Complex Incomplete Cholesky Factorization Preconditioned Bi-conjugate Gradient Method
Keywords:
Complex Incomplete Cholesky Factorization Preconditioned Bi-conjugate Gradient MethodAbstract
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 illconditioned 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 biconjugate 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.
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