Book
Numerical Methods
in Applied Sciences edited by W. Cai, Z.C. Shi, C.W. Shu and J.C.
Xu, Science Press, New York, pp 39-59, 1996
Major Publications
on Algorithms
All Journal Publications
I.
Computational Algorithms and Methodologies
- Convergence of two nonconforming finite elements, in Journal
of Computational Mathematics, Academia Sinica, 2, pp. 63-74, 1986.
- The limit problem of the Ziekiewicz finite element, in Journal
of Computational Mathematics, Academia Sinica, 4, pp. 345-353,
1986.
- Essentially Non-oscillatory Spectral
Method for Shock Wave Calculations, (with D. Gottlieb and C. W.
Shu, Mathematics of Computation, 52, (1989)
pp.389-410.
- Cell averaging Chebychev Method for
Hyperbolic Problems, (with D. Gottlieb and A. Harten), Computers and
Mathematics with Applications, vol. 24,
No. 516, pp. 37-49, September 1992.
- Uniform High
Order Spectral Methods for One and Two Dimensional Euler Equations,
(with C.W. Shu), Journal of Computational Physics, vol.
104, No. 2, pp. 427-443, 1993.
- On One-sided Filters for Spectral Fourier Approximations of
Discontinuous Functions, (with C.W. Shu and D. Gottlieb), SIAM
Numerical Analysis, Vol. 29, No. 4, pp.
905-916, August 1992.
- Coupling of
Spectral Methods and H-P Version Finite Element Methods for PDE's on
Nonsmooth Domains, (with H.C. Lee and H. -S. Oh), in Journal of
Computational Physics, vol. 108, No. 2, pp. 314-326, October 1993.
- Domain decomposition and Computation of 2-D Detonation Waves, Contemporary
Mathematics, Vol. 180, pp. 459-464, 1994.
- Adaptive
Multiresolution Collocation Method for the Initial Value Boundary
Problem of
Nonlinear PDE's, (with J.Z. Wang), SIAM Journal of Numerical Analysis,
Volume 33, Number 3, pp. 937-970, June 1996.
- Higher order
mixed current basis functions for electromagnetic scattering of curved
surfaces, Journal of Scientific Computing, Vol. 14, No. 1, pp.
73-105, 1999.
- Fast
calculation of dyadic Green's functions for electromagnetic scattering
in
a multi-layered medium, (with Tiejun Yu) Journal ofComputational
Physics, 165, 1-21, 2000.
- High Order Current Basis Functions for Electromagnetic
Scattering of Curved Surfaces, Discontinous Galerkin Methods,
Lecture Notes in Computational Science and Engineering, No. 11,
Edited by B. Cockburn, G.E. Karniadakis, and C. W. Shu, pp. 271-276,
Springer-Verlag, 2000.
- Inverse Matrix Evaluation for Linear
Systems, (with Mohsen Tadi), Inverse Problems 17, pp. 247-260,
2001.
- Level Set-Boundary Element Method for Simulation of Dynamic
Powder Consolidation of metels, (with Zhilin Li) Lecture Notes in
Computer Science 1988, Edited by L. Vulkov, J. Wasniewski, and P.
Yalamov, pp. 527-534, Springer-verlag, 2001.
- An Inverse
Method for Parabolic Equations Based on Quasi-Reversibility, (with
Mohsen Tadi, Michael Klibanov), COMPUTERS & MATHEMATICS WITH
APPLICATIONS 43 (8-9): 927-941, APR-MAY 2002.
- Singularity
Treatment and High Order RWG Basis Functions for Integral Equations of
Electromagnetic Scattering, International Journal for Numerical
Methods in Engineering, Vol. 53, No. 1, January 2002.
- Algorithmic Issues for Computational
Electromagnetic Scattering in Layered Media: Green's Function, Basis
Function and Fast Solver, Special
Issue of Advances in Computational Mathematics: Modeling
and Computation of Optics and Electromagnetics, 16:
157-174, 2002.
- An Upwinding
Embedded Boundary Methods for Maxwell equations, (with S.
Deng) Journal of Computational Phyiscs, 190, 2003.
