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Time-dependent electromagnetic scattering from dispersive materials

by J. Nick and S. Burkhard and Ch. Lubich

(Report number 2024-09)

Abstract
This paper studies time-dependent electromagnetic scattering from metamaterials that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and passive homogeneous material, determines the wave-material interaction in the scatterer. The resulting problem is nonlocal in time inside the scatterer and is posed on an unbounded domain. Well-posedness of the scattering problem is shown using a formulation that is fully given on the surface of the scatterer via a time-dependent boundary integral equation. Discretizing this equation by convolution quadrature in time and boundary elements in space yields a provably stable and convergent method that is fully parallel in time and space. Under regularity assumptions on the exact solution we derive error bounds with explicit convergence rates in time and space. Numerical experiments illustrate the theoretical results and show the effectiveness of the method.

Keywords: electromagnetic scattering, dispersive material laws, time-dependent partial differential equations, convolution quadrature, boundary element method

@Techreport{NBL24_1091,
  author = {J. Nick and S. Burkhard and Ch. Lubich},
  title = {Time-dependent electromagnetic scattering from dispersive materials},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-09.pdf },
  year = {2024}
}

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