TY - JOUR
TI - Theoretical and numerical analysis on a thermo-elastic system with discontinuities
AU - Li, Zhilin
AU - Wang, Deshen
AU - Zou, Jun
T2 - Journal of Computational and Applied Mathematics
AB - A second-order accurate numerical scheme is proposed for a thermo-elastic system which models a bar made of two distinct materials. The physical parameters involved may be discontinuous across the joint of the two materials, where there might be also singular heat and/or force sources. The solution components, the temperature and the displacement, may change rapidly across the joint. By transforming the system into a different one, time-marching schemes can be used for the new system which is well posed. The immersed interface method is employed to deal with the discontinuities of the coefficients and the singular sources. The proposed numerical method can fit both explicit and implicit formulation. For the implicit version, a stable and fast prediction-correction scheme is also developed. Convergence analysis shows that our method is second-order accurate at all grid points in spite of the discontinuities across the interface. Numerical experiments are performed to support the theoretical analysis in this paper.
DA - 1998/5//
PY - 1998/5//
DO - 10.1016/s0377-0427(98)00044-2
VL - 92
IS - 1
SP - 37-58
J2 - Journal of Computational and Applied Mathematics
LA - en
OP -
SN - 0377-0427
UR - http://dx.doi.org/10.1016/s0377-0427(98)00044-2
DB - Crossref
KW - mixed type system
KW - discontinuous coefficients
KW - Dirac delta function
KW - finite difference
KW - semi-implicit prediction-correction scheme
KW - error analysis
ER -
TY - CONF
TI - New Analysis of the {N}elder-{M}ead Algorithm
AU - Kelley, C T
A2 - Scott, D W
C2 - 1998///
C3 - Proceedings of the 29th Symposium on the Interface
DA - 1998///
SP - 407
ER -
TY - JOUR
TI - Robust Solution of {R}ichards' Equation for Non-Uniform Porous Media
AU - Miller, C T
AU - Williams, G A
AU - Kelley, C T
AU - Tocci, M D
T2 - Water Resources Research
DA - 1998///
PY - 1998///
VL - 34
SP - 2599-2610
ER -
TY - CONF
TI - The Simplex Gradient and Noisy Optimization Problems
AU - Bortz, D M
AU - Kelley, C T
A2 - Borggaard, J T
A2 - Burns, J
A2 - Cliff, E
A2 - Schreck, S
C2 - 1998///
C3 - Computational Methods in Optimal Design and Control
DA - 1998///
VL - 24
SP - 77-90
PB - Birkh{ä}user, Boston
ER -
TY - CONF
TI - Efficient and robust numerical modeling of variably saturated flow in layered porous media
AU - Miller, C T
AU - Williams, G A
AU - Kelley, C T
A2 - Burganos, V N
A2 - Karatzas, G P
A2 - Payatakes, A C
A2 - Brebbia, C A
A2 - Gray, W G
A2 - Pinder, G F
C2 - 1998///
C3 - XII Conference on Computational Methods in Water Resources, Crete, Greece
DA - 1998///
VL - 1
SP - 151-158
ER -
TY - RPRT
TI - Optimization of Automotive Valve Train Components with Implicit Filtering
AU - Choi, T D
AU - Eslinger, O J
AU - Kelley, C T
AU - David, J W
AU - Etheridge, M
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 1998/12//
PY - 1998/12//
VL - 1
SP - 9-28
PB - North Carolina State University, Center for Research in Scientific Computation
ER -
TY - JOUR
TI - Hysteresis Modeling in Magnetostrictive Materials Via Preisach Operators
AU - Smith, R.C.
T2 - Journal of Mathematical Systems, Estimation and Control
DA - 1998///
PY - 1998///
VL - 8
IS - 2
ER -
TY - JOUR
TI - Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions
AU - Tocci, MD
AU - Kelley, CT
AU - Miller, CT
AU - Kees, CE
T2 - COMPUTATIONAL GEOSCIENCES
DA - 1998///
PY - 1998///
DO - 10.1023/A:1011562522244
VL - 2
IS - 4
SP - 291-309
SN - 1420-0597
KW - Richards' equation
KW - method of lines
KW - inexact Newton methods
ER -
TY - JOUR
TI - Simulation of a vertical reactor for high pressure organometallic chemical vapor deposition
AU - Kepler, GM
AU - Hopfner, C
AU - Scroggs, JS
AU - Bachmann, KJ
T2 - MATERIALS SCIENCE AND ENGINEERING B-SOLID STATE MATERIALS FOR ADVANCED TECHNOLOGY
AB - The suitability of a vertical cylindrical reactor with highly constrained radial flow from a central gas injection port past a set of heated substrate wafers that are embedded in the top channel wall has been evaluated in the context of organometallic chemical vapor deposition (OMCVD) at elevated pressure. Numerical simulations showed that, in addition to the limitation on the channel height necessary for preventing buoyancy driven recirculation, negotiating the ninety-degree bend at the inlet is problematic and also constrains the channel height below a critical value, at which the radial flow area after the inlet bend is equal to the cross-sectional area of the central gas injection port. Restricting the channel height poses the danger of heating of the channel wall opposite to the substrate wafers causing potential problems with deposition of decomposition products and competitive polycrystalline film growth at this location. These problems can be avoided by actively cooling the channel wall opposite to the substrate and by keeping the retention time of the source vapor molecules and fragments thereof in the wafer location below a critical value.
