Vortrag
Time-dependent scattering from thin layers
Vortrag von Prof. Dr. Christian Lubich
Datum: 29.03.23 Zeit: 16.30 - 18.00 Raum: Y27H35/36
The scattering of electromagnetic waves from obstacles with wave- material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken here is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. The fields are then evaluated in the exterior domain by a known representation formula, which uses the time-dependent potential operators of Maxwell’s equations. The time-dependent boundary integral equation is discretized with Runge-Kutta based convolution quadrature in time and Raviart–Thomas boundary elements in space. The well-posedness analysis of the boundary integral equation as well as the error analysis of the numerical methods relies on frequency-explicit bounds in the Laplace domain. These are then transferred to the time domain and combined with known approximation estimates of the numerical methods. The talk is based on joint work with Balázs Kovács and Jörg Nick.