The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems

Chapter 4Parallelization of MLFMA for the Solution of Large-Scale Electromagnetics Problems

Parallelization of MLFMA is essential for the solution of very large electromagnetics problems discretized with millions of unknowns. This chapter presents the hierarchical partitioning strategy and various high-performance computing techniques for the efficient parallelization of MLFMA on distributed-memory architectures. Due to improved load balancing and reduced communications, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. Higher parallelization efficiency translates into the ability to solve larger problems with available resources. Using optimizations and load-balancing algorithms along with the hierarchical strategy allows for accurate analysis of complicated targets that are larger than 1000 on moderately parallel computers.

4.1 On the Parallelization of MLFMA

Because of the complicated structure of the algorithm, parallelization of MLFMA is not trivial and several issues must be carefully considered.

• Partitioning: The main task in the parallelization of MLFMA is partitioning the data among processors with minimal duplication. As discussed in Section 4.6.7, the hierarchical partitioning strategy allows for efficient distribution of the multilevel tree structure.
• Load balancing: Parallelization ...