundary control problems having bound constraints on the control. Results are extended from finite dimension on constraint identification. This approach permits both adaptive integration in time and inexact evaluation of the cost functional.}, number={3}, journal={SIAM Journal on Scientific Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1994}, month={May}, pages={645–667} }
 @inproceedings{ashby_kelley_saylor_scroggs_1994, place={Providence}, title={Preconditioning Via Asymptotically-defined Domain Decomposition}, volume={180}, booktitle={Proceedings of the Seventh International Conference on Domain Decomposition Methods in Science and Engineering}, publisher={AMS}, author={Ashby, S F and Kelley, C T and Saylor, P E and Scroggs, J S}, editor={Keyes, D and Xu, JEditors}, year={1994}, pages={139–150} }
 @inproceedings{morris_trew_kelley_hayes_1993, title={A Non-Quasi-Static Modular Model for {HBT}s}, booktitle={Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits}, author={Morris, A S and Trew, R J and Kelley, C T and Hayes, G J}, year={1993}, pages={440–447} }
 @article{kelley_northrup_1993, title={A fast multi-level method for the fixed point form of matrix H-equations}, volume={22}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411459308203827}, DOI={10.1080/00411459308203827}, abstractNote={In previous work quasi-Newton and multi-level algorithms for fully nonlinear integral equations were designed and analyzed. The motivating examples for that work were analogs of the Chandrasekhar H-equation for matrix-valued functions. A weakness of these algorithms was that transfer between grids was done with a piecewise linear interpolation instead of Nystroem interpolation. This choice of interpolation was used because the nonlinearity in the Chandrasekhar equation was expressed in the quadratic form for which a matrix inversion is not required. In this paper the fixed point formulation is reconsidered and a conditioning issue associated with the matrix is resolved. This allows use of Nystroem interpolation and thereby a more efficient multi-level method. Implementation details on the Alliant FX series of multiprocessor computers is also discussed. 18 refs., 3 tabs.}, number={4}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T. and Northrup, J. I.}, year={1993}, month={Aug}, pages={533–547} }
 @article{ganapol_kelley_pomraning_1993, title={Asymptotically Exact Boundary Conditions for the PN Equations}, volume={114}, ISSN={0029-5639 1943-748X}, url={http://dx.doi.org/10.13182/nse93-a24010}, DOI={10.13182/nse93-a24010}, abstractNote={It was recently demonstrated that in planar geometry, the classic P[sub N] equations are an asymptotic limit of the transport equation. A corresponding boundary layer analysis established the asymptotically consistent boundary conditions. These boundary conditions were evaluated variationally, and it was conjectured that these variational approximations are quite accurate for all values of N. Here, the authors evaluate these boundary conditions exactly (numerically) and show that the previous variational results are indeed accurate to a few percent. The exact results were computed using numerical methods previously developed for solving Chandrasekhar's H equations.}, number={1}, journal={Nuclear Science and Engineering}, publisher={Informa UK Limited}, author={Ganapol, B. D. and Kelley, C. T. and Pomraning, G. C.}, year={1993}, month={May}, pages={12–19} }
 @article{ganapol_kelley_pomraning_1993, title={Asymptotically Exact Boundary Conditions for the {P-N} Equations}, volume={114}, journal={Nuclear Science and Engineering}, author={Ganapol, B D and Kelley, C T and Pomraning, G C}, year={1993}, pages={12–19} }
 @article{kelley_mukundan_1993, title={Convergence analysis for the harmonic balance method}, volume={20}, ISSN={0362-546X}, url={http://dx.doi.org/10.1016/0362-546x(93)90141-e}, DOI={10.1016/0362-546x(93)90141-e}, number={4}, journal={Nonlinear Analysis: Theory, Methods & Applications}, publisher={Elsevier BV}, author={Kelley, C.T. and Mukundan, L.}, year={1993}, month={Feb}, pages={365–380} }
 @article{kelley_xue_1993, title={Inexact Newton Methods for singular problems}, volume={2}, ISSN={1055-6788 1029-4937}, url={http://dx.doi.org/10.1080/10556789308805545}, DOI={10.1080/10556789308805545}, abstractNote={In this paper we describe the effects of an inexact implementation of Newton's method on the behavior of the iteration for certain nonlinear equations in Banach space for which the Frechet derivative is singular at the solution. We give a termination criterion for the inner iteration that preserves not only the q-linear convergence of the Newton iterates but also the fine structure required for an acceleration method.}, number={3-4}, journal={Optimization Methods and Software}, publisher={Informa UK Limited}, author={Kelley, C. T. and Xue, Z. Q.}, year={1993}, month={Jan}, pages={249–267} }
 @article{kelley_sachs_1993, title={Pointwise Broyden Methods}, volume={3}, ISSN={1052-6234 1095-7189}, url={http://dx.doi.org/10.1137/0803020}, DOI={10.1137/0803020}, abstractNote={Pointwise quasi-Newton methods are designed for nonlinear equations and optimization problems in function spaces. They update coefficients of differential and integral operators and therefore take advantage of finer structure than conventional quasi-Newton methods. In this paper a general theory for those pointwise quasi-Newton methods that are based on Broyden’s method are given. This paper unifies the theory of pointwise methods with that for Broyden's method in Hilbert space. A new superlinearly convergent method is introduced for elliptic boundary value problems and the new theory allows for a direct extension of a pointwise method for integral equations.}, number={2}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1993}, month={May}, pages={423–441} }