DA - 1998/12/4/
PY - 1998/12/4/
DO - 10.1016/s0921-5107(98)00256-6
VL - 57
IS - 1
SP - 9-17
SN - 0921-5107
KW - organometallic chemical vapor deposition
KW - above-atmosphere pressure
KW - numerical simulation
KW - vertical reactor
KW - compressible flow
ER -
TY - JOUR
TI - LQR control of thin shell dynamics: Formulation and numerical implementation
AU - Del Rosario, RCH
AU - Smith, RC
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion and basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples.
DA - 1998/4//
PY - 1998/4//
DO - 10.1177/1045389X9800900408
VL - 9
IS - 4
SP - 301-320
SN - 1045-389X
ER -
TY - JOUR
TI - On the radio-frequency inputs in dipolar heating of adhesives
AU - Banks, H. T.
AU - Durso, S. R.
AU - Goodhart, M. A.
AU - Joyner, M. L.
T2 - Journal of Microwave Power and Electromagnetic Energy
AB - The form of the radio-frequency (RF) or dielectric input expression in the heat equation which arises in the modeling of the curing of epoxy adhesives in bonding of composites was considered. Two standard derivations of a commonly used expression for the RF heating source term were reviewed. In this context difficulties involving the associated inherent polarization assumption and asymptotic behavior of dielectric parameters as a function of the frequency of the RF signal were discussed. These difficulties cast doubt on the validity of the standard RF expression. Two standard polarization models (Debye and Lorentz) then were used to demonstrate how one can systematically derive general RF heating expressions which do not suffer the inconsistencies that arise in the standard RF expression.
DA - 1998///
PY - 1998///
DO - 10.1080/08327823.1998.11688380
VL - 33
IS - 4
SP - 231-242
ER -
TY - JOUR
TI - Robust solution of Richards' equation for nonuniform porous media
AU - Miller, CT
AU - Williams, GA
AU - Kelley, CT
AU - Tocci, MD
T2 - WATER RESOURCES RESEARCH
AB - 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.
DA - 1998/10//
PY - 1998/10//
DO - 10.1029/98WR01673
VL - 34
IS - 10
SP - 2599-2610
SN - 0043-1397
ER -
TY - JOUR
TI - A fast iterative algorithm for elliptic interface problems
AU - Li, ZL
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - A fast, second-order accurate iterative method is proposed for the elliptic equation \[ \grad\cdot(\beta(x,y) \grad u) =f(x,y) \] in a rectangularregion $\Omega$ in two-space dimensions. We assume that there is an irregular interface across which the coefficient $\beta$, the solution u and its derivatives, and/or the source term f may have jumps. We are especially interested in the cases where the coefficients $\beta$ are piecewise constant and the jump in $\beta$ is large. The interface may or may not align with an underlying Cartesian grid. The idea in our approach is to precondition the differential equation before applying the immersed interface method proposed by LeVeque and Li [ SIAM J. Numer. Anal., 4 (1994), pp. 1019--1044]. In order to take advantage of fast Poisson solvers on a rectangular region, an intermediate unknown function, the jump in the normal derivative across the interface, is introduced. Our discretization is equivalent to using a second-order difference scheme for a corresponding Poisson equation in the region, and a second-order discretization for a Neumann-like interface condition. Thus second-order accuracy is guaranteed. A GMRES iteration is employed to solve the Schur complement system derived from the discretization. A new weighted least squares method is also proposed to approximate interface quantities from a grid function. Numerical experiments are provided and analyzed. The number of iterations in solving the Schur complement system appears to be independent of both the jump in the coefficient and the mesh size.
