Approximate Schur preconditioners for efficient solutions of dielectric problems formulated with surface integral equations

We propose direct and iterative versions of approximate Schur preconditioners to increase robustness and efficiency of iterative solutions of dielectric problems formulated with surface integral equations. The performance of these preconditioners depends on the availability of fast and approximate solutions to reduced matrix systems. We show that sparse-approximate-inverse techniques provide a suitable mechanism for this purpose. The proposed preconditioners are demonstrated to significantly improve convergence rates of dielectric problems formulated with two different surface integral equations.