 @article{kelley_1992, title={Adaptive Integral Equation Methods in Transport Theory}, volume={112}, ISSN={0029-5639 1943-748X}, url={http://dx.doi.org/10.13182/nse92-a23984}, DOI={10.13182/nse92-a23984}, abstractNote={In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented.}, number={4}, journal={Nuclear Science and Engineering}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1992}, month={Dec}, pages={361–368} }
 @article{hwang_kelley_1992, title={Convergence of Broyden’s Method in Banach Spaces}, volume={2}, ISSN={1052-6234 1095-7189}, url={http://dx.doi.org/10.1137/0802025}, DOI={10.1137/0802025}, abstractNote={This paper proves new convergence theorems for convergence of Broyden’s method when applied to nonlinear equations in Banach spaces. The convergence is in the norm of the Banach space itself, rather than in the norm of some Hilbert space that contains the Banach space. It is shown that the norms in which q-superlinear convergence takes place are determined by the smoothing properties of the error in the Frechet derivative approximation and not by the inner product in which Broyden’s method is implemented. Among the consequences of the results in this paper are a proof of sup-norm local q-superlinear convergence when Broyden’s method is applied to integral equations with continuous kernels, global q-superlinear convergence of the Broyden iterates for singular and nonsingular linear compact fixed point problems in Banach space, a new method for integral equations having derivatives with sparse kernels, and q-superlinear convergence for a new method for integral equations when part of the Frechet derivative ...}, number={3}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Hwang, D. M. and Kelley, C. T.}, year={1992}, month={Aug}, pages={505–532} }
 @inbook{kelley_1992, place={Heidelberg}, title={Fast Algorithms for Compact Fixed Point Problems}, booktitle={Operations Research '91}, publisher={Physica-Verlag}, author={Kelley, C T}, editor={Gritzmann, P and Hettich, R and Horst, R and Sachs, EEditors}, year={1992}, pages={106–109} }
 @article{heinkenschloss_kelley_tran_1992, title={Fast Algorithms for Nonsmooth Compact Fixed-Point Problems}, volume={29}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0729099}, DOI={10.1137/0729099}, abstractNote={A fast algorithm for compact fixed-point problems with nonsmooth nonlinearities is designed and analyzed. The algorithm is a combination of an extension of the Atkinson–Brakhage–Nystrom algorithm for smooth problems and a generalization of work by Yamamoto and Chen for nonsmooth problems. A critical structural hypothesis in the general theory is explicitly verified in the context of problems that can be expressed as integral equations with certain types of nonsmoothness. The work is motivated by problems in combat modeling. In particular, we consider the solution of an optimality system that arises in control of competitive systems.}, number={6}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Heinkenschloss, M. and Kelley, C. T. and Tran, H. T.}, year={1992}, month={Dec}, pages={1769–1792} }
 @article{kelley_sachs_1992, title={Mesh Independence of the Gradient Projection Method for Optimal Control Problems}, volume={30}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/0330029}, DOI={10.1137/0330029}, abstractNote={The gradient projection method and its application to optimal control have been analyzed with regard to the rate of convergence quite extensively. Here another aspect of this method is considered. In finite dimension the set of active indices is identified after finitely many iterations under mild nondegeneracy assumptions. However, it is clear that this property is restricted to the finite-dimensional case. In this paper, for example, a sequence of discretized optimal control problems is considered, and it is observed that the number of steps to identify all active indices increases with the refinement of the discretization. A. result analogous to the finite-dimensional result is valid in this situation if identification of active indices is understood in the correct light. This paper shows that if a different termination criterion is imposed, then the number of necessary steps for termination is indeed mesh-independent. Numerical observations illustrating this result are reported for various examples fr...}, number={2}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1992}, month={Mar}, pages={477–493} }
 @article{stoneking_bilbro_gilmore_trew_kelley_1992, title={Yield optimization using a GaAs process simulator coupled to a physical device model}, volume={40}, ISSN={0018-9480}, url={http://dx.doi.org/10.1109/22.146318}, DOI={10.1109/22.146318}, abstractNote={A physics-based large-signal GaAs MESFET model and circuit simulator has been developed to predict and optimize the yield of GaAs MESFET designs before fabrication. Device acceptance criteria include both small- and large-signal RF operating characteristics such as small-signal gain, maximum power added efficiency, and output power at 1-dB gain compression. Channel doping details are described on the basis of processing specifications for parameters such as material deposition, ion implantation, and implant annealing. Monte Carlo techniques are used to estimate yield when disturbances in the physical parameters are modeled as multivariate Gaussian distributions. The yield estimator is integrated with an optimizer so that a design can be centered for maximum yield in the presence of process disturbances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>}, number={7}, journal={IEEE Transactions on Microwave Theory and Techniques}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Stoneking, D.E. and Bilbro, G.L. and Gilmore, P.A. and Trew, R.J. and Kelley, C.T.}, year={1992}, month={Jul}, pages={1353–1363} }
