Comparisons of FMM implementations employing different formulations and iterative solvers

In order to solve large mathematical formulations of real-life electromagnetic problems, we must use advances in both solution algorithms and computer hardware. The fast multipole method (FMM) and its multilevel version, the multilevel fast multipole algorithm (MLFMA), are two of the preferred choices for the algorithm due to their reduced computational complexities and memory requirements. A parallel architecture is preferred for the hardware due to its increased computing power, with a consequent parallel implementation of the MLFMA. Some of the high-level choices that need to be made to implement the MLFMA are as follows: integral-equation (IE) formulation - EFIE, MFIE, or combined-field IE (CFIE); iterative solver - Krylov-subspace methods such as different conjugate gradient methods or generalized minimal residual; preconditioner - near-field (NF), filtered NF, block-diagonal or diagonal preconditioners, or no preconditioner; initial guess. These parameters are extensively investigated. For this purpose, a series of scattering problems of various sizes (at different frequencies) containing different numbers of unknowns are used as a testbed.