Complex Incomplete Cholesky Factorization Preconditioned Bi-conjugate Gradient Method

Linear systems generated by finite element method (FEM) always have a symmetrical sparse system matrix, which requires a large amount of computation and memory effort to access its zero elements. To address this problem, a fully-sparse storing scheme is proposed to store only nonzero symmetrical elements of the sparse system matrix. Meanwhile, for some ill-conditioned system matrixes, conventional iterative solution methods may incur such problems as slow convergence and even failure of convergence. To solve this problem, we further develop a fast convergent preconditioned bi-conjugate gradient method (PBCG) based on a real incomplete Cholesky factorization preconditioner. Numerical experiments show that the proposed method accelerates the convergence and is applicable for the large-scale complex linear systems.