A Parallel CG Solver Based on Domain Decomposition and Non-Smooth Aggregation View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2004

AUTHORS

Yuri V. Vassilevski

ABSTRACT

Methods based on overlapping Domain Decomposition (DD) are very convenient for the construction of black-box parallel solvers on unstructured meshes. Considerations of parallel efficiency require the minimal overlap of subdomains equal to element size. The minimal overlap implies a simple technology of automatic partitioning for unstructured meshes, minimal inter-processor exchanges and avoiding a double arithmetical work. Another advantage of the overlapping DD is that the interface between subdomains may be not matching with jumps in the diffusion coefficient. The basic overlapping DD preconditioner is the additive Schwarz preconditioner [10] which, in the case of minimal overlap, is just a block diagonal matrix whose blocks are preconditioners to respective diagonal blocks of the stiffness matrix. For problems with self adjoint second order elliptic operators, the condition number of thus preconditioned system matrix depends on the subdomain diameter (∼ 1/H2), the width of the over lap (∼1/δ) and the diffusion coefficient jump (∼maxρ/minρ). If the additive Schwarz preconditioner is equipped with a coarse subspace, the condition number estimate is reduced to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C\left( \rho \right)\left( {1 + \frac{H} {\delta }} \right)^2 $$\end{document}[2] and in the case of a smooth coefficient ρ it may be improved to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ C\left( {1 + \frac{H} {\delta }} \right) $$\end{document} [3], [12]. More... »

PAGES

93-102

References to SciGraph publications

Book

TITLE

Conjugate Gradient Algorithms and Finite Element Methods

ISBN

978-3-642-62159-8
978-3-642-18560-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-18560-1_6

DOI

http://dx.doi.org/10.1007/978-3-642-18560-1_6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014716719


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