Error estimates for the time integration of Maxwell equations on heterogeneous media
Next Monday, May 2 we have a talk by Konstantin Zerulla, visitor scientist at our FAU DCN-AvH Chair:
Event: Error estimates for the time integration of Maxwell equations on heterogeneous media
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Speaker: Prof. Dr. Konstantin Zerulla
Affiliation: Karlsruher Institut für Technologie
Abstract. Alternating direction implicit (ADI) schemes are very attractive dimension splitting schemes for the time integration of linear Maxwell equations on cuboids. Indeed, they are unconditionally stable and have only linear complexity. During the error analysis, it however turns out that the error estimates depend heavily on the regularity of the solutions to the Maxwell equations.
In the talk, we study a linear isotropic time-dependent Maxwell system on a cuboid. The medium is assumed to consist of several smaller homogeneous subcuboids with different material properties. In this setting, the solutions of the Maxwell equations have in general lower regularity. Based on detailed regularity results for the Maxwell system, we present rigorous time-discrete error estimates for two ADI schemes. In particular, we make only assumptions on the material and the initial data, but none on the (unknown) solution of the Maxwell system.