An Implementation of Parallel MLFMA on a Cluster of Computers with Distributed Memory

MLFMA (multilevel fast multipole algorithm) has made a great achievement in solving electromagnetic scattering problems. In this paper we present our efforts to implement parallel MLFMA on a cluster of computers with distributed memory. In order to get a good load balancing a hybrid partition scheme for the distributed tree is used. We present a concept of virtual grids that can be used to easily determine the sender and receiver during interpolation and anterpolation for distributed levels and give some theorems governing the locations and relationships of real and virtual grids, and also give their proofs. Some test results demonstrate that our implementation has a high parallel efficiency for problems with a size of less than 2 million unknowns.