Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
type: Item
instance of: scholarly article
title: Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
zbMATH Open document ID: 0941.65100
DOI: 10.1016/S0377-0427(99)00057-6
author: V. Pereyra
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-20T00:00:00Z
review text: The authors consider a two-dimensional parabolic equation with small diffusion coefficient (but without convection terms!) and propose an overlapping Schwarz method for its solution. Whereas for theoretical details like exponential convergence they refer to unpublished work of the first author, in this paper the algorithms and numerical results are presented: an implicit Euler method for time discretization, a Bakhvalov-type grid for spatial discretization, and the Schwarz iteration on 2 or 3 levels. For the parallelization on a distributed memory multiprocessor, the message passing interface library is used. The authors conclude that it is more effective to solve some of the subproblems on the overlapping regions on coarser grids and employing time extrapolation.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1326098
zbMATH Keywords: singular perturbation
zbMATH Keywords: Schwarz method
zbMATH Keywords: parallel computation
zbMATH Keywords: multi-level methods
zbMATH Keywords: parabolic problem
zbMATH Keywords: algorithms
zbMATH Keywords: numerical results
zbMATH Keywords: implicit Euler method
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326098