Solving Electromagnetic Scattering from Conducting Objects with Novel Skeletonization Based Fast Direct Solver

In this paper, we present a novel skeletonization based fast direct solver for analyzing electromagnetic scattering from electrically conducting objects. The contributions of the present algorithm involve two aspects: reducing the cost for filling proxy matrices and enhancing the inverse process. To reduce the filling time of proxy matrices, the proxy surface is discretized by a series of points. The number of the points is considerably small compared with conventional method. Consequently, the dimensions of the proxy matrices for each group can be reduced remarkably in this way. On the other hand, a multiplicative factorization technique, recursive skeletonization factorization, is utilized in the inverse process. The projection matrices obtained by interpolative decomposition can be used directly with high efficiency. The remained block diagonal matrices after factorization can be easily solved by LU decomposition. The accuracy and efficiency of the proposed method will be validated by numerical results.