A Novel Parallel Direct Solver Using Adaptive Cross Approximation for Analysis of Electromagnetic Radiation Problems With Complex Structures

In this communication, a novel parallel fast direct solver based on adaptive cross approximation (ACA) is presented for solving complex electromagnetic radiation problems. First, considering the significant differences in matrix rank and element magnitudes between the submatrix corresponding to the system excitation and the submatrix constructed by the Electric Field Integral Equation (EFIE) + Poggio–Miller–Chang–Harrington–Wu (PMCHW) formulation, we divide the whole matrix into two parts accordingly. Then, contrary to the traditional methods of compressing the original matrix directly, we compress the off-diagonal blocks after lower/upper (LU) decomposition. As a result, the accuracy problem of the traditional methods is solved. Finally, a parallel strategy based on block-cyclic distribution is designed to achieve the distributed parallelization of the proposed solver on high performance computing (HPC) clusters. Numerical examples demonstrate the accuracy, effectiveness, and scalability of the proposed solver, which achieves more than 70% parallel efficiency when the CPU cores are increased from 72 to 720, and an excellent memory complexity of ${O}$ ( ${N}^{4/3}$ log ${N}$ ).