Direct Solver Based on the Multilevel Nonuniform Grid Approach for Quasi-Planar Electromagnetic Scattering Problems

A direct solver for quasi-planar electromagnetic scattering problems is developed. The algorithm consists of a multilevel domain decomposition, a rank revealing procedure (RRP), and a direct solution of the resulting compressed system of linear algebraic equations. The RRP is performed step by step from the bottom to top levels and is based on the singular value decomposition (SVD) using the interpolation grids of the Multilevel Nonuniform Grid (MLNG) approach. The efficiency of the solver is demonstrated by numerical experiments.