A hierarchical fast direct solver for the method of moment

A hierarchical fast direct solver is proposed for the method of moment (MoM) based on the low-rank compression method. The dense impendent matrix of MoM is decomposed into a hierarchical off-diagonal low-rank (HODLR) system with the rank deficiency of the off-diagonal matrixes for far field interactions. Furthermore, the HODLR matrix can be easily expressed with a multiplication of several diagonal matrixes. Each small diagonal matrix block can be inversed easily. So that, the current solution of the integral equation can be expressed with a series of matrix vector products (MVPs) with given excitation vectors.