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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 9
COMPUTATIONAL MECHANICS USING HIGH PERFORMANCE COMPUTING Edited by: B.H.V. Topping
Chapter 9
Domain Decomposition Methods for NonSymmetric Problems F. Nataf
CMAP, CNRS, Ecole Polytechnique, Palaiseau, France F. Nataf, "Domain Decomposition Methods for NonSymmetric Problems", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", SaxeCoburg Publications, Stirlingshire, UK, Chapter 9, pp 185197, 2002. doi:10.4203/csets.9.9
Abstract
Two algorithms,
especially suited to nonsymmetric elliptic problems, are
presented. The model equation is the convectiondiffusion
equation.
This equation is important in itself in engineering or
environnemental sciences for instance, it models the transport
and diffusion of species (e.g. pollutant
in air or water, electrons in semiconductor devices)
in a given flow. It is also a
key aspect of the NavierStokes equations. An implicit scheme in
time will demand at a solution procedure at each time step
The
first algorithm is a preconditioner for the Schur formulation
of domain decomposition problems. It is an extension of the
wellknown NeumannNeumann preconditioner to nonsymmetric problems. The second
algorithm can be seen as a modification of the Schwarz method.
The Dirichlet boundary conditions on the interfaces are
replaced by more general boundary conditions. The algorithm can
then be used on nonoverlapping subdomains and has a fast
convergence. We emphasize a presentation at the matrix level.
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