An OSRC Preconditioner for the EFIE

The Electric Field Integral Equation (EFIE) is a well-established tool to solve electromagnetic scattering problems. However, the development of efficient and easy to implement preconditioners remains an active research area. In recent years, operator preconditioning approaches have become popular for the EFIE, where the electric field boundary integral operator is regularised by multiplication with another convenient operator. A particularly intriguing choice is the exact Magnetic-to-Electric (MtE) operator as regulariser. But, evaluating this operator is as expensive as solving the original EFIE. In work by El Bouajaji, Antoine and Geuzaine, approximate local Magnetic-to-Electric surface operators for the time-harmonic Maxwell equation were proposed. These can be efficiently evaluated through the solution of sparse problems. This paper demonstrates the preconditioning properties of these approximate MtE operators for the EFIE. The implementation is described and a number of numerical comparisons against other preconditioning techniques for the EFIE are presented to demonstrate the effectiveness of this new technique.