Preconditioning techniques for domain integral equations

In this paper, we consider so-called optimal circulant preconditioners for discretized integral operators describing the scattering of steady state electromagnetic waves by penetrable objects embedded in homogeneous background media. For two-dimensional scattering problems, we show that the preconditioners may significantly increase the convergence rate of an iterative solver. Possible extensions are discussed as well and two numerical examples illustrate the performance of the preconditioner.