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Abstract
The efficient solution of block tridiagonal linear systems arising from the discretization of convection–diffusion problem is considered in this paper. Starting with the classical nested factorization, we propose a relaxed nested factorization preconditioner. Then, several combination preconditioners are developed based on relaxed nested factorization and a tangential filtering preconditioner. Influence of the relaxation parameter is numerically studied, the results indicate that the optimal relaxation parameter should be close to but less than 1. The number of iteration counts exhibit an extremely sensitive behaviour. This phenomena resembles the behaviour of relaxed ILU preconditioner. For symmetric positive-definite coefficient matrix, we also show that the proposed combination preconditioner is convergent. Finally, numerous test cases are carried out with both additive and multiplicative combinations to verify the robustness of the proposed preconditioners.
Acknowledgements
The authors thank the anonymous reviewers for their helpful comments and suggestions that considerably improve the paper. Some of the revisions were done when the first author had postdoctoral positions at KU Leuven and Fraunhofer ITWM.
Funding
Q. Niu was partially supported by National Natural Science Foundation of China [Nos. 11301420]. P. Kumar was mainly supported by CORDIS grant at INRIA, Ile-de-France. Part of the work of L. Grigori and F. Nataf has been supported by French National Research Agency (ANR) through COSINUS program [project PETAL no ANR-08-COSI-009].