Comparison of linear system solvers applied to diffusion-type finite element equations
type: Item
instance of: scholarly article
title: Comparison of linear system solvers applied to diffusion-type finite element equations
zbMATH Open document ID: 0647.65018
DOI: 10.1007/BF01396343
author: Anne Greenbaum
author: Congming Li
author: Han Zheng Chao
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133411
review text: Various iterative methods for solving the linear systems associated with finite element approximations to self-adjoint elliptic differential operators are compared based on their performance on serial and parallel machines. The methods studied are all preconditioned conjugate gradient methods, differing only in the choice of preconditioner. The preconditioners considered arise from diagonal scaling, incomplete Cholesky decomposition, hierarchical basis functions, and a Neumann- Dirichlet domain decomposition technique. The hierarchical basis function idea is shown to be especially effective on both serial and parallel architectures.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 4056878
zbMATH Keywords: iterative methods
zbMATH Keywords: preconditioned conjugate gradient methods
zbMATH Keywords: choice of preconditioner
zbMATH Keywords: diagonal scaling
zbMATH Keywords: incomplete Cholesky decomposition
zbMATH Keywords: hierarchical basis functions
zbMATH Keywords: Neumann-Dirichlet domain decomposition technique
zbMATH Keywords: serial and parallel architectures
zbMATH Keywords: finite elements
zbMATH Keywords: comparison
zbMATH Keywords: linear system solvers
describes a project that uses: LINPACK
MaRDI profile type: Publication
cites work: The hierarchical basis multigrid method
cites work: Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
cites work: Q3826063
cites work: On Best Conditioned Matrices
cites work: Methods of conjugate gradients for solving linear systems
cites work: The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
cites work: A Comparison of Domain Decomposition Techniques for Elliptic Partial Differential Equations and their Parallel Implementation
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
cites work: Solving Triangular Systems on a Parallel Computer
cites work: On the multi-level splitting of finite element spaces
OpenAlex ID: W2061399867
description: scientific article; zbMATH DE number 4056878