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GETMe网格平滑框架:一种提高有限元网格质量的几何方法-The GETMe Mesh Smoothing Framework: A Geometric Way to Quality Finite E

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标题(title):The GETMe Mesh Smoothing Framework: A Geometric Way to Quality Finite Element Meshes
GETMe网格平滑框架:一种提高有限元网格质量的几何方法
作者(author):Vartziotis, Dimitris P.; Wipper, Joachim
出版社(publisher):Chapman and Hall/CRC
大小(size):9 MB (8941183 bytes)
格式(extension):pdf
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Table of contents :
Content: Cover --
Half Title --
Title --
Copyrights --
Contents --
Chapter 1 Introduction --
Chapter 2 Elements and meshes --
2.1 Elements --
2.1.1 Elements for planar and surface meshes --
2.1.2 Elements for volumetric meshes --
2.2 Meshes --
2.2.1 Introduction --
2.2.2 Mesh types --
2.3 Quality criteria --
2.3.1 Introduction --
2.3.2 The mean ratio quality criterion --
2.3.3 Mesh quality numbers --
2.4 Mesh generation --
2.4.1 Overview --
2.4.2 Delaunay meshes --
Chapter 3 The finite element method --
3.1 History of the finite element method --
3.2 Fundamentals --
3.2.1 Elliptical boundary value problems --
3.2.2 Sobolev spaces --
3.2.3 Variational formulation --
3.2.4 Ritz-Galerkin method --
3.2.5 Linear trial functions over triangular elements --
3.3 Influence of mesh quality on solution accuracy --
Chapter 4 Mesh improvement --
4.1 Overview and classification --
4.2 Mesh smoothing --
4.2.1 Laplacian smoothing and its variants --
4.2.2 Global optimization --
4.3 Topological modifications --
4.3.1 Template-based improvement --
4.3.2 Node insertion and removal --
Chapter 5 Regularizing element transformations --
5.1 Transformation of polygonal elements --
5.1.1 Classic polygon transformations --
5.1.2 Generalized regularizing polygon transformations --
5.1.3 Customized polygon transformations --
5.2 Transformation of polyhedral elements --
5.2.1 Opposite face normals-based transformations --
5.2.2 Dual element-based transformations --
Chapter 6 The GETMe smoothing framework --
6.1 Building blocks of the GETMe framework --
6.1.1 Basic GETMe simultaneous smoothing --
6.1.2 GETMe simultaneous smoothing --
6.1.3 GETMe sequential smoothing --
6.2 Combined GETMe algorithms --
6.2.1 GETMe smoothing --
6.2.2 Adaptive GETMe smoothing --
6.3 Properties of GETMe smoothing --
6.3.1 Influence of transformation parameters. 6.3.2 Influence of initial mesh validity and quality --
6.3.3 Unrestricted surface mesh smoothing --
6.4 Extending the GETMe mesh improvement framework --
6.4.1 Surface mesh smoothing --
6.4.2 Anisotropic mesh smoothing --
6.4.3 Combining GETMe with topology modification --
6.4.4 Using GETMe for mesh untangling --
Chapter 7 Numerical examples --
7.1 Polygonal meshes --
7.1.1 Mixed planar mesh --
7.1.2 Single element type surface meshes --
7.1.3 Anisotropic meshes --
7.2 Single element type volumetric meshes --
7.2.1 Tetrahedral meshes --
7.2.2 Hexahedral meshes --
7.3 Mixed element type volumetric meshes --
7.3.1 Embedded meshes --
7.3.2 Layered mesh --
7.4 Finite element method results --
7.4.1 Model problem and error norms --
7.4.2 Planar example --
7.4.3 Volumetric example --
Chapter 8 Extending the GETMe smoothing framework --
8.1 Alternative element transformations --
8.1.1 Rotation-based transformations --
8.1.2 Geometric transformations with non-regular limits . . --
8.1.3 Gradient flow --
8.2 Variations of GETMe smoothing --
8.2.1 Geometric triangle transformation-based smoothing . --
8.2.2 GETOpt --
Bibliography --
Index.
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