TY - JOUR
TI - Numerical Study of Two Dimensional Electro-migration
AU - Gao, H
AU - Li, Zhilin
AU - Zhao, H
T2 - Journal of Computational Physics
DA - 1999///
PY - 1999///
VL - 152
SP - 281–304
ER -
TY - JOUR
TI - A numerical method for solving heat equations involving interfaces
AU - Li, Zhilin
AU - Shen, Yun-Qui
T2 - Electronic Journal of Differential Equations
DA - 1999///
PY - 1999///
VL - 3
SP - 100–108
ER -
TY - RPRT
TI - Industrial Mathematics Modeling Workshop for Graduate Students series
DA - 1999///
PY - 1999///
M3 - CRSC Technical Reports
ER -
TY - CONF
TI - Global artificial boundary conditions for computation of external flow problems with propulsive jets
AU - Tsynkov, Semyon
AU - Abarbanel, Saul
AU - Nordstrom, Jan
AU - Ryaben'kii, Victor
AU - Vatsa, Veer
T2 - 14th Computational Fluid Dynamics Conference
AB - We propose new global artificial boundary conditions (ABC''s) for computation of flows with propulsive jets. The algorithm is based on application of the difference potentials method (DPM). Previously, similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies. The proposed modification substantially extends the applicability range of the DPM-based algorithm. In the paper, we present the general formulation of the problem, describe our numerical methodology, and discuss the corresponding computational results. The particular configuration that we analyze is a slender three-dimensional body with boat-tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack. Similarly to the results obtained earlier for the flows around airfoils and wings, current results for the jet flow case corroborate the superiority of the DPM-based ABC''s over standard local methodologies from the standpoints of accuracy, overall numerical performance, and robustness.
C2 - 1999/11//
C3 - 14th Computational Fluid Dynamics Conference
DA - 1999/11//
DO - 10.2514/6.1999-3351
VL - 2
SP - 836-846
PB - American Institute of Aeronautics and Astronautics
UR - http://dx.doi.org/10.2514/6.1999-3351
DB - Crossref
N1 - AIAA Paper No. 99–3351
RN - AIAA Paper No. 99–3351
ER -
TY - RPRT
TI - Long-Time Numerical Integration of the Three-Dimensional Wave
Equation in the Vicinity of a Moving Source
AU - Ryaben’kii, V. S.
AU - Turchaninov, V. I.
AU - Tsynkov, S. V.
A3 - ICASE
DA - 1999///
PY - 1999///
M1 - 99–23, NASA/CR–1999–209350
PB - ICASE
SN - 99–23, NASA/CR–1999–209350
UR - https://ntrs.nasa.gov/search.jsp?R=19990062251
ER -
TY - JOUR
TI - The use of lacunae of the 3D-wave equation for computing a
solution at large time values
T2 - Mat. Model.
DA - 1999///
PY - 1999///
VL - 11
IS - 12
SP - 113-126
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1761052
N1 - [in Russian]
RN - [in Russian]
ER -
TY - RPRT
TI - IFFCO: Implicit Filtering for Constrained Optimization, Version 2
AU - Choi, T D
AU - Eslinger, O J
AU - Gilmore, P
AU - Patrick, A
AU - Kelley, C T
AU - Gablonsky, J M
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 1999/7//
PY - 1999/7//
M1 - CRSC-TR99-23
PB - North Carolina State University, Center for Research in Scientific Computation
SN - CRSC-TR99-23
ER -
TY - RPRT
TI - {Newton-Krylov-Schwarz} Methods for {R}ichards' Equation
AU - Jenkins, E W
AU - Berger, R C
AU - Hallberg, J P
AU - Howington, Stacy E
AU - Kelley, C T
AU - Schmidt, Joseph H
AU - Stagg, Alan
AU - Tocci, M D
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 1999/10//
PY - 1999/10//
M1 - CRSC-TR99-32
PB - North Carolina State University, Center for Research in Scientific Computation
SN - CRSC-TR99-32
ER -
TY - CONF
TI - A Model to Simulate the Interaction between Groundwater and Surface Water
AU - Howington, S E
AU - Berger, R C
AU - Hallberg, J P
AU - Peters, J F
AU - Stagg, A K
AU - Jenkins, E W
AU - Kelley, C T
T2 - North Carolina State University, Center for Research in Scientific Computation
C2 - 1999/8//
C3 - Proceedings of the High Performance Computing Users' Group Meeting
CY - Monterrey, CA
DA - 1999/8//
M1 - CRSC-TR99-27
ER -
TY - JOUR
TI - On Lacunae-Based Algorithm for Numerical Solution of 3D Wave Equation for Arbitrarily Large Time
AU - Ryaben’kii, V.S.
