基于自然邊界歸化的半無界區(qū)域上的區(qū)域分解算法.pdf

1、南京理工大學碩士學位論文基于自然邊界歸化的半無界區(qū)域上的區(qū)域分解算法姓名：劉敬剛申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：徐元20040301矮圭論文基予毫然透賽辯純鵑半玉器區(qū)域上瓣醞域分解算法II一———————————————____m___—●—————————————___——_Ⅲ__—————————————_—_H_____—————————————_________—————一AbstractInthjspaper，bas

2、edonthetheoryofnaturalboundaryreductiontilenumericalresolutionmethodsforellipticboundaryvalueproblemsonakindofunboundedhalfplanewithacavearediscussed。Intheflameofthedomaindecompositionmethod，thedomainisdecomposedintoabou

3、ndedsub—domaintowhichthefiniteelementmethodisappliedandaregularunboundedsub—domaintowhichthenatmMboundaryreductionisappliedSoiterativealgorittmasareconstructedonbothofthesubdomainsFirstoverlappingdomaindecompositioniscon

4、sideredtowhichtheSchwarzMternatiremethodisappliedByP1LLions’projectionexplanationoftheSchwarzalternativemethoditisprovedthattheconvergencerateofthealgorithmisgeometricMThennonoverlappingdomaindecompositionisconsidered，to

5、whichtheDiriehtet—Neumannmethodisapplieel，BoththeequivalencetotheRichardsoniterativemethodaadtheconvergencerateindependentofthefiniteelementmeshsizeofthealgorithmareprovedWithproperselectionoftherelaxationfactoritisprove

6、dthattheconvergenceoftheD—Nalterna—tiremethodisgeometricalandthegeneralvaluesoftherelaxationfactoraregivenKeywords：NaturalBoundaryReduction，EllipticBoundaryValueProblems，DomainDecompositionMethod，SchwarzAlternativeMethod