Two-Level Schwarz Method For Unilateral Variational Inequalities (1996)
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BibTeX
@MISC{Tarvainen96two-levelschwarz,
author = {Pasi Tarvainen and Two-level Schwarz and Method For Unilateral and P. Tarvainen},
title = {Two-Level Schwarz Method For Unilateral Variational Inequalities},
year = {1996}
}
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Abstract
. Numerical solution of variational inequalities of obstacle type associated with secondorder elliptic operators is considered. Iterative methods based on the domain decomposition approach are here proposed for discrete obstacle problems arising from the continuous, piecewise linear finite element approximation of the differential problem. A new variant of the Schwarz methodology, called the two-level Schwarz method is developed offering the possibility to make use of fast linear solvers (e.g., linear multigrid and fictitious domain methods) for the genuinely nonlinear obstacle problems. Namely, by using particular monotonicity results, the computational domain can be partitioned into (mesh) subdomains with linear and nonlinear (obstacle-type) subproblems. By taking advantage of this domain decomposition and fast linear solvers, efficient implementation algorithms for large-scale discrete obstacle problems can be developed. The last part of the paper is devoted to the illustrative nume...
Keyphrases
two-level schwarz method unilateral variational inequality fast linear solver linear multigrid domain decomposition approach schwarz methodology genuinely nonlinear obstacle problem numerical solution fictitious domain method new variant piecewise linear finite element approximation domain decomposition large-scale discrete obstacle problem efficient implementation algorithm computational domain illustrative nume particular monotonicity result obstacle type secondorder elliptic operator last part differential problem discrete obstacle problem iterative method variational inequality
