Fast Direct Surface Integral Equation Solution for Electromagnetic Scattering Analysis With Skeletonization Factorization

Abstract

A fast direct surface integral equation (SIE) solver based on a novel skeletonization factorization scheme is proposed for electromagnetic scattering from electrically large and complex conducting objects. A novel skeletonization strategy is utilized to accelerate the skeletonization with the Huygens’ principle and proxy surface. Different from the auxiliary Rao–Wilton–Glisson (RWG) bases used in conventional methods, the constant basis functions are employed to discretize Huygens’ surface in the novel skeletonization strategy. By doing these, the number of basis functions on the surface can be greatly reduced. Moreover, the skeleton basis functions in selected neighboring groups are used to account the neighboring interactions. With these ideas, the dimensions of proxy matrix constructed for selecting skeleton can be greatly reduced. Next, a recursive skeletonization factorization (RSF) is proposed to further enhance the computational efficiency. The inverse of system matrix can be expressed as the multiplication factorization form with RSF rather than conventional recursively additive low-rank update. The computational time would be significantly saved with the application of RSF. A series of the numerical results are presented to show both the accuracy and effectiveness of the proposed method.