A Fast Direct Matrix Solver for Surface Integral Equation Methods for Electromagnetic Wave Scattering from Non-penetratable Targets

摘要

A direct solver is developed herein for solving dense matrix equations resulted from the application of surface integral equation methods. The proposed algorithm exploits the smoothness of the far field and computes a low rank decomposition of the off-diagonal coupling blocks of the matrices through a set of skeletonalization processes. Then the artificial boundary is introduced to represent the far field couplings more efficiently thus accelerate the algorithm. Moreover, a recursive multi-level version of the algorithm has also been implemented. Through numerical examples, we found that the proposed multi-level direct solver scales as good as O(N~(1.3)) for moderate EM problems. Furthermore, due to the low rank feature of the so-called h-refinements, the algorithm exhibits O(N) complexity with the decrease of the discretization size.