Commun. Comput. Phys., 11 (2012), pp. 383-399.


Analysis of Convolution Quadrature Applied to the Time-Domain Electric Field Integral Equation

Q. Chen 1*, P. Monk 1, X. Wang 2, D. Weile 2

1 Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA.
2 Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA.

Received 12 December 2009; Accepted (in revised version) 11 October 2010
Available online 24 October 2011
doi:10.4208/cicp.121209.111010s

Abstract

We show how to apply convolution quadrature (CQ) to approximate the time domain electric field integral equation (EFIE) for electromagnetic scattering. By a suitable choice of CQ, we prove that the method is unconditionally stable and has the optimal order of convergence. Surprisingly, the resulting semi discrete EFIE is dispersive and dissipative, and we analyze this phenomena. Finally, we present numerical results supporting and extending our convergence analysis.

AMS subject classifications: 65M38, 65M60, 65N15, 65R20, 78A45

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Key words: Electromagnetism, scattering, time-domain, integral equation, EFIE, convolution quadrature, multistep method.

*Corresponding author.
Email: qchen@math.udel.edu (Q. Chen), monk@math.udel.edu (P. Monk), wang@udel.edu (X. Wang), weile@ee.udel.edu (D. Weile)
 

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