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Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge-Kutta convolution quadrature. (English) Zbl 1279.78019

The paper is concerned with the numerical approximation of time-dependent boundary integral equations arising in electromagnetic scattering. The authors consider the three-dimensional exterior scattering problem from a perfectly conducting obstacle in a homogeneous isotropic medium. In order to solve the resulting time-domain electric field integral equation they use a Runge-Kutta convolution quadrature for the time discretization and a Galerkin BEM with Raviart-Thomas elements of lowest order for the spatial discretization. They analyze the involved operators in the Laplace domain and obtain error estimates for the semi-discrete scheme and for the fully discrete scheme. Numerical experiments in the case of a spherical scatterer indicate that the derived error estimates are sharp.

MSC:

78M15 Boundary element methods applied to problems in optics and electromagnetic theory
78A45 Diffraction, scattering
65R20 Numerical methods for integral equations
65N38 Boundary element methods for boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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