Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering

• Authors: R. Hiptmair
• Venue: SIAM Journal on Numerical Analysis
• Year: 2003

We consider the scattering of monochromatic electromagnetic waves at a dielectric object with a rough surface. We 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, we can establish coercivity of the coupled variational problem, provided that the frequency is away from resonant frequencies. Discretization relies on both curl-conforming edge elements inside the scatterer and $\bDiv$-\break conforming boundary elements for the surface currents. The splitting idea, adjusted to the discrete setting, permits us to show uniform stability of the discretized problem. We exploit it to come up with a priori convergence estimates.