Sparsified Multi-level Adaptive Cross Approximation-Characteristic Basis Function Method for Fast Electromagnetic Scattering Analysis

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(Mlogs), 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.