A New Acceleration Factor Decision Method for ICCG Method Based on Condition Number

Abstract

The ICCG method is widely used to solve a sparse symmetric linear system which results from the finite element method. In order to improve the convergence property of the ICCG method, the introduction of the acceleration factor was proposed. The automatic acceleration factor decision method, using the incomplete Cholesky decomposition of a coefficient matrix, has been previously proposed. However, when employing the previously proposed automatic decision method, much more iterations of ICCG method are sometimes necessary, compared with using the optimum acceleration factor, which minimizes the number of ICCG iterations. In this paper, we propose a new acceleration factor decision method. The proposed method takes into account the condition number of the coefficient matrix. It is well known that the condition number represents the quality of the matrix, so the optimum acceleration factor should be decided to minimize the condition number of the coefficient matrix. However, the condition number of the coefficient matrix is not almost available due to requiring a large memory in computing. Therefore, we develop a new method using submatrix, that does not need a large memory. The procedure and demonstration of the proposed method are described in this paper.