Singular Integration in BEM by Interpolation: The EFIE Case

摘要

An approach of populating all weakly singular and near weakly singular integrals enchanted in Electrical Field Integral Equation (EFIE) Boundary Element Methods (BEM) using universal look-up-tables and multi-dimensional interpolation is outlined. The method is compared to a state-of-the-art singularity subtraction method for the lowest order Rao-Wilton-Glisson (RWG) basis functions in various PEC triangular meshes. For common triangle, weakly singular, interactions the proposed approach out-performs singularity subtraction integration by 3 - 4 decimal digits, while offering up to 100 × speed-ups. Early implementations for common edge, near weakly singular, interactions show 40 × speed-ups but at a somewhat lower, yet acceptable, accuracy.