AU - Turchaninov, V.I.
AU - Tsynkov, S.V.
T2 - Mathematical Modeling
DA - 1999///
PY - 1999///
VL - 11
IS - 12
SP - 113–127
ER -
TY - JOUR
TI - External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics
AU - Tsynkov, Semyon V.
T2 - SIAM Journal on Scientific Computing
AB - We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow numerically, we discretize the governing equations (Navier--Stokes) on a finite-difference grid. Prior to the discretization, we obviously need to truncate the original unbounded domain by introducing an artificial computational boundary at a finite distance from the body; otherwise, the number of discrete variables will not be finite. This artificial boundary is typically the external boundary of the domain covered by the grid. The flow problem (both continuous and discretized) formulated on the finite computational domain is clearly subdefinite unless supplemented by some artificial boundary conditions (ABCs) at the external computational boundary. In this paper, we present an innovative approach to constructing highly accurate ABCs for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderón's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) of Ryaben'kii. The resulting ABCs appear spatially nonlocal but are particularly easy to implement along with the existing flow solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments and comparison with the standard local methods, the DPM-based ABCs allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of multigrid convergence.
DA - 1999/1//
PY - 1999/1//
DO - 10.1137/s1064827597318757
VL - 21
IS - 1
SP - 166-206
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/s1064827597318757
DB - Crossref
KW - external flows
KW - infinite-domain problems
KW - artificial boundary conditions
KW - far-field linearization
KW - boundary projections
KW - generalized potentials
KW - difference potentials method
KW - auxiliary problem
KW - separation of variables
ER -
TY - JOUR
TI - Crack jump conditions for elliptic problems
AU - Wiegmann, A
AU - Li, Z
AU - LeVeque, RJ
T2 - APPLIED MATHEMATICS LETTERS
AB - We derive jump conditions for a potential function and its derivatives across a crack. A crack is a “thin” region of very different conductivity, for example a fracture in otherwise homogeneous material. Such a sharp change of material properties introduces a discontinuity in the coefficient of the elliptic equation governing the potential. The crack cannot be neglected, because it substantially alters the behavior of the potential. Numerically, it is very difficult to resolve the potential near the crack. A strategy is to treat the crack as a lower dimensional interface (hypersurface). Jump conditions across the crack for the potential and its derivatives are necessary for the development of numerical schemes for this approach. Besides the jump conditions, we also give an analytic example of their validity.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00083-X
VL - 12
IS - 6
SP - 81-88
SN - 0893-9659
KW - jump conditions
KW - transmission problem
KW - elliptic crack problems
ER -
TY - JOUR
TI - Modeling of nonlinear hysteresis in elastomers under uniaxial tension
AU - Banks, HT
AU - Pinter, GA
AU - Potter, LK
AU - Gaitens, MJ
AU - Yanyo, LC
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - As a fundamental component of an overall program in modeling smart material damping devices, we consider inactive host material models for moderate to highly filled rubbers undergoing uniaxial tensile deformations. Beginning from a neo-Hookean strain energy function formulation for nonlinear extension, we develop general constitutive models for both quasi-static and dynamic deformations of a viscoelastic rod. The constitutive laws are nonlinear and contain hysteresis through a Boltzmann superposition integral term. The resulting integropartial differential equations models are shown to be equivalent to the usual Lagrangian dynamic distributed parameter models coupled with linear ordinary differential equations for internal variables (internal strains). Comprehensive well-posedness results (existence, uniqueness and continuous dependence) are summarized in a discussion of theoretical aspects of the systems. The models are validated with experiments designed and carried out explicitly for this study. In particular, quasi-static Instron experimental data are used in a least squares inverse problem formulation to estimate nonlinear elastic and nonlinear viscoelastic contributions to the general stress-strain constitutive laws proposed. It is shown that the models provide an excellent prediction of nested hysteresis loops manifested in the data. These models are then used as initial estimates in determining the nonlinear hysteretic constitutive laws for the dynamic experiments. It is shown that in cases of more highly filled rubbers, multiple internal variable models lead to best fits to the data.
