Fast Direct Solution of Method of Moments Linear System

A novel algorithm, the compressed block decomposition (CBD), is presented for highly accelerated direct (noniterative) method of moments (MoM) solution of electromagnetic scattering and radiation problems. The algorithm is based on a block-wise subdivision of the MoM impedance matrix. Impedance matrix subblocks corresponding to distant subregions of the problem geometry are not calculated directly, but approximated in a compressed form. Subsequently, the matrix is decomposed preserving the compression. Examples are presented of typical problems in the range of 5000 to 70000 unknowns. The total execution time for the largest problem is about 1 h and 20 min for a single excitation vector. The main strength of the method is for problems with multiple excitation vectors (monostatic RCS computations) due to the negligible extra cost for each new excitation. For radiation and scattering problems in free space, the numerical complexity of the algorithm is shown to be N ² and the storage requirements scale with N ^3/2 .