The role of multi-method linear solvers in PDE-based simulations

S. Bhowmick, L. McInnes, B. Norris, P. Raghavan

Research output: Chapter in Book/Report/Conference proceedingChapter

14 Scopus citations

Abstract

The solution of large-scale, nonlinear PDE-based simulations typically depends on the performance of sparse linear solvers, which may be invoked at each nonlinear iteration. We present a framework for using multi-method solvers in such simulations to potentially improve the execution time and reliability of linear system solution. We consider composite solvers, which provide reliable linear solution by using a sequence of preconditioned iterative methods on a given system until convergence is achieved. We also consider adaptive solvers, where the solution method is selected dynamically to match the attributes of linear systems as they change during the course of the nonlinear iterations. We demonstrate how such multi-method composite and adaptive solvers can be developed using advanced software architectures such as PETSc, and we report on their performance in a computational fluid dynamics application.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsVipin Kumar, Marina L. Gavrilova, Chih Jeng Kenneth Tan, Pierre L’Ecuyer, Chih Jeng Kenneth Tan
PublisherSpringer Verlag
Pages828-839
Number of pages12
ISBN (Print)3540401555, 9783540448396
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2667
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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