预览加载中，请您耐心等待几秒...

四边形剖分下的组合多尺度有限元方法求解多尺度椭圆问题（英文）.docx

预览
1/2
2/2

在线预览结束，喜欢就下载吧，查找使用更方便

下载提示 文本预览

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

四边形剖分下的组合多尺度有限元方法求解多尺度椭圆问题（英文） Multiscalefiniteelementmethodsforsolvingellipticproblemsinquadrilateralmeshpartitioning Abstract: Thesolutionofellipticproblemsoncomplexdomainscanbechallengingduetothepresenceofmultiplescalesintheunderlyinggeometry.Thispaperpresentsamultiscalefiniteelementmethodforsolvingsuchproblemsonquadrilateralmeshpartitions.Themethodisbasedonacombinationofcoarse-scaleandfine-scalefiniteelementspaces,whichallowsfortheaccuraterepresentationofbothmacroscopicandmicroscopicfeaturesofthesolution.Thetheoreticalfoundationsofthemethodarediscussed,includingtheconstructionofthemultiscalebasisfunctionsandtheformulationofthemixedcoarse-fineproblem.Numericalexperimentsareperformedtovalidatetheaccuracyandefficiencyoftheproposedapproach.Theresultsdemonstratethatthemultiscalefiniteelementmethodiscapableofaccuratelycapturingthemultiscalefeaturesofthesolution,whilemaintainingcomputationalefficiency. 1.Introduction Ellipticproblemsariseinawiderangeofscientificandengineeringapplications,includingheatconduction,fluidflow,andstructuralmechanics.Solvingtheseproblemsoncomplexdomainscanbechallengingduetothepresenceofmultiplescalesintheunderlyinggeometry.Forexample,thedomainmaycontainbothmacroscopicfeatures,suchasboundariesandinterfaces,aswellasmicroscopicfeatures,suchasfine-scaleheterogeneitiesandcracks.Traditionalfiniteelementmethodsmaystruggletoaccuratelyrepresentthesolutioninthesesituations,astheyoftenrequireafinemeshtoresolvesmall-scalefeatures.However,usingafinemeshthroughoutthedomaincanleadtoprohibitivelylargecomputationalcosts. 2.Multiscalefiniteelementmethod Themultiscalefiniteelementmethodisapromisingapproachforsolvingellipticproblemsoncomplexdomainswithmultiplescales.Itinvolvestheconstructionofcoarse-scaleandfine-scalefiniteelementspaces,whichcapturethemacroscopicandmicroscopicfeaturesofthesolution,respectively.Thecoarse-scalebasisfunctionsaredefinedonacoarsemesh,whilethefine-scalebasisfunctionsaredefinedonafinemesh.Themultiscalebasisfunctionsarethenconstructedas