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Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case

Janssen, Jan and Vandewalle, Stefan (1996) Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case. SIAM Journal on Scientific Computing, 17 (1). pp. 133-155. ISSN 1064-8275. doi:10.1137/0917011.

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The efficiency of numerically solving time-dependent partial differential equations on parallel computers can be greatly improved by computing the solution on many time levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary differential equations obtained by spatial finite-element discretisation of linear parabolic initial-boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments.

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Additional Information:©1996 Society for Industrial and Applied Mathematics. Reprinted with permission. Received by the editors May 20, 1994; accepted for publication (in revised form) March 1, 1995. This text presents research results of the Belgian Incentive Program "Information Technology"---Computer Science of the Future, initiated by the Belgian State-Prime Minister’s Office for Science, Technology and Culture. The scientific responsibility is assumed by its authors. This work was supported in pan by the NSF under Cooperative Agreement No, CCR-9120008.
Subject Keywords:parabolic partial differential equations; waveform relaxation; multigrid; linear multistep methods
Issue or Number:1
Record Number:CaltechAUTHORS:JANsiamjsc96
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9406
Deposited By: Archive Administrator
Deposited On:18 Dec 2007
Last Modified:08 Nov 2021 20:59

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