Parallel Self-Tuning MLFMA Library

The Multilevel Fast Multipole Algorithm (MLFMA) has gained considerable attention for its ability to reduce the computational complexity of matrix-vector multiplies arising in the integral equation-based iterative solution of electromagnetic scattering problems. The MLFMA evaluates fields due to known source constellations comprising N discrete sources in a hierarchical framework that requires (i) breaking up the source into groups, (ii) characterizing each group’s far field signatures, and (iii) translating these far-field signatures between group centers to arrive at observer fields. Steps (ii) and (iii) are often accomplished with the aid of spherical scalar and vector interpolators and filters. The MLFMA reduces the cost of evaluating fields from O(N) to O(NLogN). However, the multiplicative constant inherent in these complexity estimates, as well as the MLFMA’s accuracy, heavily depends on the choice of some key parameters. First, there is the number of multipoles L used to compute the MLFMA’s translation operators. Second, there is the oversampling ratio s used to sample far-field signatures. And third, there is the number of interpolation points p used when locally interpolating fields during the upward traversal of the MLFMA tree. (Other parameters exist, but these are the three most important ones).