DA - 1998/2//
PY - 1998/2//
DO - 10.1137/S0036142995291329
VL - 35
IS - 1
SP - 230-254
SN - 1095-7170
KW - elliptic equation
KW - discontinuous coefficients
KW - immersed interface method
KW - Cartesian grid
KW - Schur complement
KW - GMRES method
KW - preconditioning
ER -
TY - JOUR
TI - Computer simulation of inspiratory nasal airflow and inhaled gas uptake in a rhesus monkey
AU - Kepler, GM
AU - Richardson, RB
AU - Morgan, KT
AU - Kimbell, JS
T2 - TOXICOLOGY AND APPLIED PHARMACOLOGY
AB - There is increasing evidence that inspiratory airflow patterns play a major role in determining the location of nasal lesions induced in rats by reactive, water-soluble gases such as formaldehyde and chlorine. Characteristic lesion patterns have also been seen in inhalation toxicity studies conducted in rhesus monkeys, the nasal anatomy of which resembles that of humans. To examine the hypothesis that regions of high airflow-dependent uptake and lesions occur in similar nasal locations in the primate, airflow and gas uptake patterns were simulated in an anatomically accurate computer model of the right nasal airway of a rhesus monkey. The results of finite-element simulations of steady-state inspiratory nasal airflow for the full range of resting physiological flow rates are reported. Simulated airflow patterns agreed well with experimental observations, exhibiting secondary flows in the anterior nose and streamlined flow posteriorly. Simulated airflow results were used to predict gas transport to the nasal passage walls using formaldehyde as an example compound. Results from the uptake simulations were compared with published observations of formaldehyde-induced nasal lesions in rhesus monkeys and indicated a strong correspondence between airflow-dependent transport patterns and local lesion sites. This rhesus computer model will provide a means for confirming the extrapolation of toxicity data between species by extrapolating rat simulation results to monkeys and comparing these predictions with primate lesion data.
DA - 1998/5//
PY - 1998/5//
DO - 10.1006/taap.1997.8350
VL - 150
IS - 1
SP - 1-11
SN - 0041-008X
ER -
TY - JOUR
TI - A dispersion model for the hepatic uptake and elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin
AU - Banks, HT
AU - Musante, CJ
AU - Tran, HT
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - A convection-dispersion model for the uptake and elimination of 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD) in the liver is presented. The model is adapted from the general dispersion model of Roberts and Rowland and includes the dynamics of TCDD interaction with two intracellular proteins, the Ah receptor and cytochrome P450 IA2. A “well-mixed” compartment was added to describe the venous blood concentration of TCDD. The result is a nonlinear system of seven coupled partial and ordinary differential equations with time delays.
DA - 1998/7//
PY - 1998/7//
DO - 10.1016/S0895-7177(98)00077-6
VL - 28
IS - 1
SP - 9-29
SN - 0895-7177
KW - physiologically-based pharmacokinetic (PBPK) model
KW - 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)
KW - liver transport models
KW - nonlinear partial differential equations
KW - delay equations
ER -
TY - JOUR
TI - The immersed interface method using a finite element formulation
AU - Li, ZL
T2 - APPLIED NUMERICAL MATHEMATICS
AB - A finite element method is proposed for one dimensional interface problems involving discontinuities in the coefficients of the differential equations and the derivatives of the solutions. The interfaces do not have to be one of grid points. The idea is to construct basis functions which satisfy the interface jump conditions. By constructing an interpolating function of the solution, we are able to give a rigorous error analysis which shows that the approximate solution obtained from the finite element method is second order accurate in the infinity norm. Numerical examples are also provided to support the method and the theoretical analysis. Several numerical approaches are also proposed for dealing with two dimensional problems involving interfaces.
DA - 1998/7//
PY - 1998/7//
DO - 10.1016/S0168-9274(98)00015-4
VL - 27
IS - 3
SP - 253-267
SN - 0168-9274
KW - immersed interface method
KW - finite element method
KW - modified basis function
KW - natural jump condition
KW - error analysis
ER -
TY - JOUR
TI - Termination of Newton/Chord iterations and the method of lines
AU - Kelley, CT
AU - Miller, CT
AU - Tocci, MD
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - 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.
DA - 1998/1//
PY - 1998/1//
DO - 10.1137/S1064827596303582
VL - 19
IS - 1
SP - 280-290
SN - 1064-8275
KW - termination of nonlinear iterations
KW - Richards' equation
KW - method of lines
ER -
TY - JOUR
TI - Real-time monitoring of steady-state pulsed chemical beam epitaxy by p-polarized reflectance
AU - Bachmann, KJ
AU - Sukidi, N
AU - Hopfner, C
AU - Harris, C
AU - Dietz, N
AU - Tran, HT
AU - Beeler, S
AU - Ito, K
AU - Banks, HT
T2 - JOURNAL OF CRYSTAL GROWTH
AB - The structure in the p-polarized reflectance (PR) intensity Rp4(t) - observed under conditions of pulsed chemical beam epitaxy (PCBE) - is modeled on the basis of the four-layer stack: ambient/surface reaction layer (SRL)/epilayer/substrate. Linearization of the PR intensity with regard to the phase factor associated with the SRL results in a good approximation that can be expressed as Rp4 = Rp3 + ΔRp.Rp3 is the reflectivity of the three-layer stack ambient-epilayer-substrate. ΔRp describes the properties of the SRL. An explicit relation is derived between ΔRp(t) and the time-dependent surface concentrations ch(t) (h = 1, 2, …, N) of the constituents of the SRL, which holds for conditions of submonolayer coverage of the surface by source vapor molecules. Under conditions of low temperature PCBE at high flux, the SRL is expected to exhibit nonideal behavior, mandating replacement of the surface concentrations by activities. Also, in this case, the thickness of the SRL must be represented in terms of partial molar volumina Vh. Since the relation between ΔRp(t) and the activities of reactants, intermediates and products of the chemical reactions driving heteroepitaxial growth is non-linear, the extraction of kinetic parameters from the measured time dependence of the PR signal generally requires numerical modeling.
