Multiresolution Preconditioners for Solving Realistic Multi-Scale Complex Problems

Abstract

In this work, the hierarchic multiresolution (MR) preconditioner is combined with the multilevel fast multipole algorithm-fast Fourier transform (MLFMA-FFT) and eficiently parallelized in multicore computers for computing electromagnetic scattering and radiation from complex problems exhibiting deep multi-scale features. The problem is formulated using the thin-dielectric-sheet (TDS) approximation for thin dielectric materials and the electric and combined field integral equations (EFIE/CFIE) for conducting objects. The parallel MLFMA-FFT is tailored to accommodate the MR hierarchical functions, which provide vast improvement of the matrix system conditioning by accurately handling multi-scale mesh features in different levels of detail. The higher (coarser) level hierarchical functions are treated by an algebraic incomplete LU decomposition preconditioner, which has been ef ciently embedded into the parallel framework to further accelerate the solution. Numerical examples are presented to demonstrate the precision and eficiency of the proposed approach for the solution of realistic multi-scale scattering and radiation problems.