Efficient parallelization of a CBFM-MLFMA scheme for the computation of complex electromagnetic problems

For many cases, the reduced matrix can be dealt with by using direct solvers. However, when the electrical size of the structures under analysis is very large, the characteristic basis function method (CBFM) reduced matrix can become so large as to preclude its solution without resorting to an iterative algorithm, in spite of an important reduction of the number of unknowns. In these cases, the additional problem of the large amount of memory needed to store the reduced matrix is found. This problem can be overcome by employing the multilevel fast multipole algorithm (MLFMA) which involves storing only the near-field terms of the reduced coupling matrix. In these cases, an iterative method is needed to solve the reduced matrix equation. The stabilized bi-conjugated gradient method (BiCGM) is used. The coupling terms that correspond to geometrically close blocks are calculated by means of direct matrix-vector products, while far-field coupling terms are efficiently computed through the MLFMA.