DA - 1998/1//
PY - 1998/1//
DO - 10.1016/s0022-0248(97)00410-7
VL - 183
IS - 3
SP - 323-337
SN - 0022-0248
KW - p-polarized reflectance
KW - surface kinetics
KW - chemical beam epitaxy
KW - real-time process monitoring
ER -
TY - JOUR
TI - A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations
AU - Banoczi, JM
AU - Kelley, CT
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - 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.
DA - 1998/1//
PY - 1998/1//
DO - 10.1137/S1064827596302965
VL - 19
IS - 1
SP - 266-279
SN - 1064-8275
KW - conductive-radiative heat transfer
KW - multilevel algorithm
KW - compact fixed point problems
ER -
TY - JOUR
TI - On the existence of normal modes of damped discrete-continuous systems
AU - Banks, HT
AU - Luo, ZH
AU - Bergman, LA
AU - Inman, DJ
T2 - JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
AB - In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.
DA - 1998/12//
PY - 1998/12//
DO - 10.1115/1.2791942
VL - 65
IS - 4
SP - 980-989
SN - 0021-8936
ER -
TY - JOUR
TI - Detection of non-symmetrical damage in smart plate-like structures
AU - Banks, HT
AU - Emeric, PR
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - A two-dimensional model for in-plane vibrations of a cantilever plate with a nonsymmetrical damage is used in the context of defect identification in materials with piezoelectric ceramic patches bonded to their surface. These patches can act both as actuators and sensors in a selfanalyzing fashion, which is a characteristic of smart materials. A Galerkin method is used to approximate the dynamic response of these structures. The natural frequency shifts due to the damage are estimated numerically and compared to experimental data obtained from tests on cantilever aluminum plate-like structures damaged at different locations with defects of different depths. The damage location and extent are determined by an enhanced least square identification method. Efficacy of the frequency shift based algorithms is demonstrated using experimental data.
DA - 1998/10//
PY - 1998/10//
DO - 10.1177/1045389x9800901005
VL - 9
IS - 10
SP - 818-828
SN - 1045-389X
ER -
TY - JOUR
TI - A nonlinear optimal control method for magnetostrictive actuators
AU - Smith, RC
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent in the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
DA - 1998/6//
PY - 1998/6//
DO - 10.1177/1045389X9800900608
VL - 9
IS - 6
SP - 468-486
SN - 1045-389X
ER -
TY - JOUR
TI - Utilization of coupling effects in compensator design for structural acoustic systems
AU - Banks, HT
AU - Demetriou, MA
AU - Smith, RC
T2 - JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
AB - The quantification and utilization of coupling effects in a prototypical structural acoustic system are examined in this paper. In typical systems, the coupling mechanisms are manifested in two ways. The first leads to the transfer of energy from an ambient field to an adjacent structure and is often responsible for exogenous structural excitation. The second involves the transfer of energy from the vibrating structure to an adjacent field. This is the source of structure-borne noise and is ultimately the mechanism through which structural actuators are utilized to attenuate noise. The examples presented here demonstrate that in fully coupled systems, both mechanisms should be incorporated to accurately model system dynamics. The examples also illustrate advantages and limitations of compensators which utilize the accurate modeling of the structural coupling.
DA - 1998/2//
PY - 1998/2//
DO - 10.1121/1.421205
VL - 103
IS - 2
SP - 872-887
SN - 0001-4966
ER -
TY - JOUR
TI - Local convergence of the symmetric rank-one iteration
AU - Kelley, CT
AU - Sachs, EW
T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
DA - 1998/1//
PY - 1998/1//
DO - 10.1023/A:1018330119731
VL - 9
IS - 1
SP - 43-63
SN - 0926-6003
KW - SRI update
KW - pointwise quasi-Newton method
KW - optimal control
ER -
TY - JOUR
TI - Convergence analysis of pseudo-transient continuation
AU - Kelley, CT
AU - Keyes, DE
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - 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.
DA - 1998/4//
PY - 1998/4//
DO - 10.1137/S0036142996304796
VL - 35
IS - 2
SP - 508-523
SN - 0036-1429
KW - pseudo-transient continuation
KW - nonlinear equations
KW - steady state solutions
KW - global convergence
ER -