Fast direct solution of characteristic basis function method using ACA-based LU decomposition

Abstract

This paper presents an adaptive cross approximation (ACA)-based LU decomposition scheme to accelerate direct solution of the characteristic basis function method (CBFM). It takes advantage of the rank-deficient nature of the reduced matrix in CBFM to compress the LU decomposition matrices through the ACA. Therefore, the proposed method can remarkably reduce the memory requirement and accelerate the lower and upper triangular matrices assembly computation as well as matrix-vector multiplication in the solution of the CBFM. Numerical results about the scattering problems are given to demonstrate the accuracy and efficiency of the proposed method.