Boundary element methods for Maxwell's equations on non-smooth domains

Variational boundary integral equations for Maxwell's equations on Lipschitz surfaces in ${\mathbb R}^3$ are derived and their well-posedness in the appropriate trace spaces is established. An equivalent, stable mixed reformulation of the system of integral equations is obtained which admits discretization by Galerkin boundary elements based on standard spaces. On polyhedral surfaces, quasioptimal asymptotic convergence of these Galerkin boundary element methods is proved. A sharp regularity result for the surface multipliers on polyhedral boundaries with plane faces is established.