The MDA-SVD Algorithm for Fast Direct or Iterative Solution of Discrete Integral Equations

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. In EuCAP 2006, the 3-D MLMDA was improved with new placement of equivalent functions and a SVD post-compression step. The resulting algorithm was named MDA-SVD and is comparable with the multilevel fast multipole algorithm (MLFMA) and the adaptive cross approximation (ACA) in terms of computation time and memory requirements. Like the ACA, the MDA-SVD algorithm can be implemented on top of an existing MoM code with most commonly used Green´s functions, but the MDA-SVD is much more efficient in the analysis of planar or piece-wise planar objects, like printed antennas.