 @article{kelley_sachs_1991, title={A New Proof of Superlinear Convergence for Broyden’s Method in Hilbert Space}, volume={1}, ISSN={1052-6234 1095-7189}, url={http://dx.doi.org/10.1137/0801011}, DOI={10.1137/0801011}, abstractNote={Broyden’s method is an extension of the secant method for an equation in one real variable to an arbitrary Hilbert space setting. It is a result of Griewank that the Broyden iterates converge locally superlinearly to a root if, in addition to the assumptions needed in finite dimension, the initial approximation for the Frechet derivative differs from the Frechet derivative at the root only by a compact operator. In this paper a new and much simpler proof of this theorem is given based on the concept of collective compactness.}, number={1}, journal={SIAM Journal on Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1991}, month={Feb}, pages={146–150} }
 @inproceedings{woolard_trew_littlejohn_kelley_1991, title={A Study of Electron Transit-Time in Ballistic Diodes Using a Multi-Valley Hydrodynamic Transport Model}, booktitle={Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits}, author={Woolard, D L and Trew, R J and Littlejohn, M A and Kelley, C T}, year={1991}, pages={131–140} }
 @inproceedings{winslow_trew_gilmore_kelley_1991, title={Doping Profiles For Optimum Class {B} Performance of {GaAs} MESFET Amplifiers}, booktitle={Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits}, author={Winslow, T A and Trew, R J and Gilmore, P and Kelley, C T}, year={1991}, pages={188–197} }
 @article{kelley_sachs_1991, title={Fast Algorithms for Compact Fixed Point Problems with Inexact Function Evaluations}, volume={12}, ISSN={0196-5204 2168-3417}, url={http://dx.doi.org/10.1137/0912038}, DOI={10.1137/0912038}, abstractNote={A class of fast algorithms for computation of fixed points of completely continuous maps on Banach spaces is described and analyzed. These algorithms are motivated by parabolic boundary control problems where the time integration is done by a high order backward difference formula, a variable stepsize, variable order method, or a combination of such methods. In these cases, the nonlinear maps do not have the smoothness or collective compactness properties required by known fast algorithms. This paper shows how a multilevel technique of Atkinson can be modified to attack such problems, discusses how quasi-Newton methods can improve performance, and finally, shows how this approach can be applied to parabolic boundary control problems.}, number={4}, journal={SIAM Journal on Scientific and Statistical Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1991}, month={Jul}, pages={725–742} }
 @article{kelley_sachs_1991, title={Mesh Independence of Newton-like Methods for Infinite Dimensional Problems}, volume={3}, ISSN={0897-3962}, url={http://dx.doi.org/10.1216/jiea/1181075649}, DOI={10.1216/jiea/1181075649}, abstractNote={Globally convergent modifications of Newton’s method, such as the Armijo rule, can be applied to infinite dimensional problems and their discretizations. We show that if the construction of the discretizations is done properly, then the convergence behavior of the iteration is the same for the discrete problems as it is for the infinite-dimensional problem. Basic to these results is the use of the concept of discrete convergence as a tool to measure the performance of algorithms and a new setting of Banach spaces with incomplete metrics, for example, norms generated by continuous inner products. The motivating problems are integral equations with continuous kernels. This result extends to the globally convergent case results of Allgower, Bohmer, Potra, and Rheinboldt, and the authors. In addition, we strengthen the previous results on mesh independence of quasi-Newton methods. Numerical results are reported that illustrate the results.}, number={4}, journal={Journal of Integral Equations and Applications}, publisher={Rocky Mountain Mathematics Consortium}, author={Kelley, C.T. and Sachs, E.W.}, year={1991}, month={Dec}, pages={549–573} }
 @article{kahaner_kelley_1991, title={Observations on Computational Mathematics in {J}apan}, volume={16}, journal={ONRFE Scientific Information Bulletin}, author={Kahaner, David K and Kelley, C T}, year={1991}, pages={49–54} }
 @article{kelley_sachs_watson_1991, title={Pointwise quasi-Newton method for unconstrained optimal control problems, II}, volume={71}, ISSN={0022-3239 1573-2878}, url={http://dx.doi.org/10.1007/bf00941402}, DOI={10.1007/bf00941402}, number={3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Kelley, C. T. and Sachs, E. W. and Watson, B.}, year={1991}, month={Dec}, pages={535–547} }
 @article{kelley_wright_1991, title={Sequential quadratic programming for certain parameter identification problems}, volume={51}, ISSN={0025-5610 1436-4646}, url={http://dx.doi.org/10.1007/bf01586941}, DOI={10.1007/bf01586941}, number={1-3}, journal={Mathematical Programming}, publisher={Springer Science and Business Media LLC}, author={Kelley, C. T. and Wright, S. J.}, year={1991}, month={Jul}, pages={281–305} }
 @inproceedings{winslow_trew_gilmore_kelley_1991, title={Simulated Performance Optimization of {GaAs} {MESFET} Amplifiers}, booktitle={Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits}, author={Winslow, T A and Trew, R J and Gilmore, P and Kelley, C T}, year={1991}, pages={393–402} }
 @inproceedings{stoneking_bilbro_trew_gilmore_kelley_1991, title={Yield Optimization Using a {GaAs} Process Simulator Coupled to a Physical Device Model}, booktitle={Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits}, author={Stoneking, D E and Bilbro, G L and Trew, R J and Gilmore, P and Kelley, C T}, year={1991}, pages={374–383} }
