Modified tangential frequency filtering decomposition and its fourier analysis

Qiang Niu; Laura Grigori; Pawan Kumar; Frédéric Nataf

doi:10.1007/s00211-010-0298-3

Modified tangential frequency filtering decomposition and its fourier analysis

Qiang Niu^*
, Laura Grigori
, Pawan Kumar
, Frédéric Nataf

^*Corresponding author for this work

Department of Applied Mathematics

Institut national de recherche en informatique et en automatique
Universite Paris 6

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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^-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.

Original language	English
Pages (from-to)	123-148
Number of pages	26
Journal	Numerische Mathematik
Volume	116
Issue number	1
DOIs	https://doi.org/10.1007/s00211-010-0298-3
Publication status	Published - 2010

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title = "Modified tangential frequency filtering decomposition and its fourier analysis",

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-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.",

author = "Qiang Niu and Laura Grigori and Pawan Kumar and Fr{\'e}d{\'e}ric Nataf",

note = "Funding Information: Q. Niu was funded by CSC (China Scholarship Council) and his work was performed during his visit at INRIA Saclay. 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).",

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doi = "10.1007/s00211-010-0298-3",

language = "English",

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T1 - Modified tangential frequency filtering decomposition and its fourier analysis

AU - Niu, Qiang

AU - Grigori, Laura

AU - Kumar, Pawan

AU - Nataf, Frédéric

N1 - Funding Information: Q. Niu was funded by CSC (China Scholarship Council) and his work was performed during his visit at INRIA Saclay. 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).

PY - 2010

Y1 - 2010

N2 - 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-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.

AB - 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-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.

UR - https://www.scopus.com/pages/publications/77954216053

U2 - 10.1007/s00211-010-0298-3

DO - 10.1007/s00211-010-0298-3

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VL - 116

SP - 123

EP - 148

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 1

ER -

Modified tangential frequency filtering decomposition and its fourier analysis

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