Ralf Hiptmair (Tuebingen. Germany)

FEM-BEM Coupling in electromagnetic scattering

Abstract

I consider the scattering of monochromatic electromagnetic waves at a dielectric object with a rough surface. I investigate the coupling of a weak formulation of Maxwell's equations inside the scatterer with boundary integral equations that arise from the homogeneous problem in the unbounded region outside the scatterer. The symmetric coupling approach based on the full Calderón projector for Maxwell's equations is employed. By splitting both the electric field inside the scatterer and the surface currents into components of predominantly electric and magnetic nature, I can establish coercivity of the coupled variational problem, provided that the frequency is off a resonant frequency of the dielectric object. Discretization relies on both curl-conforming edge elements inside the scatterer and div$_\Gamma$-conforming boundary elements for the surface currents. The splitting idea adjusted to the discrete setting permits me to show uniform stability of the discretized problem. I exploit it to come up with a-priori convergence estimates.