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Time Domain Integral Equation Methods in Computational Electromagnetism

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Book cover Computational Electromagnetism

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2148))

Abstract

Time domain integral equations have become a major tool in the computational analysis of electromagnetic scattering problems. Classically it was difficult to ensure a stable numerical solution of standard boundary integral formulations of the problem. In this chapter we shall discuss both theoretical and numerical aspects of one approach that solves the stability problem: convolution quadrature. We start with scattering from a perfectly conducting object and develop the electric field integral equation, as well as an error analysis of the fully discrete problem using finite elements in space. After presenting a brief discussion of some special numerical features of this problem, and some numerical results, we move on to scattering by a penetrable object. We end with a general discussion of computational electromagnetism illustrating the role that time domain integral equations can play.

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Acknowledgements

The authors acknowledge partial support for their research from NSF grant #DMS-1114889. The research of P.M. is also supported in part by a grant from AFOSR #FA9550-13-1-0199.

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Authors and Affiliations

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

    Jielin Li & Daniel Weile

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

    Peter Monk

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  1. Jielin Li
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Correspondence to Peter Monk .

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  1. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Alfredo Bermúdez de Castro

  2. Dipartimento di Matematica, Università di Trento, Povo (Trento), Italy

    Alberto Valli

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Li, J., Monk, P., Weile, D. (2015). Time Domain Integral Equation Methods in Computational Electromagnetism. In: Bermúdez de Castro, A., Valli, A. (eds) Computational Electromagnetism. Lecture Notes in Mathematics(), vol 2148. Springer, Cham. https://doi.org/10.1007/978-3-319-19306-9_3

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