Efficient Solution of Electromagnetic Scattering From Dielectric Objects via Characteristic Basis Function Method Based on Large-Size Blocks With Multilevel Subdivision

The characteristic basis function method (CBFM) based on large-size blocks with multilevel subdivision is proposed to improve the analysis of electromagnetic scattering from dielectric objects. The small-size blocks' strategy is widely used to alleviate the computational burden on generating the characteristic basis functions (CBFs) in the perfectly electrical conducting (PEC) object problems. However, when transplanted into the dielectric objects, this strategy performs poorly according to our empirical results. For adapting the CBFM to dielectric objects, the large-size blocks' strategy is proposed for the first time. Primarily, it remarkably reduces the number of CBFs required for the reduced matrix. Furthermore, the multilevel subdivision on the blocks is adopted to convert the full-rank impedance matrices of the blocks into hierarchical matrices, leading to great advantage in two aspects. In the CBFs' generation, the self-impedance matrices with hierarchical structure can be easily inversed by a recursive inversion algorithm based on the Sherman-Morrison-Woodbury (SMW) formula, which significantly cuts down the consumption in terms of CPU time and memory requirement. In addition, the hierarchical structure is taken advantage of by the multiscale adaptive cross approximation (MS-ACA) to accelerate the filling of the mutual-impedance matrices of the adjacent blocks. The numerical results of several dielectric objects are presented to demonstrate the accuracy and efficiency of the proposed method.