Accelerated Direct Solution of Electromagnetic Scattering via Characteristic Basis Function Method With Sherman-Morrison-Woodbury Formula-Based Algorithm

The characteristic basis function method has been proposed to accelerate the direct solution of the method of moments by reducing the number of unknowns. However, with the increase in the target size, the reduced matrix will still become too large to directly solve and store. In this communication, the algorithm based on the Sherman-Morrison-Woodbury (SMW) formula is employed to address this problem for the first time. It compresses the reduced matrix into a product of block diagonal matrices with the aid of the SMW formula and the adaptive cross approximation. Subsequently, the inverse of the reduced matrix can be easily obtained by the inverses of these block diagonal matrices. The numerical results about the electromagnetic scattering are shown to demonstrate the performance of the proposed method.