 @article{kelley_sachs_1990, title={Approximate quasi-Newton methods}, volume={48}, ISSN={0025-5610 1436-4646}, url={http://dx.doi.org/10.1007/bf01582251}, DOI={10.1007/bf01582251}, number={1-3}, journal={Mathematical Programming}, publisher={Springer Science and Business Media LLC}, author={Kelley, C. T. and Sachs, E. W.}, year={1990}, month={Mar}, pages={41–70} }
 @inbook{kelley_1990, place={Providence, RI}, title={Operator prolongation methods for nonlinear equations}, volume={26}, booktitle={Computational Solution of Nonlinear Systems of Equations}, publisher={American Mathematical Society}, author={Kelley, C T}, editor={Allgower, Eugene L and Georg, KurtEditors}, year={1990}, pages={359–388} }
 @article{kelley_rulla_1990, title={Solution of the time discretized Stefan problem by Newton's method}, volume={14}, ISSN={0362-546X}, url={http://dx.doi.org/10.1016/0362-546x(90)90025-c}, DOI={10.1016/0362-546x(90)90025-c}, number={10}, journal={Nonlinear Analysis: Theory, Methods & Applications}, publisher={Elsevier BV}, author={Kelley, C.T. and Rulla, Jim}, year={1990}, month={Jan}, pages={851–872} }
 @article{kelley_1989, title={A fast two-grid method for matrix H-equations}, volume={18}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411458908204320}, DOI={10.1080/00411458908204320}, abstractNote={Abstract We present a new two-grid method for solution of matrix H-equations that is a generalization of a method due to Atkinson. Our new algorithm provides mesh independent q-linear convergence and can be accelerated to a superlinearly convergent algorithm by means of a quasi-Newton method. In addition the algorithm requires far less storage than Newton's method. Such considerations are especially important for the large problems generated by discretizations of H-equations for matrix-valued functions. Such equations arise in radiative transfer, polarization, and multi-group neutron transport. As a numerical example we show measured convergence rates and discuss timings for a matrix H-equation arising in radiative transfer.}, number={2}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1989}, month={Apr}, pages={185–203} }
 @article{kelley_sachs_1989, title={A pointwise quasi-Newton method for unconstrained optimal control problems}, volume={55}, ISSN={0029-599X 0945-3245}, url={http://dx.doi.org/10.1007/bf01406512}, DOI={10.1007/bf01406512}, number={2}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kelley, C. T. and Sachs, E. W.}, year={1989}, month={Mar}, pages={159–176} }
 @article{woolard_pelourad_trew_littlejohn_kelley_1989, title={Hydrodynamic Hot Electron Transport Simulation based on the {M}onte {C}arlo Method}, volume={32}, journal={Solid-State Electronics}, author={Woolard, D L and Pelourad, J-L. and Trew, R J and Littlejohn, M A and Kelley, C T}, year={1989}, pages={1347–1351} }
 @article{woolard_pelouard_trew_littlejohn_kelley_1989, title={Hydrodynamic hot-electron transport simulation based on the Monte Carlo method}, volume={32}, ISSN={0038-1101}, url={http://dx.doi.org/10.1016/0038-1101(89)90238-4}, DOI={10.1016/0038-1101(89)90238-4}, abstractNote={A hydrodynamic hot electron model is used to study electron transport through a submicron N+  N  N+ GaAs structure. This study is used to investigate improvements which the unique features of this model offer to analysis of devices operating under nonstationary transport conditions. The model is based upon semiclassical “hydrodynamic” conservation equations for the average carrier density, momentum and energy. The general model includes particle relaxation times, momentum relaxation times, energy relaxation times, electron temperature tensors and heat flow vectors as a function of average carrier energy for the Γ, X and L valleys of GaAs. For this study, we utilized a simplified single electron gas version of our model to clearly reveal the impact of the nonstationary terms in the model. Results from both a drift-diffusion model approach and a Monte Carlo analysis are used to show the relative accuracy and facility this new model offers for investigating practical submicron device structures operating under realistic conditions.}, number={12}, journal={Solid-State Electronics}, publisher={Elsevier BV}, author={Woolard, D.L. and Pelouard, J-L. and Trew, R.J. and Littlejohn, M.A. and Kelley, C.T.}, year={1989}, month={Dec}, pages={1347–1351} }
 @inproceedings{hwang_kelley_1989, title={Sequential quadratic programming for parameter identification problems}, booktitle={Proceedings of the {IFAC} Symposium on Control of Distributed Parameter Systems}, author={Hwang, D M and Kelley, C T}, editor={Jai, A El and Amouroux, MEditors}, year={1989}, pages={105–109} }
 @article{kelley_northrup_1988, title={A Pointwise Quasi-Newton Method for Integral Equations}, volume={25}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0725065}, DOI={10.1137/0725065}, abstractNote={For fully nonlinear integral equations, conventional quasi-Newton methods, such as Broyden’s method, may not possess good convergence properties. In this paper we present a new method that gives superlinear convergence for such integral equations and provides for savings over Newton’s method in the cost of solution of the linear equation for the quasi-Newton step.}, number={5}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Northrup, J. I.}, year={1988}, month={Oct}, pages={1138–1155} }
 @article{clapp_eberhardt_kelley_1988, title={Development and Validation of a Method for Approximating Road Surface Texture‐Induced Contact Pressure in Tire‐Pavement Interaction}, volume={16}, ISSN={0090-8657}, url={http://dx.doi.org/10.2346/1.2148796}, DOI={10.2346/1.2148796}, abstractNote={Abstract}, number={1}, journal={Tire Science and Technology}, publisher={The Tire Society}, author={Clapp, T. G. and Eberhardt, A. C. and Kelley, C. T.}, year={1988}, month={Jan}, pages={2–17} }
