New and more efficient formulation of MLMDA for arbitrary 3D antennas and scatterers

The Multilevel Matrix Decomposition Algorithm (MLMDA) was originally developed by Michielsen and Boag for 2-D TMz scattering problems and later implemented in 3-D by Rius et al. The 3-D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for arbitrary 3-D problems it was not as efficient as the Multilevel Fast Multipole Algorithm (MLFMA). This paper will introduce some improvements in 3-D MLMDA, like new placement of equivalent functions and SVD post-compression, that make it comparable with MLFMA in terms of computation time and memory requirements, but more accurate.