Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios-中国Betway体育网页登陆

摘要 AbstractInthispaperwestudysomenonoverlappingdomaindecompositionmethodsforsolvingaclassofellipticproblemsarisingfromcompositematerialsandflowsinporousmediawhichcontainmanyspatialscales.Ourpreconditionerdiffersfromtraditionaldomaindecompositionpreconditionersbyusingacoarsesolverwhichisadaptivetosmallscaleheterogeneousfeatures.Whiletheconvergencerateoftraditionaldomaindecompositionalgorithmsusingcoarsesolversbasedonlinearorpolynomialinterpolationsmaydeteriorateinthepresenceofrapidsmallscaleoscillationsorhighaspectratios,ourpreconditionerisapplicabletomultiple-scaleproblemswithoutrestrictiveassumptionsandseemstohaveaconvergenceratenearlyindependentoftheaspectratiowithinthesubstructures.ArigorousconvergenceanalysisbasedontheSchwarzframeworkiscarriedout,andwedemonstratetheefficiencyandrobustnessoftheproposedpreconditionerthroughnumericalexperimentswhichincludeproblemswithmultipl

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Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios

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