Extending substructure based iterative solvers to multiple load and repeated analyses
type: Item
instance of: scholarly article
title: Extending substructure based iterative solvers to multiple load and repeated analyses
zbMATH Open document ID: 0851.73059
DOI: 10.1016/0045-7825(94)90083-3
author: C. Farhat
author: Luis A. Crivelli
author: François Xavier Roux
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1996-06-24T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19940019031
review text: We present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over \(K\)-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K99
zbMATH DE Number: 880981
zbMATH Keywords: domain decomposition
zbMATH Keywords: series of minimization problems
zbMATH Keywords: preconditioned conjugate gradient algorithm
zbMATH Keywords: linear structural dynamics problem with 11640 degrees of freedom
zbMATH Keywords: 32 processor iPSC-860 system
MaRDI profile type: Publication
OpenAlex ID: W2006402699
cites work: Q4040002
cites work: Iterative Methods for the Solution of Elliptic Problems on Regions Partitioned into Substructures
cites work: A method of finite element tearing and interconnecting and its parallel solution algorithm
cites work: Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics
cites work: Q4693818
cites work: An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems
cites work: Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations
cites work: Q3486809
cites work: A transient FETI methodology for large‐scale parallel implicit computations in structural mechanics
description: scientific article; zbMATH DE number 880981