Block Size Optimization of CBFM for Scattering Problems

Abstract

The characteristic basis function method (CBFM) was developed as an algorithm to accelerate the analysis based on direct matrix solver. In CBFM, the optimum block size greatly influences the overall analysis time. In this paper, we propose a guideline for setting the optimal block size that can be applied to every algorithm based on CBFM. Rough estimation of the optimal block size is L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rough</sup> ≈ 0.05N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6/29</sup> , and the exact optimal block size can be determined through preprocessing based on rough estimation. Numerical results of electromagnetic scattering problems are shown to demonstrate the performance of the proposed method.