 @article{clapp_kelley_eberhardt_1988, title={Development and validation of a method for approximation of road surface texture-induced contact pressure in tire/pavement interaction}, volume={16}, journal={Tire Science and Technology}, author={Clapp, T G and Kelley, C T and Eberhardt, A C}, year={1988}, pages={2–17} }
 @article{kelley_1988, title={The FN method in slab geometries with a polynomial basis}, volume={17}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411458808230869}, DOI={10.1080/00411458808230869}, abstractNote={Abstract We show how the FN method for one speed neutron transport in finite slabs can be viewed as a transform of a problem on an infinite interval. This allows us to use an analysis based on the singular value decomposition to prove convergence of the method. Unlike previous work, the problem on the infinite interval is not the equation for the flux.}, number={2-3}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1988}, month={Jan}, pages={295–303} }
 @article{kelley_1988, title={The {F_N} method in finite slabs with a polynomial basis}, volume={17}, journal={Trans. Th. Stat. Phys.}, author={Kelley, C T}, year={1988}, pages={295–303} }
 @article{kelley_sachs_1987, title={A Quasi-Newton Method for Elliptic Boundary Value Problems}, volume={24}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0724037}, DOI={10.1137/0724037}, abstractNote={For some boundary value problems for equations of the form $\nabla ^2 u + f(x,u,\nabla u) = 0$ with linear boundary conditions we give a convergence analysis for a quasi-Newton method that converges superlinearly in the $C^1 $ norm. This scheme for infinite-dimensional problems becomes a method for the finite-dimensional problems that are produced by discretizing the differential equation. This method is a generalization of a method proposed by Hart and Soul for discretizations of two point boundary value problems.}, number={3}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1987}, month={Jun}, pages={516–531} }
 @inproceedings{kelley_1987, place={Philadelphia}, title={Algorithm Design on Microcomputers: Iterative Methods for Problems with Singular {J}acobian}, booktitle={New Computing Environments: Microcomputers in Large-Scale Computing}, publisher={SIAM}, author={Kelley, C T}, editor={Wouk, ArthurEditor}, year={1987}, pages={13–25} }
 @inproceedings{kelley_sachs_1987, place={Basel}, title={Applications of Quasi-{N}ewton Methods to Pseudoparabolic Control Problems}, booktitle={Optimal Control of Partial Differential Equations II - Theory and Applications, May, 1986}, publisher={Birkhäuser}, author={Kelley, C T and Sachs, E W}, year={1987} }
 @inproceedings{kelley_northrup_1987, place={New York}, title={Pointwise quasi-{N}ewton methods and some applications}, booktitle={Distributed Parameter Systems}, publisher={Springer-Verlag}, author={Kelley, C T and Northrup, J I}, editor={Kappel, F and Kunisch, K and Schappacher, WEditors}, year={1987}, pages={167–180} }
 @article{kelley_sachs_1987, title={Quasi-Newton Methods and Unconstrained Optimal Control Problems}, volume={25}, ISSN={0363-0129 1095-7138}, url={http://dx.doi.org/10.1137/0325083}, DOI={10.1137/0325083}, abstractNote={Quasi Newton methods play an important role in the numerical solution of problems in unconstrained optimization. Optimal control problems in their discretized form can be viewed as optimization problems and therefore be solved by quasi Newton methods. Since the discretized problems do not solve the original infinite-dimensional control problem but rather approximate it up to a certain accuracy, various approximations of the control problem need to be considered. It is known that an increase in the dimension of optimization problems can have a negative effect on the convergence rate of the quasi Newton method which is used to solve the problem. We want to investigate this behavior and to explain how this drawback can be avoided for a class of optimal control problems. We show how to use the infinite dimensional original problem to predict the speed of convergence of the BFGS-method [1, 7, 10, 22] for the finite-dimensional approximations. In several papers [6, 14, 24, 27] the DFP-method [4, 8] and its application to optimal control problems were considered but rates of convergence were given at best for quadratic problems. In [25, 26] a linear rate of convergence was proved in Hilbert spaces and applied to optimal control. All the applications to optimal control problems were carried out for finite dimensional approximations. This fact is important, because in [23] it was shown, that contrary to the finite dimensional case [2], the BFGS-method can converge very slowly when applied to an infinite dimensional problem. Hence it is desirable to know whether this convergence behavior can occur also for fine discretizations of control problems. Sufficient ([19]) and characteristic ([12]) conditions for the superlinear rate were given in other analyses. Like in the linear case for Broyden's method [28] and the conjugate gradient method [3], [9] an additional assumption on the initial approximation of the Hessian, i.e. it approximates the true Hessian up to a compact operator, is needed to guarantee superlinear convergence, see [11]. In [9] a connection to quadratic control problems is shown. Here we want to consider nonlinear control problems and their discretization.}, number={6}, journal={SIAM Journal on Control and Optimization}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Sachs, E. W.}, year={1987}, month={Nov}, pages={1503–1516} }
 @article{kelley_1986, title={A Shamanskii-like acceleration scheme for nonlinear equations at singular roots}, volume={47}, number={176}, journal={Mathematics of Computation}, publisher={American Mathematical Society}, author={Kelley, C.T.}, year={1986}, pages={609–623} }