DA - 1999/2//
PY - 1999/2//
DO - 10.1106/8M8M-F8DQ-GJ2V-PGK1
VL - 10
IS - 2
SP - 116-134
SN - 1045-389X
ER -
TY - JOUR
TI - Estimation of the effective permeability in magnetorheological fluids
AU - Simon, TM
AU - Ito, K
AU - Banks, HT
AU - Reitich, F
AU - Jolly, MR
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR fluids.
DA - 1999/11//
PY - 1999/11//
DO - 10.1106/6KW6-7V12-NRQ3-BW6V
VL - 10
IS - 11
SP - 872-879
SN - 1045-389X
ER -
TY - JOUR
TI - Remarks on well-posedness theorems for damped second-order systems
AU - Banks, HT
T2 - APPLIED MATHEMATICS LETTERS
AB - We consider an operator theoretic formulation for distributed damped second-order (in time) forced linear elastic systems. A brief summary of previous well-posedness results is presented along with new results which allow relaxed spatial regularity (which is important in smart material systems applications) on the forcing or input function. Extensions to nonlinear systems are also indicated. The results are presented in a variational format for easy development of finite element approximation methods.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00073-7
VL - 12
IS - 6
SP - 21-24
SN - 0893-9659
ER -
TY - JOUR
TI - Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials
AU - Banks, HT
AU - Zou, J
T2 - NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
AB - In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete finite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We also establish that the solution has higher regularity in time even though the input source may be a windowed signal of distributional type. This regularity is then utilized to show the strong convergence of the finite element solution.
DA - 1999///
PY - 1999///
DO - 10.1080/01630569908816914
VL - 20
IS - 7-8
SP - 609-627
SN - 0163-0563
ER -
TY - JOUR
TI - A trust region method for parabolic boundary control problems
AU - Kelley, CT
AU - Sachs, EW
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - 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.
DA - 1999///
PY - 1999///
DO - 10.1137/S1052623496308965
VL - 9
IS - 4
SP - 1064-1081
SN - 1052-6234
KW - trust region methods
KW - inexact Newton methods
KW - optimal control
ER -
TY - JOUR
TI - Simulations of particle dynamics in magnetorheological fluids
AU - Ly, HV
AU - Reitich, E
AU - Jolly, MR
AU - Banks, HT
AU - Ito, K
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - We present particle dynamics simulations for the response of magnetorheological (MR) fluids upon application of a magnetic field. The particles motion is considered to be governed by magnetic, hydrodynamic, and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater significance, on the other hand (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be effectively used to study a number of experimental observables such as effective magnetic permeabilities and response time-scales which are of crucial importance in the design of MR fluids.
DA - 1999/10/10/
PY - 1999/10/10/
DO - 10.1006/jcph.1999.6335
VL - 155
IS - 1
SP - 160-177
SN - 1090-2716
KW - particle dynamics
KW - fast multipole method
KW - MR fluids
KW - effective permeability
KW - response time scale
ER -
TY - JOUR
TI - Domain wall theory for ferroelectric hysteresis
AU - Smith, RC
AU - Hom, CL
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. First, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theories with domain interactions incorporated through mean field relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. Second, hysteresis is incorporated through the consideration of domain wall dynamics and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.
DA - 1999/3//
PY - 1999/3//
DO - 10.1106/LJBM-RW18-MXW1-QXD0
VL - 10
IS - 3
SP - 195-213
SN - 1530-8138
ER -
TY - JOUR
TI - Types of reductive monoids
AU - Li, Zhilin
AU - Putcha, M.
T2 - Journal of Algebra
AB - Let M be a reductive monoid with a reductive unit group G. Clearly there is a natural G × G action on M. The orbits are the J-classes (in the sense of semigroup theory) and form a finite lattice. The general problem of finding the lattice remains open. In this paper we study a new class of reductive monoids constructed by multilined closure. We obtain a general theorem to determine the lattices of these monoids. We find that the (J, σ)-irreducible monoids of Suzuki type and Ree type belong to this new class. Using the general theorem we then list all the lattices and type maps of the (J, σ)-irreducible monoids of Suzuki type and Ree type.
DA - 1999///
PY - 1999///
DO - 10.1006/jabr.1999.7946
VL - 221
IS - 1
SP - 102–116
ER -
TY - JOUR
TI - The immersed finite volume element methods for the elliptic interface problems
AU - Ewing, RE
AU - Li, ZL
AU - Lin, T
AU - Lin, YP
T2 - MATHEMATICS AND COMPUTERS IN SIMULATION
AB - An immersed finite element space is used to solve the elliptic interface problems by a finite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satisfied. Optimal error estimates in an energy norm are obtained. Numerical results are supplied to justify the theoretical work and to reveal some interesting features of the method.
