A parallel aitken-additive schwarz waveform relaxation method for parabolic problems

Hatem Ltaief; Marc Garbey

doi:10.1007/978-3-540-92744-0_17

A parallel aitken-additive schwarz waveform relaxation method for parabolic problems

Hatem Ltaief^*, Marc Garbey

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The objective of this paper is to describe a parallel acceleration framework of the additive schwarz waveform relaxation for parabolic problems. The problem is in three space dimension and time. This new parallel domain decomposition algorithm generalizes the Aitken-like Acceleration method of the additive Schwarz algorithm for elliptic problems. Although the standard Schwarz Waveform Relaxation algorithm has a linear rate of convergence and low numerical efficiency, it is beneficent to cache use and scales with the memory. The combination with the Aitken-like Acceleration method transforms the Schwarz algorithm into a direct solver for the heat operator. This solver combines all in one the load balancing, the efficiency, the scalability and the fault tolerance features which make it suitable for grid environments.

Original language	English (US)
Title of host publication	Parallel Computational Fluid Dynamics 2007
Subtitle of host publication	Implementations and Experiences on Large Scale and Grid Computing
Pages	139-146
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-540-92744-0_17
State	Published - 2009
Externally published	Yes
Event	Parallel Computational Fluid Dynamics, Parallel CFD 2007 - Antalya, Turkey Duration: May 21 2007 → May 24 2007

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	67 LNCSE
ISSN (Print)	1439-7358

Other

Other	Parallel Computational Fluid Dynamics, Parallel CFD 2007
Country/Territory	Turkey
City	Antalya
Period	05/21/07 → 05/24/07

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-540-92744-0_17

Cite this

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title = "A parallel aitken-additive schwarz waveform relaxation method for parabolic problems",

abstract = "The objective of this paper is to describe a parallel acceleration framework of the additive schwarz waveform relaxation for parabolic problems. The problem is in three space dimension and time. This new parallel domain decomposition algorithm generalizes the Aitken-like Acceleration method of the additive Schwarz algorithm for elliptic problems. Although the standard Schwarz Waveform Relaxation algorithm has a linear rate of convergence and low numerical efficiency, it is beneficent to cache use and scales with the memory. The combination with the Aitken-like Acceleration method transforms the Schwarz algorithm into a direct solver for the heat operator. This solver combines all in one the load balancing, the efficiency, the scalability and the fault tolerance features which make it suitable for grid environments.",

author = "Hatem Ltaief and Marc Garbey",

year = "2009",

doi = "10.1007/978-3-540-92744-0_17",

language = "English (US)",

isbn = "9783540927433",

series = "Lecture Notes in Computational Science and Engineering",

pages = "139--146",

booktitle = "Parallel Computational Fluid Dynamics 2007",

note = "Parallel Computational Fluid Dynamics, Parallel CFD 2007 ; Conference date: 21-05-2007 Through 24-05-2007",

}

Ltaief, H & Garbey, M 2009, A parallel aitken-additive schwarz waveform relaxation method for parabolic problems. in Parallel Computational Fluid Dynamics 2007: Implementations and Experiences on Large Scale and Grid Computing. Lecture Notes in Computational Science and Engineering, vol. 67 LNCSE, pp. 139-146, Parallel Computational Fluid Dynamics, Parallel CFD 2007, Antalya, Turkey, 05/21/07. https://doi.org/10.1007/978-3-540-92744-0_17

A parallel aitken-additive schwarz waveform relaxation method for parabolic problems. / Ltaief, Hatem; Garbey, Marc.
Parallel Computational Fluid Dynamics 2007: Implementations and Experiences on Large Scale and Grid Computing. 2009. p. 139-146 (Lecture Notes in Computational Science and Engineering; Vol. 67 LNCSE).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The objective of this paper is to describe a parallel acceleration framework of the additive schwarz waveform relaxation for parabolic problems. The problem is in three space dimension and time. This new parallel domain decomposition algorithm generalizes the Aitken-like Acceleration method of the additive Schwarz algorithm for elliptic problems. Although the standard Schwarz Waveform Relaxation algorithm has a linear rate of convergence and low numerical efficiency, it is beneficent to cache use and scales with the memory. The combination with the Aitken-like Acceleration method transforms the Schwarz algorithm into a direct solver for the heat operator. This solver combines all in one the load balancing, the efficiency, the scalability and the fault tolerance features which make it suitable for grid environments.

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T2 - Parallel Computational Fluid Dynamics, Parallel CFD 2007

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A parallel aitken-additive schwarz waveform relaxation method for parabolic problems

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