Domain decomposition methods in computational fluid dynamics

Rodrigo R. Paz*, Mario A. Storti, Lisandro Dalcin, Gustavo Rios Rodríguez

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this work, the development of a parallelizable preconditioner for domain decomposition methods in the context of Finite Element solution of partial differential equations arising in the context of CFD problems is studied. The preconditioner is based on solving a problem in a narrow strip around the interface of the partitioned problem. The theoretical basis and concepts that inspired the proposition of this interface strip preconditioner (ISP) are presented. The performance of this preconditioner (that has been implemented in a FEM production code called PETSC-FEM) is assessed with an analytical study of Schur complement matrix eigenvalues and numerical experiments conducted in a parallel computational environment. Also, we compare the convergence to the analytical solution or measured data for problems that have been considered as 'benchmarks' in the computational fluid dynamic literature. For this purpose, we study the solution obtained via parallelized iterative methods that have been extensively used (e.g. preconditioned CG and GMRES global iteration and its variants, Additive Schwarz preconditioners) in CFD computations and those obtained with the Interface Strip preconditioner for the Schur Complement method.

Original languageEnglish (US)
Title of host publicationComputational Mechanics Research Trends
PublisherNova Science Publishers, Inc.
Pages495-555
Number of pages61
ISBN (Print)9781608760572
StatePublished - Dec 1 2010

ASJC Scopus subject areas

  • Computer Science(all)

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