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Introduction to Applications of Numerical Analysis in Time Domain Computational Electromagnetism

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Frontiers in Numerical Analysis - Durham 2010

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 85))

Abstract

We discuss two techniques for the solution of the time domain Maxwell system. The first is a partial differential equation based approach using conforming finite elements and implicit time stepping that is suitable when stiff problems are encountered, and where the medium is inhomogeneous. In particular we analyze the use of edge elements and certain A-stable schemes using the Fourier-Laplace transform. For a homogeneous medium, an integral equation approach can be used and we describe and analyze the convolution quadrature method applied to the electric field integral equation. In either case we emphasize that the convergence analysis depends on energy estimates for the continuous problem.

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Acknowledgements

Our research is supported in part by a grant from NSF (DMS-0811104). PM would like to thank BICOM at Brunel University, UK for a visiting position during the writing of most of this paper.

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  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Qiang Chen & Peter Monk

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  1. Qiang Chen
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Correspondence to Peter Monk .

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  1. , Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    James Blowey

  2. , Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    Max Jensen

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Chen, Q., Monk, P. (2011). Introduction to Applications of Numerical Analysis in Time Domain Computational Electromagnetism. In: Blowey, J., Jensen, M. (eds) Frontiers in Numerical Analysis - Durham 2010. Lecture Notes in Computational Science and Engineering, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23914-4_3

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