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RegularizedmeshlessmethodforsolvingLaplaceequationwithmultipleholesSpeaker:Kuo-LunWuCoworker:Jeng-HongKao、

Kue-HongChenandJeng-TzongChen以正規(guī)化無網(wǎng)格法求解含多孔洞拉普拉斯方程式工學(xué)院

2005/04/01OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationformultipleholesNumericalexamplesConclusions2OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationformultipleholesNumericalexamplesConclusions3MotivationNumericalMethodsMeshMethodsFiniteDifferenceMethodMeshlessMethodsFiniteElementMethodBoundaryElementMethod(MFS)(RMM)4OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationformultipleholesNumericalexamplesConclusions5StatementofproblemLaplaceequationwithmultipleholes:potentialflowaroundcylinderselectrostaticfieldofwirestorsionbarwithholesMZ6OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulation

formultipleholesNumericalexamplesConclusions7Methodoffundamentalsolutions(MFS)Methodoffundamentalsolutions(MFS):

SourcepointCollocationpoint—Physicalboundary--Off-setboundaryd=off-setdistancedDouble-layerpotentialapproach

Single-layerPotentialapproach

DirichletproblemNeumannproblemDirichletproblemNeumannproblemDistributedtype8Theartificialboundary(off-setboundary)distanceisdebatable.Thediagonalcoefficientsofinfluencematricesaresingularwhenthesourcepointcoincidesthecollocationpoint.9OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulation

formultipleholesNumericalexamplesConclusions10Regularizedmeshlessmethod(RMM)

SourcepointCollocationpoint—PhysicalboundaryRegularizedmeshlessmethod(RMM)Double-layerpotentialapproach

DirichletproblemNeumannproblemwhereI=InwardnormalvectorO=Outwardnormalvector11Inasimilarway,1213OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationwithmultipleholesNumericalexamplesConclusions14Formulationwithmultipleholes

SourcepointCollocationpoint—Physicalboundaryinnerholes=m-1outerhole=mth15innerholes=m-1outerhole=mth

SourcepointCollocationpoint—PhysicalboundaryP=116innerholes=m-1outerhole=mth

SourcepointCollocationpoint—Physicalboundary17innerholes=m-1outerhole=mth

SourcepointCollocationpoint—Physicalboundary18innerholes=m-1outerhole=mth

SourcepointCollocationpoint—PhysicalboundaryP=m19innerholes=m-1outerhole=mth

SourcepointCollocationpoint—PhysicalboundaryP=m20Thelinearalgebraicsystemsssxx21OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationformultipleholesNumericalexamplesConclusions22NumericalexamplesyxyxCase1DirichletB.C.Case2Mixed-typeB.C.23Contourofpotential(case1)ExactsolutionRMM(360points)BEM(360elements)24Contourofpotential(case2)ExactsolutionRMM(400points)BEM(800elements)25Errorconvergence(case2)26OutlinesMotivationStatementofproblemMethodoffundamentalsolutionsRegularizedmeshlessmethodFormulationformultipleholesNumericalexamplesConclusions27ConclusionsOnlyboundarynodesontherealboundaryarerequired.Singularityof

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