DA - 1999/11//
PY - 1999/11//
DO - 10.1016/S0378-4754(99)00061-0
VL - 50
IS - 1-4
SP - 63-76
SN - 0378-4754
KW - finite volume
KW - convergence
KW - error estimate
KW - interface problems
ER -
TY - JOUR
TI - Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition
AU - Kelley, CT
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - 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.
DA - 1999/11/29/
PY - 1999/11/29/
DO - 10.1137/S1052623497315203
VL - 10
IS - 1
SP - 43-55
SN - 1095-7189
KW - Nelder-Mead algorithm
KW - sufficient decrease
KW - stagnation
ER -
TY - JOUR
TI - A priori bounds and structural stability for double-diffusive convection incorporating the Soret effect
AU - Straughan, B
AU - Hutter, K
T2 - PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
AB - An analysis is presented for the equations for convective motion in a fluid saturated porous medium under the Brinkman scheme. The temperature field is non-constant and a solute is also diffused throughout the porous body. This is thus a double diffusive convection problem, although we concentrate on studying the influence the Soret effect has on the solution9behaviour. An a priori result is established whereby we show the solution depends continuously in L 2 norm on changes in the Soret coefficient.
DA - 1999/3/8/
PY - 1999/3/8/
DO - 10.1098/rspa.1999.0334
VL - 455
IS - 1983
SP - 767-777
SN - 1471-2946
KW - structural stability
KW - Soret effect
KW - double-diffusive convection
KW - a priori estimates
KW - continuous dependence
ER -
TY - JOUR
TI - A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations in two space dimensions
AU - Banoczi, JM
AU - Kelley, CT
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - 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.
DA - 1999///
PY - 1999///
DO - 10.1137/S1064827597322756
VL - 20
IS - 4
SP - 1214-1228
SN - 1064-8275
KW - conductive-radiative heat transfer
KW - multilevel algorithm
KW - compact fixed point problems
ER -
TY - JOUR
TI - Pointwise convergence of approximation schemes for parameter estimation in parabolic equations
AU - Banks, HT
AU - Zia, LL
T2 - APPLIED MATHEMATICS LETTERS
AB - A finite element-based approximation scheme is presented for parameter estimation problems for parabolic PDEs on a two-dimensional domain. Pointwise convergence results relating the approximating subspaces to the full infinite-dimensional state space are discussed.
DA - 1999/10//
PY - 1999/10//
DO - 10.1016/S0893-9659(99)00097-X
VL - 12
IS - 7
SP - 27-30
SN - 0893-9659
KW - finite elements
KW - bicubic splines
KW - 2-D domain
KW - transport models
KW - parameter estimation
ER -
TY - JOUR
TI - Approximation results for parameter estimation in a class of abstract nonlinear hyperbolic systems
AU - Banks, HT
AU - Pinter, GA
T2 - APPLIED MATHEMATICS LETTERS
AB - In this paper, we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00091-9
VL - 12
IS - 6
SP - 129-133
SN - 0893-9659
KW - nonlinear hyperbolic systems
KW - parameter estimation
KW - approximation
ER -
TY - JOUR
TI - Optimal design of a high pressure organometallic chemical vapor deposition reactor
AU - Bachmann, KJ
AU - Banks, HT
AU - Hopfner, C
AU - Kepler, GM
AU - LeSure, S
AU - McCall, SD
AU - Scroggs, JS
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - A team composed of material scientists, physicists, and applied mathematicians have used computer simulations as a fundamental design tool in developing a new prototype High Pressure Organometallic Chemical Vapor Deposition (HPOMCVD) reactor for use in thin film crystal growth. Early design of the HPOMCVD reactor dramatically evolved long before any physical reactor was built. This effort offers a strong endorsement of such multidisciplinary, computationally based modeling teams in the design of new products in areas of emerging technologies where heretofore extensive and costly experimental design was the central paradigm.
DA - 1999/4//
PY - 1999/4//
DO - 10.1016/S0895-7177(99)00071-0
VL - 29
IS - 8
SP - 65-80
SN - 0895-7177
ER -
TY - JOUR
TI - Estimates for the Nash-Sofer preconditioner for the reduced Hessian for some elliptic variational inequalities
AU - Choi, TD
AU - Kelley, CT
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - 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.
