DSC time-domain solution of Maxwell's equations

A new computational algorithm, the discrete singular convolution (DSC), is introduced for solving scattering and guided wave problems described by time-domain Maxwell's equations. The DSC algorithm is utilized for the spatial discretization and the fourth-order Runge Kutta scheme is used for the time advancing. Staggered meshes are used for electromagnetic fields. Four standard test problems, a hollow air-filled waveguide, a dielectric slab-loaded rectangular waveguide, a shield microstrip line and a dielectric square, are employed to illustrate the usefulness, to test the accuracy and to explore the limitation of the DSC algorithm. Results are compared with those of finite difference, scaling function multi-resolution time domain, and finite element-based high frequency structure simulator. Numerical experiments indicate that the present algorithm is a promising approach for achieving high accuracy in electromagnetic wave computations.

[1]  David W. Zingg,et al.  Comparison of High-Accuracy Finite-Difference Methods for Linear Wave Propagation , 2000, SIAM J. Sci. Comput..

[2]  本間 利久,et al.  Advanced computational electromagnetics , 1995 .

[3]  M. Salazar-Palma,et al.  Second-order Ndlec tetrahedral element for computational electromagnetics , 2000 .

[4]  G. Wei,et al.  A new algorithm for solving some mechanical problems , 2001 .

[5]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[6]  Jiming Song,et al.  Fast Illinois solver code (FISC) , 1998 .

[7]  Guo-Wei Wei,et al.  Lagrange Distributed Approximating Functionals , 1997 .

[8]  Siyang Yang,et al.  Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations , 2002 .

[9]  G. Wei,et al.  VIBRATION ANALYSIS BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[10]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications , 2002 .

[11]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[12]  Shan Zhao,et al.  Numerical solution of the Helmholtz equation with high wavenumbers , 2004 .

[13]  R. J. Joseph,et al.  Advances in Computational Electrodynamics: The Finite - Di erence Time - Domain Method , 1998 .

[14]  S.,et al.  Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media , 1966 .

[15]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[16]  Yang Xiang,et al.  Plate vibration under irregular internal supports , 2002 .

[17]  G. Bridges,et al.  Integer lattice gas automata for computational electromagnetics , 2000 .

[18]  J. M. Sanz-Serna,et al.  High-order methods , 1994 .

[19]  M. Krumpholz,et al.  MRTD: new time-domain schemes based on multiresolution analysis , 1996 .

[20]  I. Sebestyen,et al.  Applied electromagnetics and computational technology , 1997 .

[21]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm , 2002 .

[22]  E. Tentzeris,et al.  Stability and dispersion analysis of Battle-Lemarie-based MRTD schemes , 1999 .

[23]  G. W. Wei.  A unified method for solving Maxwell's equations , 1999, 1999 Asia Pacific Microwave Conference. APMC'99. Microwaves Enter the 21st Century. Conference Proceedings (Cat. No.99TH8473).

[24]  Ya Yan Lu,et al.  One-Way Large Range Step Methods for Helmholtz Waveguides , 1999 .

[25]  G. Wei,et al.  A unified approach for the solution of the Fokker-Planck equation , 2000, physics/0004074.

[26]  Guo-Wei Wei,et al.  Discrete singular convolution for the solution of the Fokker–Planck equation , 1999 .

[27]  Vijaya Shankar,et al.  Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure , 1991 .

[28]  Allen Taflove,et al.  Computational Electromagnetics , 1993, The Electrical Engineering Handbook - Six Volume Set.

[29]  Qing Huo Liu,et al.  The PSTD algorithm: A time-domain method requiring only two cells per wavelength , 1997 .

[30]  G. W. Wei,et al.  Conjugated filter approach for solving Burgers' equation with high Reynolds number , 2000 .

[31]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[32]  Chi-Wang Shu,et al.  On the Gibbs Phenomenon and Its Resolution , 1997, SIAM Rev..

[33]  Yilong Lu,et al.  Microwave and Optical Waveguide Analysis by the Finite Element Method , 1996 .

[34]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[35]  David W. Zingg,et al.  Numerical Solution of the Time-Domain Maxwell Equations Using High-Accuracy Finite-Difference Methods , 2000, SIAM J. Sci. Comput..

[36]  Guo-Wei Wei,et al.  Discrete Singular Convolution-Finite Subdomain Method for the Solution of Incompressible Viscous Flows , 2002 .

[37]  J. Hesthaven,et al.  Nodal high-order methods on unstructured grids , 2002 .

[38]  Yehuda Leviatan,et al.  Wavelets in electromagnetics: the impedance matrix compression (IMC) method , 1998 .

[39]  Time-domain wavelet Galerkin modeling of two-dimensional electrically large dielectric waveguides , 2001 .

[40]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[41]  Tobin A. Driscoll,et al.  A Block Pseudospectral Method for Maxwell's Equations , 1998 .

[42]  G. Wei,et al.  Wavelets generated by using discrete singular convolution kernels , 2000 .

[43]  O. C. Zienkiewicz,et al.  Achievements and some unsolved problems of the finite element method , 2000 .

[44]  T. Driscoll,et al.  Note on Nonsymmetric Finite Differences for Maxwell's Equations , 2000 .

[45]  John L. Volakis,et al.  Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics , 1999 .

[46]  S. Rao.  Time domain electromagnetics , 1999 .