- An Exact
Absorbing Boundary Condition for Exterior Helmholtz Equation in Layered
Media (with H.T. Yang), in Advances in Computation: Theory and
Practice, Science Press, NY, p97, 2004
- Discontinuous
Galerkin Methods for Dispersive and Lossy Maxwell's Equations and PML
Boundary Conditions, T. Lu, P.W. Zhang, W. Cai, Journal of
Computational Physics, 200 (2004), pp. 549-580.
- Numerical Methods for Maxwell's Equations in
Inhomogeneous Media with Material Interfaces, W. Cai, Journal of
Computational Mathematics, Vol. 22, No. 2, pp. 156-167, 2004.
- Analysis and Application of an
Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element
Methods, Applied Numerical Analysis and Computational
Mathematics, 2(3):311-330, 2005
- FIFA - “ Fast Interpolation
and Filtering Algorithm for Calculating Dyadic Green's Function
in the Electromagnetic Scattering of Multi-layered Structures,
the Communication in Computational Physics, Vol. 1, No. 2, pp.
228-258,
2006.
- A
Fourth-Order Upwinding
Embedded Boundary Method (UEBM) for Maxwell's Equations in Media
with Material Interfaces: Part I, S. Deng, W. Cai, the
Communication
in Computational Physics, Volume 1, Number 4, June 2006, pp. 744-764.
- Discrete Image Approximations of
Ionic Solvent Induced Reaction Field to Charges, S.Z. Deng, W. Cai,
the Communications in Computational Physics, 2 (2007),
p.1007-1026.
- A
Comparable study of image
approximations to the reaction fields, Shaozhong Deng, Wei Cai,
Donald Jacobs, Computer Physics Communications, Vol. 177, 9, Nov.
(2007),
pp. 689-699.
- Image
Methods for Electrostatics Potentials,
to appear in Advances in mathematics and applications, 2008.
- A Fourier
Spectral-Discontinuous Galerkin
Methods for Time Dependent 3-D Schrodinger-Poission Equations with
Discontinuous Potentials, T. Lu, W. Cai, the
Journal of Computational and Applied Mathematics, 220, (2008), 558-614.
- Transmission
and Dispersion
Characteristic of a Discontinuous Galerkin Method for Maxwell's
Equations in Dispersive Inhomogeneuos Media, X. Ji, W. Cai, P.W.
Zhang, Journal of Computational Mathematics, 26, (2008), pp.
347-364.
- A Generalized Discontinuous Galerkin
Method (GDG) for Schrodinger Equations with Nonsmooth Solutions,
Kai Fan, Wei Cai, Xia Ji, the Journal of Computational Physics,
227 (2008), pp. 2387-2410.
- A Schwarz Generalized Eigen-oscillation
Spectral Element Method (GeSEM) for 2-D High Frequency Electromagnetic
Scattering in Dispersive Inhomogeneous Media, W. Cai, X. Ji, J.G.
Sun, S.H. Shao, the Journal of Computational Physics, 227 (2008)
9933–9954.
- Fast Spectral Collocation
Method for Surface Integral Equations of Potential Problems in a
Spheroid, Zhenli Xu, W. Cai, submitted to the Communications in
Computational Physics, Sept. 2008
- Image charge
methods for a three-dielectric-layer hybrid solvation model of
biomolecules, P.H. Qin, Z.L. Xu, W. Cai and D. Jacobs, submitted to
the Communications in Computational Physics, October,2008.
- A
Sixth-order Image Approximation to the Ionic Solvent Induced Reaction
Field, M. Xiang, S. Z. Deng, W. Cai, submitted in revised version
to
the Journal of Scientific computing, 2/2009.
- High-order
Numerical Methods for the Computation of Cellular Structure of 2-D
Detonation Waves, AIAA Journal, Vol. 33, No. 7, PP 1248-1255,
(July, 1995)
- Direct numerical calculation of neutral stability curve for
one-dimensional detonations, (with W.H. Oh, Y.L. Zhu), SIAM Journal
of Scientific Computing, Volume 17, Number 4, pp. 814-829, July
1996.
