An Efficient Matrix Equation Parallel Direct Solver for Higher-Order Method of Moments in Solution of Complex Electromagnetic Problems

An efficient parallel direct solver with a new pivoting scheme is presented for solving impedance matrix equations generated by the higher-order method of moments in high-frequency electromagnetic computation. Given the diagonal dominance characteristic of the dense complex impedance matrices, a local-block pivoted parallel LU decomposition algorithm is developed in the solver, which requires less communication time than the Intel math kernel library and the communication avoiding LU solver, because the pivoting operations execute in local blocks of the processes. To demonstrate the stability and performance of the algorithm, electromagnetic radiation and scattering from complex models containing metallic and dielectric structures are computed. When up to 1200 CPU cores are used, numerical results show that the solving time of the proposed LU solver is significantly reduced.