A Domain Derivative for Electromagnetic Scattering by Perfect Conductors in the Time Domain
Year: 2026
Type: preprint
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. Numerical experiments validate the convergence orders in time and space. Eventually, the domain derivative is applied in an iterative shape reconstruction algorithm, in which the electric near field is measured at some receiver positions away from the perfect conductor. Numerical examples show the feasibility of this algorithm and in particular highlight its robustness, when additional noise is applied to the data.
Source: arXiv (Cornell University)
Author: Knöller, Marvin
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: China Scholarship Council
OpenAlex ID: W7214018426