Profiling General-Purpose Fast Multipole Method (FMM) Using Human Head Topology

In this study, we characterize the performance of the fast multipole method (FMM) in solving the Laplace and Helmholtz equations. We use the FMM library developed by the group of Dr. L. Greengard. This version of the FMM algorithm is multilayer with no priori limit on the number of levels of the FMM tree, although, after about thirty levels, there may be floating point issues. A collection of high-resolution human head models is used as test objects. We perform a detailed analysis of the runtime and memory consumption of the FMM in a wide range of frequencies, problem sizes, and precisions required. Although we focus on two-manifold test cases, the results are generalizable to other topologies as well. The tests are conducted on both Windows and Linux platforms. The results obtained in this study can serve as a general benchmark for the performance of FMM. It can also be employed to pre-estimate the efficiency of numerical modeling methods (e.g., the boundary element method) accelerated by FMM.