- An Adaptive
Spline Wavelet ADI (SW-ADI) Method for two-dimensional Reaction
Diffusion Equations, (with Wu Zhang), Journal of Computational
Physics, Vol. 139, pp. 92-126 (1998).
III.
Electromagnetic Scattering in Microwave devices
- High
Order mixed RWG basis functions for electromagnetic applications, IEEE
transaction on Microwave Theory and Technology, Vol. 49,
No. 7, pp. 1295-1303, July 2001.
- High Order Window
Functions and Fast
Algorithms for Calculating Dyadic Electromagnetic Green?s Functions in
Multilayered Media, (with Tiejun Yu), Radio Science, July,
2001.
- Discontinuous
Galerkin Time Domain Methods
for GPR Simulation in Dispersive Media, T. Lu, W. Cai, Pingwen
Zhang, IEEE Transaction GRS, Volume: 43 , Issue: 1 , Pages:72 - 80, Jan.
2005.
IV.
Circuit Simulation and Model Reductions
- A
fast wavelet collocation method
for high speed circuit simulation (with Dian Zhou), IEEE
transaction on circuits and systems, Vol.
46, No. 8, pp. 920-930, 1999.
- An
adaptive wavelet method for
nonlinear circuit simulation (with Dian Zhou and W,
Zhang), IEEE transaction on circuits and systems, Vol. 46,
No. 8, pp. 931-938, 1999.
- An efficient DC-gain matched balanced truncation realization for
VLSI interconnect circuit order reduction, Microelectronic Engineering,
Vol. 60, issue 1-2, p. 3-15, 2002.
- Behavioral modeling for analog system-level simulation by wavelet
collocation method, X. Li, X. Zeng, D. Zhou, X. Ling, W. Cai, IEEE
Transactions on Circuits and Systems II: Analog and Digital Signal
Processing, Vol.
50, Issue: 6, 299-314, (2003).
- Analog behavioral modeling by multi-companding and wavelet
collocation method, J. Tao, X. Zeng, W. Cai, D. Zhou, C. Chiang,
Analogue Integrated Circuits and Signal Processing, An International
Journal, vol. 49, pp 291-297，Sept, 2006.
- Adaptive stochastic collocation method for parameterized
statistical timing analysis with quadratic delay model, Y. Wang, X.
Zeng, J. Tao, H.L. Zhu and W. Cai, IEICE TRANSACTIONS on
Fundamentals of Electronics, Communications and Computer Sciences
Vol.E91-A No.12 pp.3465-3473, 2008.
V. Photonics and
Plasmon Systems
- Numerical
Study of Light Propagation via
Whispering Gallery Modes in Microcylinder Coupled Resonator Optical
Waveguides, Optics Express, 12, 6468-6480
(2004).
- Discontinuous
Spectral Element Methods for
Optical Transfer by Whispering Gallery Modes in a Photonic
Waveguide of Coupled Microcylinders, S. Deng, W. Cai, Journal of
Optical Society of America, A, Vol. 22, No. 5/May 2005.
- Discontinuous
Galerkin Time Domain
(DGTD) Methods for the Study of Waveguide Coupled Microring Resonators,
X. Ji, T. Lu, W. Cai, and P.W. Zhang, the Journal of Lightwave
Technology, VOL. 23, NO. 11, pp. 3864-3874, NOVEMBER 2005.
- Optical
Coupling at a distance between
detuned spherical cavities, A. Kanaev, V. Astratov, W. Cai,
Applied Physics Letter, 88, 111111 (2006).
- A Boundary
Integral Equation Method for
Photonic Crystal Fiber, M. Cho, W. Cai, T. Her, the Journal of
Scientific Computing, vol. 28, No. 2-3, Sept. 2006, pp. 263-278.
- High Order
DGTD Methods for Dispersive
Maxwell's Equations and Modelling of Silver Nanowire Coupling, X.
Ji, W. Cai, P. Zhang, the International Journal of Numerical
Methods in Engineering, In Press, July, 2006.
- A Full
Vectorial Generalized Discontinuous
Galerkin Beam Propagatiom Method (GDG-BPM) for Inhomogeneous Optical
Waveguide, K. Fan, W. Cai, X. Ji, the Journal of
Computational Physics, 227 (2008), pp. 7178.
