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. Thesecan 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.

翻译：电场积分方程（EFIE）是求解电磁散射问题的经典工具。然而，开发高效且易于实现的预处理器仍是一个活跃的研究领域。近年来，算子预处理方法在EFIE中逐渐流行，其基本思想是通过将电场边界积分算子与另一个便捷算子相乘来实现正则化。其中特别引人关注的选择是使用精确的磁电（MtE）算子作为正则化算子。但计算该算子的代价与求解原始EFIE相当。在El Bouajaji、Antoine和Geuzaine的工作中，针对时谐Maxwell方程提出了近似局部磁电表面算子。这些算子可通过求解稀疏问题高效计算。本文论证了这些近似MtE算子对EFIE的预处理特性。文中描述了实现方法，并与其他EFIE预处理技术进行了多项数值对比，以展示该新技术的有效性。