 @article{kelley_1986, title={Convergence of the FN - method for multi-group transport}, volume={15}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411458608212717}, DOI={10.1080/00411458608212717}, abstractNote={Abstract This note extends previous results of Mullikin and the author on convergence of the FN method to isotropic multi-group problems in half-space geometries.}, number={6-7}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Kelley, C. T.}, year={1986}, month={Oct}, pages={821–828} }
 @article{kelley_1986, title={Convergence of the {F_N} method for multi-group transport}, volume={15}, journal={Trans. Th. Stat. Phys.}, author={Kelley, C T}, year={1986}, pages={821–828} }
 @article{hollis_kelley_1986, title={Vector algorithms for H-equations arising in radiative transfer through inhomogeneous media}, volume={15}, ISSN={0041-1450 1532-2424}, url={http://dx.doi.org/10.1080/00411458608210443}, DOI={10.1080/00411458608210443}, abstractNote={Abstract The exit distribution problem for one speed isotropic radiative transfer in an inhomogeneous slab can be solved in terms of an analog of the Chandrasekhar H-Function. This function is the solution to a nonlinear integral equation in two variables for one group problems and in more variables for multi-group problems. In this paper we give algorithms for vector computers, in particular the CDC Cyber 205, that make it practical to solve such equations.}, number={1-2}, journal={Transport Theory and Statistical Physics}, publisher={Informa UK Limited}, author={Hollis, S. L. and Kelley, C. T.}, year={1986}, month={Feb}, pages={33–48} }
 @inproceedings{clapp_kelley_eberhardt_1985, place={Baltimore}, title={Analytical determination of normal contact stresses for arbitrary geometries with application to the tire/pavement interaction mechanism}, booktitle={Measuring Road Roughness and its Effects on User Cost and Comfort}, author={Clapp, T G and Kelley, C T and Eberhardt, A C}, editor={Gillespie, T D and Sayers, MEditors}, year={1985}, pages={162–178} }
 @article{kelley_sachs_1985, title={Broyden's method for approximate solution of nonlinear integral equations}, volume={9}, number={1}, journal={Journal of Integral Equations}, author={Kelley, C.T. and Sachs, E.W.}, year={1985}, pages={25–44} }
 @article{decker_kelley_1985, title={Broyden’s Method for a Class of Problems Having Singular Jacobian at the Root}, volume={22}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0722034}, DOI={10.1137/0722034}, abstractNote={For a class of nonlinear equations $F(x) = 0$, in $\mathbb{R}^n $, with the Jacobian $F'$ being singular at a root, $x^ * $, Broyden’s method is shown to yield a sequence that converges linearly to $x^ * $ if the initial guess is chosen in a special region. The asymptotic linear rate is ${{(\sqrt 5 - 1)} / 2}$.}, number={3}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Kelley, C. T.}, year={1985}, month={Jun}, pages={566–574} }
 @article{decker_kelley_1985, title={Expanded Convergence Domains for Newton’s Method at Nearly Singular Roots}, volume={6}, ISSN={0196-5204 2168-3417}, url={http://dx.doi.org/10.1137/0906064}, DOI={10.1137/0906064}, abstractNote={We consider Newton's method for a class of nonlinear equations for which the derivative is nearly singular at the root. We show that there is a larger than expected domain of attraction for the Newton iterates but that convergence appears to be only linear in most of this domain. We give a modification of Newton's method that improves this slow convergence.}, number={4}, journal={SIAM Journal on Scientific and Statistical Computing}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Kelley, C. T.}, year={1985}, month={Oct}, pages={951–966} }
 @article{kelley_mullikin_1985, title={Why does the -method work?}, volume={14}, journal={Transport Theory and Statistical Physics}, author={Kelley, C.T. and Mullikin, T.W.}, year={1985}, pages={513–526} }
 @article{kelley_mullikin_1985, title={Why does the {F_N}-Method work?}, volume={14}, journal={Trans. Th. Stat. Phys.}, author={Kelley, C T and Mullikin, T W}, year={1985}, pages={513–526} }
 @article{kelley_1984, title={Applications of the method to transport calculations, Trans}, volume={13}, journal={Transport Theory and Statistical Physics}, author={Kelley, C.T.}, year={1984}, pages={85–96} }
 @article{kelley_1984, title={Applications of the {F_N} method to transport calculations}, volume={13}, journal={Trans. Th. Stat. Phys.}, author={Kelley, C T}, year={1984}, pages={85–96} }
 @article{kelley_suresh_1983, title={A New Acceleration Method for Newton’s Method at Singular Points}, volume={20}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0720070}, DOI={10.1137/0720070}, abstractNote={When Newton’s method is used to find a root of a map from a Banach space into itself and the derivative is singular at that root, convergence of the Newton sequence is in general linear. In this paper we give a modification of Newton’s method that, under certain conditions, converges superlinearly. Our method is applicable under more general conditions than other techniques. In particular it may be used for certain quadratic problems and problems in which the dimension of the null space of the derivative is larger than one.}, number={5}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T. and Suresh, R.}, year={1983}, month={Oct}, pages={1001–1009} }
 @article{decker_keller_kelley_1983, title={Convergence Rates for Newton’s Method at Singular Points}, volume={20}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0720020}, DOI={10.1137/0720020}, abstractNote={If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence.}, number={2}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Keller, H. B. and Kelley, C. T.}, year={1983}, month={Apr}, pages={296–314} }
 @article{kelley_1983, title={Convergence of the method for exponential atmospheres}, volume={12}, journal={Transport Theory and Statistical Physics}, author={Kelley, C.T.}, year={1983}, pages={183–194} }
