Fourier analysis of frequency filtering decomposition preconditioners

Qiang Niu; Lin Zhang Lu

doi:10.1016/j.amc.2009.12.024

Fourier analysis of frequency filtering decomposition preconditioners

Qiang Niu^*, Lin Zhang Lu

^*Corresponding author for this work

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

Abstract

In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O (h^{- 1}), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ (M_SFFD^{- 1} A) ≤ κ (M_FFD^{- 1} A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.

Original language	English
Pages (from-to)	1805-1818
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	216
Issue number	6
DOIs	https://doi.org/10.1016/j.amc.2009.12.024
Publication status	Published - 15 May 2010
Externally published	Yes

Keywords

Fourier analysis
Frequency filtering decomposition
Linear system
Preconditioner

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10.1016/j.amc.2009.12.024

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@article{a513ac0e58e9468b9209bc617fa91a9b,

title = "Fourier analysis of frequency filtering decomposition preconditioners",

abstract = "In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O (h- 1), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ (MSFFD- 1 A) ≤ κ (MFFD- 1 A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.",

keywords = "Fourier analysis, Frequency filtering decomposition, Linear system, Preconditioner",

author = "Qiang Niu and Lu, {Lin Zhang}",

note = "Funding Information: Part of the work was performed during the first author visit INRIA funded by CSC (China Scholarship Council) ; he would like to thank Dr. Laura Grigori, Professor Fr{\'e}d{\'e}ric Nataf, and Pawan Kumar for their hospitality and many enjoyable discussions of the problem, he also thank CSC and INRIA for their financial supports. Finally, we would like to thank professor Z.-Z. Bai and two anonymous referees for their valuable suggestions which improve the work considerably. ",

year = "2010",

month = may,

day = "15",

doi = "10.1016/j.amc.2009.12.024",

language = "English",

volume = "216",

pages = "1805--1818",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

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TY - JOUR

T1 - Fourier analysis of frequency filtering decomposition preconditioners

AU - Niu, Qiang

AU - Lu, Lin Zhang

N1 - Funding Information: Part of the work was performed during the first author visit INRIA funded by CSC (China Scholarship Council) ; he would like to thank Dr. Laura Grigori, Professor Frédéric Nataf, and Pawan Kumar for their hospitality and many enjoyable discussions of the problem, he also thank CSC and INRIA for their financial supports. Finally, we would like to thank professor Z.-Z. Bai and two anonymous referees for their valuable suggestions which improve the work considerably.

PY - 2010/5/15

Y1 - 2010/5/15

N2 - In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O (h- 1), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ (MSFFD- 1 A) ≤ κ (MFFD- 1 A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.

AB - In this paper, frequency filtering decomposition (FFD) preconditioner is analyzed by the approach of Fourier analysis. The condition number estimation of a preconditioned 2-D model problem is presented. Analysis reveals that condition number of the preconditioned matrix grows like O (h- 1), with h be the mesh size. By using the framework of FFD, a stabilized frequency filtering decomposition (SFFD) method is proposed and analyzed by Fourier method. Results show that SFFD preconditioner is superior to FFD preconditioner in the sense that κ (MSFFD- 1 A) ≤ κ (MFFD- 1 A). Numerical tests are performed to illustrate the theoretical results and the superiority of SFFD preconditioner.

KW - Fourier analysis

KW - Frequency filtering decomposition

KW - Linear system

KW - Preconditioner

UR - http://www.scopus.com/inward/record.url?scp=77953132154&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2009.12.024

DO - 10.1016/j.amc.2009.12.024

M3 - Article

AN - SCOPUS:77953132154

SN - 0096-3003

VL - 216

SP - 1805

EP - 1818

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 6

ER -

Fourier analysis of frequency filtering decomposition preconditioners

Abstract

Keywords

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