Solving Electromagnetic Scattering Problems with Over 10 Billion Unknowns with the Parallel MLFMA

We present in this paper a flexible and efficient ternary parallelization approach for MLFMA for the solution of extremely large 3D scattering problems that are modelled with over 10 billion unknowns. In the ternary parallelization approach, the MLFMA tree is categorized into plane wave partitioning, hierarchical-structure partitioning and box partitioning levels via a top-down approach. An inner-group transition level is designed for switching partitions on the intermediate level between the hierarchical-structure partitioning and box partitioning levels. The ternary strategy can realize as high parallel efficiency as the hierarchical partitioning strategy while maintaining flexibility in selecting the total number of processes. A scalable and efficient auxiliary-tree-based parallel mesh refinement technique and a simple and effective hybrid octree storage strategy are designed to facilitate the realization of fast full-wave simulation on a scale of over 10 billion unknowns with the ternary MLFMA. The accuracy of the solutions is evaluated by comparing the radar cross-sections (RCSs) of a sphere of diameter 3,042 wavelengths with 10,773,415,728 unknowns that were calculated via MLFMA and the Mie series. It is the largest number of unknowns solved to date. Furthermore, the solutions for complicated objects, namely, a ship and an aircraft with the size larger than 10 thousand wavelengths and over 10 billion unknowns, are presented.