Multiscale Compressed and Spliced Sherman–Morrison–Woodbury Algorithm With Characteristic Basis Function Method

In this paper, a multiscale compressed and spliced Sherman-Morrison-Woodbury algorithm (MSCS-SMWA), based on the characteristic basis function method (CBFM), has been presented to accelerate direct solutions of electromagnetic scattering. The impedance matrix or reduced matrix can be compressed into block diagonal matrices with the adaptive cross approximation (ACA) and easily obtained the matrix inverse with this method. The MSCS-SMWA method is combined with a multiscale compressed ACA and a multiscale spliced singular value decomposition (SVD). The numerical results of several perfect electric conducting (PEC) objects are validated to demonstrate the performance of this method. Compared with the conventional methods, SMWA with the ACA and CBFM, the simulation results of the proposal method have been shown that the computation time and storage requirements have reduced about 10.77% and 44.22%, for the sphere with 10λ radius. Also, it costs 49.16% less CPU time and 1.54% less memory than the conventional method with SVD.