Optimization of block size for volume integral equation‐based characteristic basis function method

Abstract

The block size of the characteristic basis function method (CBFM) based on volume integral equation (VIE) is optimized to improve the efficiency on analyzing the scattering from dielectric objects in this study. Several literatures have discussed the optimum block size of surface integral equation (SIE)based CBFM, which achieved the minimum CPU time for analyzing conductor objects. However, due to the differences of basis functions, the conclusions derived from SIE-based CBFM are not applicable for VIE-based CBFM. This study presents the relationship between the Schaubert-Wilton-Glisson (SWG) basis functions and characteristic basis functions (CBFs), which paves the way for evaluating the computational complexity of VIE-based CBFM. In addition, the Sherman-Morrison-Woodbury formula-based algorithm (SMWA) and adaptive cross approximation (ACA) algorithm are combined to accelerate the CBFs generation and reduced matrix construction. Based on the computational complexity of the VIE-based CBFM combined with SMWA and ACA, the optimal number of blocks for VIE-based CBFM is derived theoretically.Numerical results of homogeneous and inhomogeneous dielectric objects scattering problems are presented to validate the feasibility and accuracy of the proposed optimization method.