Modified tangential frequency filtering decomposition and its fourier analysis

Niu, Qiang; Grigori, Laura; Kumar, Pawan; Nataf, Frédéric

doi:10.1007/s00211-010-0298-3

Cited by 13 publications

(12 citation statements)

References 39 publications

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“…The 3D convection-diffusion problem was also considered in previous papers on filtering and nested preconditioners, see for example [1,2,18,10]. They are all related to the following boundary value problem, isotropic and discontinuous,…”

Section: Numerical Resultsmentioning

confidence: 97%

Parallel design and performance of nested filtering factorization preconditioner

Grigori

Nataf

2013

Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

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We present the parallel design and performance of the nested filtering factorization preconditioner (NFF), which can be used for solving linear systems arising from the discretization of a system of PDEs on unstructured grids. NFF has limited memory requirements, and it is based on a two level recursive decomposition that exploits a nested block arrow structure of the input matrix, obtained priorly by using graph partitioning techniques. It also allows to preserve several directions of interest of the input matrix to alleviate the effect of low frequency modes on the convergence of iterative methods. For a boundary value problem with highly heterogeneous coefficients, discretized on three-dimensional grids with 64 millions unknowns and 447 millions nonzero entries, we show experimentally that NFF scales up to 2048 cores of Genci's Bull system (Curie), and it is up to 2.6 times faster than the domain decomposition preconditioner Restricted Additive Schwarz implemented in PETSc.

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Section: Numerical Resultsmentioning

confidence: 97%

Parallel design and performance of nested filtering factorization preconditioner

Grigori

Nataf

2013

Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis

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“…The choice of the filtering vector is an important issue, and is widely studied in [20,16,17,28,12,14,15]. Generally, the filtering vector should enable the preconditioner to effectively damp the error components in different frequencies.…”

Section: On the Choice Of The Filtering Vectorsmentioning

confidence: 99%

“…According to the analysis in [25,18,28,23], such kind of left filtering is equivalent to imposing a zero sum constraint on the residual vectors computed by the preconditioned iterative solver. By setting an appropriate initial approximate solution, this constraint ensures the mass conservation property, which is very important for solving linear systems arising from reservoir simulations [25,18,23].…”

Section: On the Choice Of The Filtering Vectorsmentioning

confidence: 99%

Two sides tangential filtering decomposition

Grigori

Nataf

Niu

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper we study a class of preconditioners that satisfy the so-called left and/or right filtering conditions. For practical applications, we use a multiplicative combination of filtering based preconditioners with the classical ILU(0) preconditioner, which is known to be efficient. Although the left filtering condition has a more sound theoretical motivation than the right one, extensive tests on convection-diffusion equations with heterogeneous and anisotropic diffusion tensors reveal that satisfying left or right filtering conditions lead to comparable results. On the filtering vector, these numerical tests reveal that e = [1, . . . , 1] T is a reasonable choice, which is effective and can avoid the preprocessing needed in other methods to build the filtering vector. Numerical tests show that the composite preconditioners are rather robust and efficient for these problems with strongly varying coefficients.

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“…For the block tridiagonal coefficient matrix A, the Modified Tangential Frequency Filtering Decomposition (MTFFD) preconditioner M is given by [39] …”

Section: Modified Tangential Frequency Filtering Preconditionermentioning

confidence: 99%

Numerical Studies of a Class of Composite Preconditioners

Niu

Ng²

2014

JCM

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In this paper, we study a composite preconditioner that combines the modified tangential frequency filtering decomposition with the ILU(0) factorization. Spectral property of the composite preconditioner is examined by the approach of Fourier analysis. We illustrate that condition number of the preconditioned matrix by the composite preconditioner is asymptotically bounded by O(h − 2 3 p ) on a standard model problem. Performance of the composite preconditioner is compared with other preconditioners on several problems arising from the discretization of PDEs with discontinuous coefficients. Numerical results show that performance of the proposed composite preconditioner is superior to other relative preconditioners.Mathematics subject classification: 65F10, 65N22.

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Modified tangential frequency filtering decomposition and its fourier analysis

Cited by 13 publications

References 39 publications

Parallel design and performance of nested filtering factorization preconditioner

Parallel design and performance of nested filtering factorization preconditioner

Two sides tangential filtering decomposition

Numerical Studies of a Class of Composite Preconditioners

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