The influence of interface conditions on convergence of Krylov-Schwarz domain decomposition for the advection-diffusion equation

Several variants of Schwarz domain decomposition, which differ in the choice of interface conditions, are studied in a finite volume context. Krylov subspace acceleration, GMRES in this paper, is used to accelerate convergence. Using a detailed investigation of the systems involved, we can minimize...

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Published in:Journal of scientific computing 1997-03, Vol.12 (1), p.11-30
Main Authors: BRAKKEE, E, WILDERS, P
Format: Article
Language:English
Subjects:
Advection-diffusion equation
Algorithms
Convergence
Decomposition
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, boundary value problems
Sciences and techniques of general use
Subspaces
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description Several variants of Schwarz domain decomposition, which differ in the choice of interface conditions, are studied in a finite volume context. Krylov subspace acceleration, GMRES in this paper, is used to accelerate convergence. Using a detailed investigation of the systems involved, we can minimize the memory requirements of GMRES acceleration. It is shown how Krylov subspace acceleration can be easily built on top of an already implemented Schwarz domain decomposition iteration, which makes Krylov-Schwarz algorithms easy to use in practice. The convergence rate is investigated both theoretically and experimentally. It is observed that the Krylov subspace accelerated algorithm is quite insensitive to the type of interface conditions employed.
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subjects Advection-diffusion equation
Algorithms
Convergence
Decomposition
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, boundary value problems
Sciences and techniques of general use
Subspaces
title The influence of interface conditions on convergence of Krylov-Schwarz domain decomposition for the advection-diffusion equation
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