Fictitious domain method for unsteady problems: Application to electromagnetic scattering

In this work, we present and implement a fictitious domain method for time dependent problems of scattering by obstacles. We focus our attention on the case of 2D electromagnetic waves and perfectly conducting boundaries. Such a method allows us to work with uniform meshes for the electric field, independently of the geometry of the obstacle. The boundary condition is taken into account via the introduction of a Lagrange multiplier that can be interpreted as a surface current. After a brief description of the method and a presentation of its main properties, we show the superior accuracy of this new method over the method using a staircase-like approximation of the boundary.