Hierarchical Matrix-Based Direct Solver for Permuted Poggio-Miller-Chang-Harrington-Wu-Tsai Equation

With some rearrangement of the basis and testing functions, a permuted impedance matrix of the Poggio- Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation is obtained, where the canonical hierarchical matrix-based direct solver can effectively function. In this paper, the feasibility of hierarchical matrix schemes in permuted PMCHWT is derived. Compared with using four hierarchical matrices on four submatrices in the classic formula, the method using hierarchical matrices on the permuted formula can reduce both the memory of storage and the time of decomposition. Several numerical results are provided to validate the permutation combined with the hierarchical matrix and to reveal the efficiency and accuracy of the proposed scheme.