Matrix compresion technique based on the multilevel characteristic basis function method

An efficient procedure for the solution of large electromagnetic problems using Method of Moments (MoM) [1] rigorous analysis is presented in this work. Computational burden of the method is overcome using a technique that reduces the number of the unknowns and, hence, the matrix size. It is based in the generation of Characteristic Basis Functions [2, 3] (CBFs) over large arbitrary surfaces using a multilevel scheme. The first step is to partition the original object into subdomains and then derive the CBFs for these domains by solving for the currents induced by a set of components of the Plane Wave Spectrum (PWS). Next, we aggregate the adjacent domains to obtain enlarged CBFs by expanding the original ones in terms of the weighted plane waves used to compute them. This process can be performed iteratively and involves fast, non-expensive matrix manipulation. We obtain a progressive decrease of the number of unknowns, as we increase the domain size, by following the procedure described above.