Accelerated Sherman–Morrison–Woodbury Formula-Based Preconditioner With Characteristic Basis Function Method

Abstract

Based on the Sherman–Morrison–Woodbury (SMW) formula and the characteristic basis function method (CBFM) in the iterative solution of the electric field integral equation, a fast preconditioner algorithm is proposed in this letter. The SMW preconditioner is an improved version of the conventional block diagonal preconditioner and can be constructed as a sparse approximate inverse matrix of the impedance matrix to reduce the number of iterations. The CBFM is applied to reduce the storage costs of the compressed impedance and the preconditioner. The reduced preconditioner can efficiently accelerate the matrix-vector product. For validation, the numerical results of several perfect electric conductor objects are obtained to demonstrate the performance of the iterative solution time and the memory requirement of the preconditioner.