 @article{kelley_1983, title={Convergence of the {F_N} method for exponential atmospheres}, volume={12}, journal={Trans. Th. Stat. Phys.}, author={Kelley, C T}, year={1983}, pages={183–194} }
 @article{kelley_1983, title={Energy dependent radiative transfer in inhomogeneous slabs}, volume={5}, journal={Journal of Integral Equations}, author={Kelley, C.T.}, year={1983}, pages={33–48} }
 @article{decker_kelley_1983, title={Sublinear convergence of the Chord method at singular points}, volume={42}, ISSN={0092-599X 0945-3245}, url={http://dx.doi.org/10.1007/bf01395307}, DOI={10.1007/bf01395307}, number={2}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Decker, D. W. and Kelley, C. T.}, year={1983}, month={Jun}, pages={147–154} }
 @article{kelley_1982, title={Approximate methods for the solution of the Chandrasekhar H‐equation}, volume={23}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.525251}, DOI={10.1063/1.525251}, abstractNote={We consider two methods of approximate solution to matrix valued analogs of the Chandrasekhar H-equation. We give conditions under which they converge. The first method is a generalization of approximation of the integral by a quadrature. The second is Newton’s method.}, number={11}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T.}, year={1982}, month={Nov}, pages={2097–2100} }
 @article{kelley_1982, title={Approximation of solutions to some quadratic integral equations in transport theory}, volume={4}, journal={Journal of Integral Equations}, author={Kelley, C.T.}, year={1982}, pages={221–237} }
 @article{kelley_mullikin_1982, title={Collocation methods for some singular integral equations in linear transport theory}, volume={4}, journal={Journal of Integral Equations}, author={Kelley, C.T. and Mullikin, T.W.}, year={1982}, pages={77–88} }
 @article{decker_kelley_1982, title={Convergence Acceleration for Newton’s Method at Singular Points}, volume={19}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0719012}, DOI={10.1137/0719012}, abstractNote={If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, linear convergence of the Newton sequence to the root is the best...}, number={1}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Kelley, C. T.}, year={1982}, month={Feb}, pages={219–229} }
 @article{kelley_1981, title={A note on the approximation of functions of several variables by sums of functions of one variable}, volume={33}, ISSN={0021-9045}, url={http://dx.doi.org/10.1016/0021-9045(81)90068-x}, DOI={10.1016/0021-9045(81)90068-x}, abstractNote={For a class of functions of several variables, which includes the continuous functions, we show that there exists a sum of functions of one variable that minimizes the distance from the given function to the space of such sums. For functions of two variables we show that such a minimizing sum may be constructed by an iterative scheme.}, number={3}, journal={Journal of Approximation Theory}, publisher={Elsevier BV}, author={Kelley, C.T.}, year={1981}, month={Nov}, pages={179–189} }
 @article{siewert_kelley_garcia_1981, title={An analytical expression for the H matrix relevant to Rayleigh scattering}, volume={84}, ISSN={0022-247X}, url={http://dx.doi.org/10.1016/0022-247x(81)90183-9}, DOI={10.1016/0022-247x(81)90183-9}, abstractNote={The matrix Riemann-Hilbert problem relevant to the scattering of polarized light is solved up to the resolution of two existence questions. The solution obtained is used to establish an explicit expression for the related H matrix, and evidence that the mentioned existence questions can be answered in the affirmative is provided by a numerical evaluation of the final result.}, number={2}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Siewert, C.E and Kelley, C.T and Garcia, R.D.M}, year={1981}, month={Dec}, pages={509–518} }
 @article{kelley_1981, title={Approximate methods for exit distribution problems in inhomogeneous slabs}, volume={8}, ISSN={0149-1970}, url={http://dx.doi.org/10.1016/0149-1970(81)90017-2}, DOI={10.1016/0149-1970(81)90017-2}, abstractNote={Abstract A generalization of the Chandrasekhar H-equation is solved by a class of approximate methods. The exit distribution problem for radiative transfer, either multigroup or one group, may be solved in terms of the solution to this equation.}, number={2-3}, journal={Progress in Nuclear Energy}, publisher={Elsevier BV}, author={Kelley, C.T.}, year={1981}, month={Jan}, pages={227–234} }
 @article{kelley_1981, title={Multi-group neutron transport in inhomogeneous slabs}, volume={3}, journal={Journal of Integral Equations}, author={Kelley, C.T.}, year={1981}, pages={261–275} }
 @article{kelley_1980, title={A comparison of iteration schemes for Chandrasekhar H‐equations in multigroup neutron transport}, volume={21}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.524430}, DOI={10.1063/1.524430}, abstractNote={An iteration scheme for the Chandrasekhar H-equations in multigroup neutron transport is shown to converge to the solution of physical interest. Moreover, the convergence is more rapid than that provided by direct iteration.}, number={2}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T.}, year={1980}, month={Feb}, pages={408–409} }
 @article{siewert_kelley_1980, title={An analytical solution to a matrix Riemann-Hilbert problem}, volume={31}, ISSN={0044-2275 1420-9039}, url={http://dx.doi.org/10.1007/bf01590661}, DOI={10.1007/bf01590661}, number={3}, journal={Zeitschrift für angewandte Mathematik und Physik ZAMP}, publisher={Springer Science and Business Media LLC}, author={Siewert, C. E. and Kelley, C. T.}, year={1980}, month={May}, pages={344–351} }
 @article{decker_kelley_1980, title={Newton's method at singular points {II}}, volume={17}, journal={SIAM J. Numer. Anal.}, author={Decker, D W and Kelley, C T}, year={1980}, pages={465–471} }
