Modified Multilevel Fast Multipole Algorithm for Stationary Iterative Solvers

A modified multilevel fast multipole algorithm (MLFMA) is proposed to accelerate the partial matrix vector products required in each iteration of the buffered block forward backward method (BBFB), which is a stationary iterative solver used to solve electromagnetic wave propagation and scattering problems. Applying the standard MLFMA to the computation of the partial matrix vector products results in significant redundancy, causing a loss of efficiency of the stationary method. The efficiency can be regained by implementing a modified MLFMA that is based on two simple algorithms. These involve determining precisely what a small subset of cubes is in need of having their associated fields recomputed in the MLFMA upward or downward process during each step of the BBFB process. Numerical experiments are presented to demonstrate the efficiency and the accuracy of the proposed method over the standard method. Although the modified MLFMA is only applied for the BBFB in this paper, it can, in principle, be extended for application to other stationary methods.