自适应计算:理论与算法(6)(英文版)
出版时间:
2007-03
版次:
1
ISBN:
9787030184214
定价:
78.00
装帧:
精装
开本:
其他
纸张:
胶版纸
页数:
424页
-
《自适应计算:理论与算法(6)(英文版)》根据2005年在北京大学数学院举行的暑期班的几位主讲教授的讲稿组成。主要讨论自适应网格方法的程序﹑实现和理论基础。《自适应计算:理论与算法(6)(英文版)》每章的作者均是这一领域的重要专家,内容是近十年的一些新结果和新进展。《自适应计算:理论与算法(6)(英文版)》和暑期班的目的是一致的,就是为了推动国内外在这一重要领域的研究。 Chapter1ConvergenceofAdaptiveFiniteElementMethods
1.1Involution
1.2Preliminaries
1.3Residualtypeerrorestimator
1.4Convergenceofanadaptivefiniteelementmethod
1.5Optimalityoftheadaptivefiniteelementmethod
Bibliography
Chapter2APosterioriErrorEstimatorbyPost.Processing
2.1Introduction
2.2Linearfiniteelementonpatchsymmetricgrids
2.3Linearfiniteelementonmildlystructured2dds
2.4Linearfiniteelementongeneralunstructuredgrids
Bibliography
Chapter3AnisotropicMeshAdaptationandMovement
3.1Introduction
3.1.1Sobolevspaces
3.1.2Meshterminology
3.1.3Twoalgebraicinequalities
3.2Basicprinciplesinmeshadaptation
3.2.1GeometricmeaningofSVDdecomposition
3.2.2Alignmentandequidistribution
3.2.3Alignmentandequidistributionforfiniteelementmeshes
3.3InterpolationtheoryinSobolevspaces
3.3.1Finiteelementterminology
3.3.2Element.Wiseestimateoninterpolationerror
3.4Isotropicerrorestimates
3.4.1Chainrule
3.4.2Isotropicerrorestimationonageneralmesh
3.4.3Errorboundonregulartriangulations
3.5Anisotropicerrorestimates
3.5.1Ananlsotroplcerrorbound
3.5.2Anisotropicerrorestimatesindependentofcoordinatesystem
3.5.3Bibliographicnotes
3.6Meshqualitymeasuresandmonitorfunctions
3.6.lMeshqualitymeasures
3.6.2Theisotropiccase
3.6.3Theanisotropiccase:J=1
3.6.4Theanisotropiccase:2=2
3.7Anisotropicmeshadaptation:Refinementapproach
3.7.1Metrictensor
3.7.2Numericalexperiments
3.8Anisotropicmeshadoption:Variationapproach
3.8.1Functionalformeshalignment
3.8.2Functionalforequidistribution
3.8.3Meshadoptionfunctional
3.8.4Meshequation
3.8.5Numericalexperiments
3.9Adaptivemovingmeshmethods:MMPDEapproach
3.9.1TheMMPDEmethod
3.9.2Numericalexamples
3.10Adaptivemovingmeshmethods:GCLapproach
3.10.1GCLmethod
3.10.2RelationtotheLagrangemethodandthedeformationmapMethod
3.10.3Choiceofw,Vref,andP
3.10.4Numericalexamples
3.11Conclusions
Bibliography
Chapter4ConvergenceTheoryofMovingGridMethods
Chapter5ComputationofCrystallineMicrostructureswithTheMeshTransformationMethod
Chapter6OnTheUseofMovingMeshMethodstoSolvePEDs
Chapter7TheoryandApplicationofAdaptiveMovingGridMethods
Chapter8RecoveryTechniquesinFiniteElementMethods
Index
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内容简介:
《自适应计算:理论与算法(6)(英文版)》根据2005年在北京大学数学院举行的暑期班的几位主讲教授的讲稿组成。主要讨论自适应网格方法的程序﹑实现和理论基础。《自适应计算:理论与算法(6)(英文版)》每章的作者均是这一领域的重要专家,内容是近十年的一些新结果和新进展。《自适应计算:理论与算法(6)(英文版)》和暑期班的目的是一致的,就是为了推动国内外在这一重要领域的研究。
-
目录:
Chapter1ConvergenceofAdaptiveFiniteElementMethods
1.1Involution
1.2Preliminaries
1.3Residualtypeerrorestimator
1.4Convergenceofanadaptivefiniteelementmethod
1.5Optimalityoftheadaptivefiniteelementmethod
Bibliography
Chapter2APosterioriErrorEstimatorbyPost.Processing
2.1Introduction
2.2Linearfiniteelementonpatchsymmetricgrids
2.3Linearfiniteelementonmildlystructured2dds
2.4Linearfiniteelementongeneralunstructuredgrids
Bibliography
Chapter3AnisotropicMeshAdaptationandMovement
3.1Introduction
3.1.1Sobolevspaces
3.1.2Meshterminology
3.1.3Twoalgebraicinequalities
3.2Basicprinciplesinmeshadaptation
3.2.1GeometricmeaningofSVDdecomposition
3.2.2Alignmentandequidistribution
3.2.3Alignmentandequidistributionforfiniteelementmeshes
3.3InterpolationtheoryinSobolevspaces
3.3.1Finiteelementterminology
3.3.2Element.Wiseestimateoninterpolationerror
3.4Isotropicerrorestimates
3.4.1Chainrule
3.4.2Isotropicerrorestimationonageneralmesh
3.4.3Errorboundonregulartriangulations
3.5Anisotropicerrorestimates
3.5.1Ananlsotroplcerrorbound
3.5.2Anisotropicerrorestimatesindependentofcoordinatesystem
3.5.3Bibliographicnotes
3.6Meshqualitymeasuresandmonitorfunctions
3.6.lMeshqualitymeasures
3.6.2Theisotropiccase
3.6.3Theanisotropiccase:J=1
3.6.4Theanisotropiccase:2=2
3.7Anisotropicmeshadaptation:Refinementapproach
3.7.1Metrictensor
3.7.2Numericalexperiments
3.8Anisotropicmeshadoption:Variationapproach
3.8.1Functionalformeshalignment
3.8.2Functionalforequidistribution
3.8.3Meshadoptionfunctional
3.8.4Meshequation
3.8.5Numericalexperiments
3.9Adaptivemovingmeshmethods:MMPDEapproach
3.9.1TheMMPDEmethod
3.9.2Numericalexamples
3.10Adaptivemovingmeshmethods:GCLapproach
3.10.1GCLmethod
3.10.2RelationtotheLagrangemethodandthedeformationmapMethod
3.10.3Choiceofw,Vref,andP
3.10.4Numericalexamples
3.11Conclusions
Bibliography
Chapter4ConvergenceTheoryofMovingGridMethods
Chapter5ComputationofCrystallineMicrostructureswithTheMeshTransformationMethod
Chapter6OnTheUseofMovingMeshMethodstoSolvePEDs
Chapter7TheoryandApplicationofAdaptiveMovingGridMethods
Chapter8RecoveryTechniquesinFiniteElementMethods
Index
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