Large scale finite element computations with GMRES-like methods on a Cray Y-MP
type: Item
instance of: scholarly article
title: Large scale finite element computations with GMRES-like methods on a Cray Y-MP
zbMATH Open document ID: 0855.65025
DOI: 10.1016/0168-9274(95)00021-L
published in: Applied Numerical Mathematics
publication date: 1996-09-05T00:00:00Z
review text: The author is interested in methods for solving large non-symmetric systems such as arise from finite element discretization of convection-diffusion equations. These methods should be appropriate for implementation in a commercial finite element computer program such as DIANA. Methods of interest in the present paper include GMRES, GCR, and GMRESR with various preconditioning strategies. The author presents several approaches for optimizing the implementation of matrix-vector products on vector and parallel computer architectures, concentrating on elemental methods rather than ones which require explicit construction of the stiffness matrix. Element-by-element preconditioners are also discussed. The discussion is heavily influenced by the architecture of vector computers such as the Cray Y-MP, although other computers are mentioned. The author presents numerical experiments performed with two non-trivial convection-diffusion equations. GMRES, GCR, and GMRESR methods are compared with several different preconditioning strategies. There is no decisive victor in the comparison, but GMRESR emerges as a very attractive candidate.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 897499
zbMATH Keywords: DIANA code
zbMATH Keywords: parallel computation
zbMATH Keywords: large non-symmetric systems
zbMATH Keywords: finite element
zbMATH Keywords: convection-diffusion equations
zbMATH Keywords: GMRES
zbMATH Keywords: preconditioning
zbMATH Keywords: matrix-vector products
zbMATH Keywords: vector computers
zbMATH Keywords: numerical experiments
author: Martin B. van Gijzen
reviewed by: Myron Sussman
describes a project that uses: CGS
MaRDI profile type: Publication
cites work: The principle of minimized iterations in the solution of the matrix eigenvalue problem
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cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
cites work: GMRESR: a family of nested GMRES methods
cites work: An analysis of element-by-element preconditioners for nonsymmetric problems
cites work: A polynomial preconditioner for the GMRES algorithm
full work available at URL: 0168-9274(95)00021-l
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description: scientific article; zbMATH DE number 897499