Fast Direct Solution of Electromagnetic Scattering with Modified HODLR Solver

An efficient fast direct solver of method of moments (MoM) is developed based on hierarchically off-diagonal low-rank (HODLR) structure. HODLR structure exploit that the off-diagonal matrices are rank deficient. In this paper, a modified method is proposed to construct off-diagonal matrices of HODLR structure. With admissible condition, the off-diagonal matrices are decomposed into far field interactions and near field interactions. The far field interactions and near field interactions are compressed into low-rank sub-matrices respectively. The off-diagonal matrices can be recompressed into low-rank matrices by aggregating all sub-matrices. Numerical results indicate the efficacy and accuracy of the proposed method compared with conventional methods.