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arXiv · 2609.24822

A Domain Derivative for Electromagnetic Scattering by Perfect Conductors in the Time Domain

Marvin Knöller
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Abstract

A domain derivative for time-dependent electromagnetic scattering from perfect conductors is established. By proceeding through the Laplace domain, frequency-dependent bounds on solutions to Maxwell's equations are derived. These bounds are used both for establishing time regularity properties of the domain derivative and for proving convergence of the proposed Runge--Kutta convolution quadrature semi-discretization in time. A full convergence analysis is also carried out for pointwise evaluations of the domain derivative, when this time discretization is combined with a Galerkin method in space. Eventually, the domain derivative is applied in an iterative shape reconstruction algorithm, in which measurements of the electric near field at some receiver positions, away from the perfect conductor are measured. Numerical examples show the feasibility of this algorithm and in particular highlight its robustness, when additional noise is applied to the data.

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Marvin Knöller. 2026-09-21. A Domain Derivative for Electromagnetic Scattering by Perfect Conductors in the Time Domain. https://arxiv.org/abs/2609.24822

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