A Ternary Parallelization Approach of MLFMA for Solving Problems with Billions of Unknowns

摘要

A flexible ternary parallelization approach of the multilevel fast multipole algorithm (MLFMA) is presented for the efficient solution of extremely large 3D scattering problems. In the ternary parallelization approach, the MLFMA tree is categorized into plane-wave partitioning, hierarchical-structure partitioning and box partitioning levels. A grouped transition level is specially designed to switch partitions on the intermediate level between the hierarchical-structure partitioning and box partitioning levels. The ternary strategy can achieve as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in choosing the number of processes. The accuracy of the solutions is demonstrated by comparing radar cross section (RCS) of a sphere with 2400 wavelengths diameter and 4,231,421,328 unknowns calculated by MLFMA and mie series. Furthermore, the solution of complicated objects with length 6131 wavelengths and 4,739,139,936 unknowns is also presented, which is the largest problem solved by MLFMA to date.