Sparsified Multi-level Adaptive Cross Approximation-Characteristic Basis Function Method for Fast Electromagnetic Scattering Analysis. Issue 7 (2nd October 2016) - Chen, Xinlei
ABSTRACT: With the increase of block size, the amount of calculation and storage of the recently developed sparsified adaptive cross approximation for compressing the impedance submatrix of well-separated blocks will become as large as O ( s 2 M ) and O ( sM ), respectively, where M is the number of unknowns in each block, and s is the effective rank of the impedance submatrix. To address this issue, an improved sparsified adaptive cross approximation, termed as sparsified multi-level adaptive cross approximation, is presented in this article. The sparsified multi-level adaptive cross approximation uses the multi-level adaptive cross approximation to exhibit a faster and sparser compression of the sparsified adaptive cross approximation inner matrices. As a result, the computational time and storage can be reduced to O ( s 3 ) + O ( sM ) and O ( s 2 ) + O ( M log s ), respectively, where log s « s « M . Furthermore, the characteristic basis function method is used to further reduce the storage of the sparsified multi-level adaptive cross approximation by compressing its outer matrices. Numerical results about the electromagnetic scattering are given to verify the advantages of the proposed sparsified multi-level adaptive cross approximation-characteristic basis function method.