In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic mul...In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.展开更多
The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume disc...The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion equations.The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing considerations.The spectral property of the preconditioned matrix is then analyzed.The practical strategy is considered sequentially and in parallel.Finally,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.展开更多
文摘In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.
基金supported by the National Natural Science Foundation of China(Grant 11971414)Hunan National Applied Mathematics Center(Grant 2020ZYT003)the Research Foundation of Education Bureau of Hunan(Grant 21B0162).
文摘The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the threedimensional multi-group radiation diffusion equations.The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing considerations.The spectral property of the preconditioned matrix is then analyzed.The practical strategy is considered sequentially and in parallel.Finally,numerical results illustrate the numerical robustness,computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems,showing its competitiveness with many existing block preconditioners.