 @article{decker_kelley_1980, title={Newton's method at singular points {I}}, volume={17}, journal={SIAM J. Numer. Anal.}, author={Decker, D W and Kelley, C T}, year={1980}, pages={66–70} }
 @article{decker_kelley_1980, title={Newton’s Method at Singular Points. I}, volume={17}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0717009}, DOI={10.1137/0717009}, abstractNote={A theorem due to Reddien giving sufficient conditions for convergence of Newton iterates for singular problems is extended.}, number={1}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Kelley, C. T.}, year={1980}, month={Feb}, pages={66–70} }
 @article{decker_kelley_1980, title={Newton’s Method at Singular Points. II}, volume={17}, ISSN={0036-1429 1095-7170}, url={http://dx.doi.org/10.1137/0717039}, DOI={10.1137/0717039}, abstractNote={A result giving sufficient conditions for convergence of Newton iterates is given for a class of singular problems. The singularities considered are of second order. Convergence of asymptotic linear ratio $\frac{2}{3}$ is obtained.}, number={3}, journal={SIAM Journal on Numerical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Decker, D. W. and Kelley, C. T.}, year={1980}, month={Jun}, pages={465–471} }
 @article{kelley_1980, title={Solution of the Chandrasekhar H‐equation by Newton’s Method}, volume={21}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.524647}, DOI={10.1063/1.524647}, abstractNote={For any value of the parameter c, c≠1, for which a solution to the Chandrasekhar H-equation exists, Newton’s method may be used to compute the solution by iteration.}, number={7}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T.}, year={1980}, month={Jul}, pages={1625–1628} }
 @article{kelley_1980, title={The Chandrasekhar H-equation for radiative transfer through inhomogeneous media}, volume={2}, journal={Journal of Integral Equations}, author={Kelley, C.T.}, year={1980}, pages={155–170} }
 @article{berger_kelley_1979, title={A variational equivalent to diagonal scaling}, volume={72}, ISSN={0022-247X}, url={http://dx.doi.org/10.1016/0022-247x(79)90290-7}, DOI={10.1016/0022-247x(79)90290-7}, abstractNote={This paper is concerned with the problem of diagonally scaling a given nonnegative matrix a to one with prescribed row and column sums. The approach is to represent one of the two scaling matrices as the solution of a variational problem. This leads in a natural way to necessary and sufficient conditions on the zero pattern of a so that such a scaling exists. In addition the convergence of the successive prescribed row and column sum normalizations is established. Certain invariants under diagonal scaling are used to actually compute the desired scaled matrix, and examples are provided. Finally, at the end of the paper, a discussion of infinite systems is presented.}, number={1}, journal={Journal of Mathematical Analysis and Applications}, publisher={Elsevier BV}, author={Berger, Marc A and Kelley, C.T}, year={1979}, month={Nov}, pages={291–304} }
 @article{kelley_1979, title={Operator-valued Chandrasekhar H-functions}, volume={70}, journal={Journal of Mathematical Analysis and Applications}, author={Kelley, C.T.}, year={1979}, pages={579–588} }
 @article{kelley_1979, title={Solution of H-Equations by Iteration}, volume={10}, ISSN={0036-1410 1095-7154}, url={http://dx.doi.org/10.1137/0510080}, DOI={10.1137/0510080}, abstractNote={A generalization of the Chandrasekhar H-equation is solved by iteration. Such equations are of interest in heat transfer.}, number={4}, journal={SIAM Journal on Mathematical Analysis}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Kelley, C. T.}, year={1979}, month={Jul}, pages={844–849} }
 @article{kelley_1978, title={Analytic continuation of an operator‐valued H‐function with applications to neutron transport theory}, volume={19}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.523672}, DOI={10.1063/1.523672}, abstractNote={An operator-valued generalization of Chandrasekhar’s H-function satisfies a nonlinear integral equation. A bifurcation analysis of this equation gives an analytic continuation of the H-function. This result is applied to a criticality problem in neutron transport theory, and asymptotic results are obtained.}, number={2}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T.}, year={1978}, month={Feb}, pages={494–499} }
 @article{kelley_mullikin_1978, title={Solution by iteration of H‐equations in multigroup neutron transport}, volume={19}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.523673}, DOI={10.1063/1.523673}, abstractNote={The Chandrasekhar H-equations for matrix-valued functions are solved by an iterative method. Complex variables and positivity techniques are used to obtain convergence. This approach may be applied to subcritical neutron transport in a slab with isotropic scattering.}, number={2}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T. and Mullikin, T. W.}, year={1978}, month={Feb}, pages={500–501} }
 @article{kelley_1977, title={Convolution and H‐equations for operator‐valued functions with applications to neutron transport theory}, volume={18}, ISSN={0022-2488 1089-7658}, url={http://dx.doi.org/10.1063/1.523305}, DOI={10.1063/1.523305}, abstractNote={The Wiener–Hopf factorization of certain-valued functions is related to operator-valued generalizations of Chandrasekhar’s H-functions. These functions satisfy a nonlinear system and may be computed by an iterative scheme. A general transport equation is solved in terms of these functions. The equation for steady-state transport in one space dimension with isotropic scattering and continuous energy dependence is discussed as an application.}, number={4}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Kelley, C. T.}, year={1977}, month={Apr}, pages={764–769} }