Nonlinear elasticity solved by a domain decomposition method on a hypercube
type: Item
instance of: scholarly article
title: Nonlinear elasticity solved by a domain decomposition method on a hypercube
zbMATH Open document ID: 0787.73078
DOI: 10.1016/0168-9274(93)90105-Z
author: Yann-Hervé De Roeck
published in: Applied Numerical Mathematics
publication date: 1993-10-06T00:00:00Z
review text: The author has proposed a domain decomposition method for the solution of large three-dimensional problems in nonlinear elasticity on distributed memory supercomputers. The original problem is approximated by a standard finite element method and linearized by a Newton technique. The linearized problem is solved by a mixed solver which is based on the Schur complement method. In this solver, a preconditioned conjugate gradient method is used for solving the interface problem, while local problems within each subdomain are solved by direct solvers. Compared to the linear case, the present study shows that domain decomposition can do more in the nonlinear case, at least as far as coarse grain parallelism and computational efficiency are concerned. Various details of implementation are given that show how to match the solution algorithm with the hardware specificity of the hypercube, especially because of the message passing interconnection procedure.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 65N55
zbMATH DE Number: 425895
zbMATH Keywords: distributed memory supercomputers
zbMATH Keywords: finite element method
zbMATH Keywords: Newton technique
zbMATH Keywords: mixed solver
zbMATH Keywords: Schur complement method
zbMATH Keywords: preconditioned conjugate gradient method
zbMATH Keywords: interface problem
zbMATH Keywords: interconnection procedure
reviewed by: Prem Narain
MaRDI profile type: Publication
cites work: Q4734715
cites work: Domain decomposition methods for large linearly elliptic three-dimensional problems
cites work: A domain-decomposed solver for nonlinear elasticity
full work available at URL: 0168-9274(93)90105-z
OpenAlex ID: W2134553944
description: scientific article; zbMATH DE number 425895