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Numerical solution of Maxwell’s equations in the time domain using irregular nonorthogonal grids.(English)Zbl 0672.73029

Summary: Several different methods for solving Maxwell’s equations in the time- domain through the use of irregular nonorthogonal grids are presented. Employing quadrilateral and/or triangular elements, these methods allow more accurate modeling of nonrectangular structures. The traditional “star-stepping” boundary approximations associated with standard orthogonal-grid finite-difference methods are avoided. Numerical results comparing all of the methods are given. A modified finite-volume method, which is a direct generalization of the standard finite-difference method to arbitrary polygonal grids, is shown to be the most accurate.

MSC:

74J99 Waves in solid mechanics
78A99 General topics in optics and electromagnetic theory
74S05 Finite element methods applied to problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics

Software:

THREDE

Cite

References:

[1]Yee, K. S., Numerical solution of initial boundary value problems in isotropic media, IEEE Trans. Antennas Propagat., 14, 302-307 (1966) ·Zbl 1155.78304
[2]Taflove, A.; Brodwin, M. E., Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations, IEEE Trans. Microwave Theory Tech., 23, 623-630 (1975)
[3]Holland, R., THREDE: A free-field EMP coupling and scattering code, IEEE Trans. Nuc. Sci., 24, 2416-2421 (1977)
[4]Kunz, K. S.; Lee, K. M., A three-dimensional finite-difference solution of the external response of an aircraft to a complex transient EM environment: Part I—The method and its implementation, IEEE Trans. Electromagn. Compat., 20, 328-333 (1978)
[5]Taflove, A.; Umashankar, K. R., The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems, J. Elec. Waves Appl., 1, 243-267 (1987)
[6]Cangellaris, A. C.; Lin, C. C.; Mei, K. K., Point-matched time domain finite element methods for electromagnetic radiation and scattering, IEEE Trans. Antennas Propagat., 35, 1160-1173 (1987) ·Zbl 0946.78515
[7]Lee, R. L.; Madsen, N. K., A finite element technique for solving the two-dimensional Maxwell’s equations in the time domain, (Tech. Rept. (1988), Lawrence Livermore National Laboratory, UCRL-97930: Lawrence Livermore National Laboratory, UCRL-97930 Livermore, CA)
[8]Ziolkowski, R. W.; Madsen, N. K., Modelling Maxwell’s equations in the time domain: a discrete differential form approach, (Tech. Rept. (1987), Lawrence Livermore National Laboratory, UCRL-97397: Lawrence Livermore National Laboratory, UCRL-97397 Livermore, CA)
[9]Engelman, M. S.; Sani, R. L.; Gresho, P. M., The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible fluid flow, Int. J. Num. Meth. Fluids, 2, 225-238 (1982) ·Zbl 0501.76001
[10]Harrington, R. F., Time Harmonic Electromagnetic Fields (1977), McGraw-Hill: McGraw-Hill New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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