2023 Volume 31 Pages 875-884
This paper focuses on a solution process of a sequence of linear systems having an asymmetric coefficient matrix. We propose a new subspace correction (SC) preconditioning method based on error vector sampling for asymmetric coefficient matrices. In the method, we identify approximate left and right singular vectors associated with small singular values using the sampled error vectors calculated after the first solution step. Using these singular vectors, we construct auxiliary matrices to specify the subspace used in the SC preconditioning. We applied the proposed preconditioning method to an ILU(0)-Bi-CGSTAB solver in additive Schwarz manner. To examine the proposed preconditioning method, we conducted numerical tests using matrices downloaded from the SuiteSparse Matrix Collection database. Numerical tests showed that the proposed method could reduce the number of iterations to convergence and the solution time in many test cases, which confirms the effectiveness of the method. Moreover, the proposed method succeeded to get convergence for some test problems that the ILU(0) preconditioned solver could not solve.