DA - 1999/4/20/
PY - 1999/4/20/
DO - 10.1137/S1052623497323364
VL - 9
IS - 2
SP - 327-341
SN - 1052-6234
KW - preconditioners
KW - reduced Hessian
KW - elliptic variational inequalities
ER -
TY - JOUR
TI - A complete steady state model of solute and water transport in the kidney
AU - Kottler, NE
AU - Tran, HT
AU - Wessell, DE
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The purpose of this paper is to incorporate a detailed model, along with an optimized set of parameters for the proximal tubule, into J. L. Stephenson's current central core model of the nephron. In this model a set of equations for the proximal tubule are combined with Stephenson's equations for the remaining four tubules and interstitium, to form a complete nonlinear system of 34 ordinary differential and algebraic equations governing fluid and solute flow in the kidney. These equations are then discretized by the Crank-Nicholson scheme to form an algebraic system of nonlinear equations for the unknown concentrations, flows, hydrostatic pressure, and potentials. The resulting system is solved via factored secant update with a finite-difference approximation to the Jacobian. Finally, numerical simulations performed on the model showed that the modeled behavior approximates, in a general way, the physiological mechanisms of solvent and solute flow in the kidney.
DA - 1999/3//
PY - 1999/3//
DO - 10.1016/S0895-7177(99)00055-2
VL - 29
IS - 6
SP - 63-82
SN - 1872-9479
KW - transport model
KW - biomathematics
KW - differential algebraic system
KW - inserve problem
KW - numerical methods
ER -
TY - JOUR
TI - Data express - Gigabit junction with the next-generation Internet
AU - Collins, JC
AU - Dunn, J
AU - Emer, P
AU - Johnson, M
T2 - IEEE SPECTRUM
AB - Important as a very high-performance backbone is to the next generation of the Internet, it is no less important that the points at which people connect to the backbone-the so-called points of presence, or POPs-provide an equivalent level of performance. For almost three years, members of the academic, research, and business community in the North Carolina region known as the Research Triangle-the area lying amid the cities of Raleigh, Durham, and Chapel Hill-have been working to create a high-performance regional network. As partners in the North Carolina Network Initiative (NCNI), they have built a network that can serve as a POP handling the multigigabit traffic to be delivered by the next-generation Internet. Thence comes its name: a GigaPOP. Like a great railway junction, the GigaPOP is a central distribution point where huge amounts of digital freight are moved between various end points and the main line (such as the very high-performance Backbone Network Services, or VBNS). The NCNI is one of a handful of regional networking organizations around the country. The others include the California Research and Education Network 2 (Calren2), the Metropolitan REN (MREN) serving the Chicago area, the Houston Area Computational Science Consortium (HACSC), and the New York State Educational and Research Network (Nysernet). NCNI's work, which predates most initiatives for the Internet's second generation, serves as a model of how various regions can latch onto the coming information superhighway to good effect.
DA - 1999/2//
PY - 1999/2//
DO - 10.1109/6.744872
VL - 36
IS - 2
SP - 18-25
SN - 0018-9235
ER -
TY - JOUR
TI - Fast and accurate numerical approaches for Stefan problems and crystal growth
AU - Li, ZL
AU - Soni, B
T2 - NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
AB - New numerical approaches for moving boundary interface applications tailored for Stefan problems and crystal growth simulation are proposed in this article. The focus is on the issues of accuracy and speed-up. A modified Crank-Nicolson method that is second-order accurate and stable is developed. The alternating directional implicit (ADI) method is also developed to speed up the simulation for a certain class of problems. The ADI method is shown to be asymptotically stable and at least first-order accurate. Numerical results, however, show that the ADI method actually provides second-order accuracy if the velocity can be calculated accurately. The level set method is used to update the moving interface so that the topological changes can be handled easily. Numerical experiments are compared to exact solutions and results in the literature.
