Solution of Volume–Surface Integral Equation Accelerated by MLFMA and Skeletonization

A fast algorithm for solving large multi-scale scattering problems by the volume–surface integral equation (VSIE) is proposed. The sub-matrices of the near-field interactions (NFIs) in terms of the multi-level fast multipole algorithm (MLFMA) are compressed by the skeletonization after the theoretical and numerical investigations on their low-rankness are carried out. A block-diagonal preconditioner (BDP) based on the recursive skeletonization (RS) is developed to improve the conditioning of the impedance matrix of the VSIE. The rules to select hyperparameters in the proposed method are given. Numerical experiments conducted on scattering problems show the performance of the proposed algorithm.