VI. Quantum
Transport in Nano-devices
- Conservative
Local Discontinuous Galerkin
Methods for Time Dependent Schroedinger Equation, T. Lu, W. Cai,
and P.W. Zhang, International Journal of Numerical Analysis and
Modeling, Vo. 1, 45-65, 2005.
- Accurate
Calculation of Green's Functions
of Schrodinger Equations in Block Layered Potentials, S. H. Shao,
W. Cai, H. Z. Tang, the Journal of Computational Physics, 216
(2006), pp. 733-748.
- Boundary Treatments
in the Nonequilibrium
Green's functions (NEGF) methods for transport in Nano-MOSFETs, H.
Y. Jiang, S.H. Shao, W. Cai, P.W. Zhang, the Journal of
Computational Physics, 227, (2008), pp. 6553.
- Adaptive conservative cell-averaged
spectral element methods for
transient Wigner equation for quantum transport, S. H. Shao, W.
Cai, T.
Lu, submitted to the Communcations in Computational
Physics, May, 2009.
- Effect of Boundary Treatment on
Quantum Transport Current in the Green's Function and Wigner
Distribution Methods for a Nano-scale DG-MOSFET, H. Y. Jiang, W.
Cai, submitted to the Journal of Computational Physics, May,
2009.
VII.
Electrostatics and Generalized Born Theory for Biomolecules
- Extending
the Fast Multipole Method to
Charges Inside or Outside a Dielectric Sphere, W. Cai, S. Z. Deng,
D. Jacobs, the Journal of Computational Physics, 223 (2007), pp.
846-864.
- Extending
the fast multipole method for
charges inside a dielectric sphere in an ionic solvent: high order
image approximations for reaction fields, S.Z. Deng, W. Cai, the
Journal of Computational Physics, 227 (2007), 1246-1266.
- A
new FFT-based algorithm to compute Born
radii in the generalized Born theory of biomolecule solvation,
Wei Cai, Zhenli Xu, A. Baumketner, the Journal of Computational
Physics, 227 (2008) 10162–10177
- Image
Charge Approximations of
Reaction Fields in Solvation with Arbitrary Ionic Strength,
Zhenli Xu, Shaozhong Deng, submitted to the Journal of Computational
Physics, Jan. 2008.
- Optimal integral expressions for
effective radii in the
generalized Born modelof molecular solvation, Z.L. Xu, W. Cai, and
A.
Baumketner, submitted to the Journal of Chemical Physics, January,
2009.
- An Image-based reaction field method for
electrostatic interactions in molecular dynamics simulations of aqueous
solutions, Yuchun Lin, Andriy Baumketner, Shaozhong Deng, Zhenli
Xu,
Donald Jacobs, Wei Cai, to be submitted to the Journal of Chemical
Physics.
VIII.
Mask Simulation in Lithogography
- Highly
Parallel Rigorous Simulation of Phase
Shift Masks with a Generalized Eigen-oscillation Spectral Element
Method (GeSEM), K. Zong, X. Zeng, X. Ji and W. Cai, submitted to
the Journal of Micro/Nanolithography, MEMS, and MOEMS, special
issue on Computational Lithography, October, 2008.
IX. Stochastic
Simulation of Process Variations
- A sparse
grid based spectral stochastic collocation method for variations-Aware
capacitance extraction of interconnects under nanometer process
technology, H.L. Zhu, X. Zeng, W. Cai, J.T. Xue, D. Zhou, IEEE/ACM
DATE’2007.
- Generalized
stochastic collocation method for variation-aware capacitance
extraction of interconnects considering arbitrary random probability,
H. L. Zhu, X. Zeng, X. Luo, W. Cai, to appear in the IEICE TRANS.
ELECTRON, 2009.
- A contact
mechanics based model for general rough pads in chemical mechanical
polishing processes, C. Y. Feng, X. Zeng, Changhao Yan , Jun Tao
,W.
Cai, submitted to the Journal of The Electrochemical Society, January,
2009.