Modified tangential frequency filtering decomposition and its fourier analysis |
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Authors: | Qiang Niu Laura Grigori Pawan Kumar Frédéric Nataf |
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Institution: | (1) Service des Milieux Continus (, Université Libre de Bruxelles, CP 194/5), 50, avenue F.D. Roosevelt, B 1050 Brussels, Belgium;(2) Department of Mathematics, University of Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands |
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Abstract: | 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
O(h-\frac23){{\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. |
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Keywords: | |
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