Search results for "Schwarz alternating method"

showing 3 items of 3 documents

Two-level Schwarz method for unilateral variational inequalities

1999

The numerical solution of variational inequalities of obstacle type associated with second-order elliptic operators is considered. Iterative methods based on the domain decomposition approach are 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 of making 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 (mes…

Mathematical optimizationIterative methodApplied MathematicsGeneral MathematicsDomain decomposition methodsFinite element methodPiecewise linear functionComputational MathematicsMultigrid methodVariational inequalityAdditive Schwarz methodApplied mathematicsSchwarz alternating methodMathematicsIMA Journal of Numerical Analysis
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Parallel Schwarz methods for convection-dominated semilinear diffusion problems

2002

AbstractParallel two-level Schwarz methods are proposed for the numerical solution of convection-diffusion problems, with the emphasis on convection-dominated problems. Two variants of the methodology are investigated. They differ from each other by the type of boundary conditions (Dirichlet- or Neumann-type) posed on a part of the second-level subdomain interfaces. Convergence properties of the two-level Schwarz methods are experimentally compared with those of a variant of the standard multi-domain Schwarz alternating method. Numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods.

Parallel computingApplied MathematicsNumerical analysisMathematical analysisParallel algorithmDomain decomposition methodsSingularly perturbed semilinear convection–diffusion problemMulti-level Schwarz methodsComputational MathematicsAdditive Schwarz methodDistributed memoryBoundary value problemSchwarz alternating methodConvection–diffusion equationMathematicsJournal of Computational and Applied Mathematics
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Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems

1999

Abstract Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments …

Predictor–corrector methodParallel computingSingular perturbationPartial differential equationDiscretizationApplied MathematicsMathematical analysisExtrapolationMathematicsofComputing_NUMERICALANALYSISDomain decomposition methodsComputational MathematicsMulti-level Schwarz methodApplied mathematicsSingularly perturbed parabolic problemDistributed memorySchwarz alternating methodMathematicsJournal of Computational and Applied Mathematics
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