Massively Parallel Multilevel Fast Multipole Algorithm for Extremely Large-Scale Electromagnetic Simulations: A Review

Since the first working multilevel fast multipole algorithm (MLFMA) for electromagnetic simulations was proposed by Chew’s group in 1995, this algorithm has been recognized as one of the most powerful tools for numerical solutions of extremely large electromagnetic problems with complex geometries. It has been parallelized with different strategies to explore the computing power of supercomputers, increasing the size of solvable problems from millions to tens of billions of unknowns, thereby addressing the crucial demand arising from practical applications in a sense. This paper provides a comprehensive review of state-of-the-art parallel approaches of the MLFMA, especially on a newly proposed ternary parallelization scheme and its acceleration on graphics processing unit (GPU) clusters. We discuss and numerically study the advantages of the ternary parallelization scheme and demonstrate its flexibility and efficiency.