Peter Monk

Time Domain Electric Field Integral Equation for Computational Electromagnetism

Scattering problems for Maxwell’s equations can be solved in the frequency or time domain. In the frequency domain both finite element and boundary integral methods are in common use, and their relative strengths and weaknesses are well understood. In contrast, in the time domain the principal technique is the finite difference time domain method or the Discontinuous Galerkin Method. However, time-domain integral equations have become much more popular in recent years, although they still represent a considerable coding challenge. This can be mitigated by using the convolution quadrature approach (CQ)1, together with a Galerkin boundary integral equation method in space.

I shall outline the CQ method applied to Maxwell’s equations using the electric field integral equation to compute waves scattered by a perfect conducting object as a model problem. After discussing some theoretical aspects such as error estimates and other properties of the scheme, I shall present a few numerical results.

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