Two sides tangential filtering decomposition
Journal of Computational and Applied Mathematics
Parallel design and performance of nested filtering factorization preconditioner
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter is determined by Fourier analysis. With the choice of optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is $${{\mathcal O}(h^{-\frac{2}{3}})}$$, and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD preconditioner is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner.