Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems-中国期刊网

摘要 Thenumericalquadraturemethodsfordealingwiththeproblemsofsingularandnear-singularintegralscausedbyBurton-Millermethodareproposed,bywhichtheconventionalandfastmultipoleBEMs(boundaryelementmethods)for3Dacousticproblemsbasedonconstantelementsareimproved.Tosolvetheproblemofsingularintegrals,aHadamardfinite-partintegralmethodispresented,whichisasimplifiedcombinationofthemethodsproposedbyKirkupandWolf.Theproblemofnear-singularintegralsisovercomebythesimplemethodofpolartransformationandthemorecomplexmethodofPART(ProjectionandAngular&RadialTransformation).Theeffectivenessofthesemethodsforsolvingthesingularandnear-singularproblemsisvalidatedthroughcomparingwiththeresultscomputedbytheanalyticalmethodand/orthecommercialsoftwareLMSVirtual.Lab.Inaddition,theinfluenceofthenear-singularintegralproblemonthecomputationalprecisionsisanalyzedbycomputingtheerrorsrelativetotheexactsolution.ThecomputationalcomplexitiesoftheconventionalandfastmultipoleBEMareanalyzedandcomparedthroughnumericalcomputations.Alarge-scaleacousticscatteringproblem,whosedegreeoffreedomsisabout340,000,isimplementedsuccessfully.Theresultsshowthat,thenearsingularityisprimarilyintroducedbythehyper-singularkernel,andhasgreatinfluencesontheprecisionofthesolution.TheprecisionoffastmultipoleBEMisthesameasconventionalBEM,butthecomputationalcomplexitiesaremuchlower.

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Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

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Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

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