×

A uniformly stable conformal FDTD-method in Cartesian grids. (English) Zbl 1014.78014

Summary: A conformal finite-difference time-domain algorithm for the solution of electrodynamic problems in general perfectly conducting 3D geometries is presented. Unlike previous conformal approaches it has the second-order convergence without the need to reduce the maximal stable time step of conventional staircase approach. A novel proof for the local error rate for general geometries is given, and the method is verified and compared to other approaches by means of several numerical 2D examples.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yee, IEEE Transaction on Antennas and Propagation 14 pp 302– (1966)
[2] Holland, IEEE Transactions on Electromagnetic Compatibility 35 pp 434– (1993)
[3] Cangellaris, IEEE Transaction on Antennas and Propagation 39 pp 1518– (1991)
[4] Jurgens, IEEE Transaction on Antennas and Propagation 40 pp 357– (1992)
[5] Railton, Electronics Letters 31 pp 1585– (1995)
[6] Dey, IEEE Microwave and Guided Wave Letters 7 pp 273– (1997)
[7] Zur numerischen Lösung der Maxwellschen Gleichungen im Zeitbereich. Dissertation Dl7: TH Darmstadt, 1997.
[8] Holland, IEEE Transactions on Electromagnetic Compatibility 33 pp 281– (1991)
[9] Die Nichtorthogonale Finite-Integrations-Methode zur Simulation elektromagnetischer Felder. Dissertation D17: TH Darmstadt, 1999.
[10] Yee, IEEE Transaction on Antennas and Propagation 45 pp 354– (1997)
[11] Hao, IEEE Transactions on Microwave Theory and Techniques 46 pp 82– (1998)
[12] Yu, IEEE Antennas and Propagation Magazine 42 pp 28– (2000)
[13] Yang, IEEE Transactions on Microwave Theory and Techniques 48 pp 969– (2000)
[14] Ditkowski, Journal of Computational Physics 170 pp 39– (2001)
[15] Collino, Journal of Computational Physics 138 pp 907– (1997)
[16] Weiland, Electronics and Communication (AEÜ) 31 pp 116– (1977)
[17] Weiland, Particle Accelerators 15 pp 245– (1984)
[18] Weiland, Particle Accelerators 17 pp 227– (1985)
[19] Weiland, International Journal of Numerical Modelling 9 pp 295– (1996)
[20] Space and time stability of discrete time domain algorithm. Proceedings of the Fourth International Workshop on Computational Electromagnetics in the Time Domain (CEM-TD), Nottingham, UK 2001; 155-161.
[21] Foundations of Electrical Engineering. Pergamon Press: London, 1963. · Zbl 0125.44902
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.