DA - 1999/6//
PY - 1999/6//
DO - 10.1080/104077999275848
VL - 35
IS - 4
SP - 461-484
SN - 1040-7790
ER -
TY - JOUR
TI - Representation of GaP formation by a reduced order surface kinetics model using p-polarized reflectance measurements
AU - Beeler, S
AU - Tran, HT
AU - Dietz, N
T2 - JOURNAL OF APPLIED PHYSICS
AB - This contribution presents results on the parameter estimation of rate constants and optical response factors in a reduced order surface kinetics (ROSK) model, which has been developed to describe the decomposition kinetics of the organometallic precursors involved and their incorporation into the film deposition. As a real-time characterization technique, we applied p-polarized reflectance spectroscopy (PRS) during low temperature growth of epitaxial GaP heterostructures on Si(001) substrates by pulsed chemical beam epitaxy. The high surface sensitivity of PRS allows us to follow alterations in the composition and thickness of the surface reaction layer as they are encountered during periodic precursor supply. Linkage of the PRS response to the ROSK model provides the base for the parameter estimation of the reduced order surface kinetics model, giving insights into the organometallic precursor decomposition and growth kinetics.
DA - 1999/7/1/
PY - 1999/7/1/
DO - 10.1063/1.370783
VL - 86
IS - 1
SP - 674-682
SN - 1089-7550
ER -
TY - JOUR
TI - A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid
AU - Li, ZL
AU - Zhao, HK
AU - Gao, HJ
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - A numerical method for studying migration of voids driven by surface diffusion and electric current in a metal conducting line is developed. The mathematical model involves moving boundaries governed by a fourth order nonlinear partial differential equation which contains a nonlocal term corresponding to the electrical field and a nonlinear term corresponding to the curvature. Numerical challenges include efficient computation of the electrical field with sufficient accuracy to afford fourth order differentiation along the void boundary and to capture singularities arising in topological changes. We use the modified immersed interface method with a fixed Cartesian grid to solve for the electrical field, and the fast local level set method to update the position of moving voids. Numerical examples are performed to demonstrate the physical mechanisms by which voids interact under electromigration.
DA - 1999/6/10/
PY - 1999/6/10/
DO - 10.1006/jcph.1999.6249
VL - 152
IS - 1
SP - 281-304
SN - 0021-9991
ER -
TY - JOUR
TI - Well-posedness for a class of abstract nonlinear parabolic systems with time delay
AU - Banks, HT
AU - Musante, CJ
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
DA - 1999/3//
PY - 1999/3//
DO - 10.1016/S0362-546X(98)00053-4
VL - 35
IS - 5
SP - 629-648
SN - 0362-546X
KW - nonlinear parabolic distributed parameter systems with delays
KW - existence
KW - uniqueness
KW - variational form
KW - toxicokinetic modeling
KW - liver transport models
ER -
TY - BOOK
TI - Iterative Methods for Optimization
AU - Kelley, C T
AB - 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.
CN - QA402.5 .K44 1999
DA - 1999///
PY - 1999///
DO - 10.1137/1.9781611970920
PB - SIAM
SN - 0898714338
ER -
TY - JOUR
TI - Convergence of the sinc overlapping domain decomposition method
AU - Morlet, AC
AU - Lybeck, NJ
AU - Bowers, KL
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - The sinc-collocation overlapping method is developed for two-point boundary-value problems for second-order ordinary differential equations. The discrete system is formulated and the bordering algorithm used for the solution of this system is described. It is then shown that the convergence rate is exponential even if the solution has boundary singularities. The details of the convergence proof are given for a sinc-collocation method for two-point boundary-value problems when the original domain is divided into two subdomains. The extension to multiple domains is then straightforward. The analytical results are illustrated with numerical examples that exhibit the exponential convergence rate.
DA - 1999/2//
PY - 1999/2//
DO - 10.1016/S0096-3003(97)10168-0
VL - 98
IS - 2-3
SP - 209-227
SN - 0096-3003
KW - domain decomposition
KW - sinc method
KW - sinc collocation
KW - overlapping
ER -
TY - JOUR
TI - Convergence analysis of the immersed interface method
AU - Huang, HX
AU - Li, ZL
T2 - IMA JOURNAL OF NUMERICAL ANALYSIS
AB - A rigorous error analysis is given for the immersed interface method (IIM) applied to elliptic problems with discontinuities and singularities. The finite difference scheme using IIM is shown to satisfy the conditions of a maximum principle for a certain class of problems. Comparison functions are constructed to obtain error bounds for some of the approximate solutions. The asymptotic error expansion provides further useful insights and details of the behaviour and convergence properties of IIM, which leads to a sharper estimate of the error bound. Second-order convergence of IIM is indicated by the analysis. Numerical examples are also given to support the analytical results.
DA - 1999/10//
PY - 1999/10//
DO - 10.1093/imanum/19.4.583
VL - 19
IS - 4
SP - 583-608
SN - 0272-4979
ER -