A Fast Converging Boundary Element Method for the Scattering by Perfectly Conducting Non-orientable Objects

Abstract

The electric field integral equation can describe scattering by closed and open surfaces, surfaces containing junctions, and even non-orientable surfaces. The boundary element discretisation of this equation results in linear systems whose condition number grows as the square of the inverse mesh size. This eventually leads to systems that in practice cannot be solved, not even when using powerful iterative solvers such as GMRES and efficient matrix compression algorithms such as the fast multipole algorithm or an H-matrix based low rank representation. As a remedy, Calderón preconditioners are used to significantly reduce the number of iterations required to reach an acceptable solution. This type of preconditioners are available for open and closed surfaces, and recently also for surfaces containing junctions. In this contribution, a Calderón type preconditioner will be constructed for the electric field integral equation applied to non-orientable surfaces such as the Moebius strip. It is based on a redundant representation for the induced current, and a block-diagonal preconditioning strategy. Numerical experiments corroborate the correctness and efficiency of this approach.