Delaunay triangulation and meshing: applications to finite elements
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Hermes
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII 413 S. graph. Darst. |
| ISBN: | 2866016920 |
Internformat
MARC
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| 100 | 1 | |a George, Paul-Louis |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Delaunay triangulation and meshing |b applications to finite elements |c Paul-Louis George ; Houman Borouchaki |
| 264 | 1 | |a Paris |b Hermes |c 1998 | |
| 300 | |a VII 413 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 7 | |a Eindige-elementenmethode |2 gtt | |
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 7 | |a Triangulation |2 ram | |
| 650 | 7 | |a Trigonometrie |2 gtt | |
| 650 | 7 | |a Éléments finis, Méthode des |2 ram | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Finite element method | |
| 650 | 4 | |a Numerical grid generation (Numerical analysis) | |
| 650 | 4 | |a Triangulation | |
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Datensatz im Suchindex
| _version_ | 1804126863200616448 |
|---|---|
| adam_text | Contents
1 Triangle, tetrahedron, triangulation, mesh 5
1.1 Introduction 5
1.2 About the triangle 5
1.3 About the tetrahedron 9
1.4 Simplex 13
1.5 Triangulation 13
1.6 Mesh 20
1.7 Useful element sets 23
1.7.1 Element sets 23
1.7.2 About the construction of such sets 25
1.7.3 About the construction of the edges of a triangulation 30
1.7.4 About the construction of the faces of a triangulation 32
1.7.5 About set membership 32
1.8 Notes 32
2 Delaunay triangulation 33
2.1 Introduction 33
2.2 From Dirichlet to Delaunay 34
2.3 Delaunay lemma 38
2.4 Incremental method 41
2.5 Other methods 46
2.5.1 Method by edge swapping in two dimensions .... 46
2.5.2 Divide and conquer 47
2.5.3 Sweeping algorithm 49
2.6 Computational aspects 50
2.6.1 Robustness and complexity 50
2.6.2 Reduced incremental method scheme 51
2.6.3 Cavity correction 52
2.6.4 Using the kernel 57
2.6.5 Access to the base 57
II CONTENTS
2.6.6 Inheritance 58
2.6.7 Computational background 61
2.6.8 Dynamic management of the background 62
2.7 About some results 63
2.8 Applications 68
2.9 Notes 71
3 Constrained triangulation 73
3.1 Introduction 73
3.2 Constraints and triangulation 74
3.2.1 Some definitions 74
3.2.2 Constrained triangulation problems 76
3.3 The two dimensional case 76
3.3.1 Construction of a Delaunay admissible constraint . . 76
3.3.2 Method by constraint partitioning 79
3.3.3 Method by enforcing the constraints 80
3.4 Constrained Delaunay triangulation 85
3.5 The three dimensional case 86
3.5.1 Construction of a Delaunay admissible constraint . . 86
3.5.2 Method by constraint partitioning 87
3.5.3 Method by enforcing the constraints 89
3.6 Higher dimensions 99
3.6.1 Constraint partitioning method 99
3.7 Computational aspects in three dimensions 103
3.7.1 Searching the missing constraints 103
3.7.2 Local configurations 103
3.7.3 Tentative scheme for an algorithm 103
3.8 Some application examples 104
3.9 Applications 110
3.10 Notes Ill
4 Anisotropic triangulation 113
4.1 Introduction 113
4.2 Notion of a metric 114
4.2.1 Metrics and distances 115
4.2.2 Multiple metrics 116
4.3 Incremental method 119
4.3.1 Euclidean space 120
4.3.2 Riemannian space 121
4.3.3 Discrete approximations in two dimensions 123
4.3.4 Discrete approximations in three dimensions 125
CONTENTS III
4.4 Computational aspects 128
4.5 Some results 129
4.6 Applications 129
4.7 Notes 130
5 Meshing in two dimensions 131
5.1 Introduction 131
5.2 The empty mesh construction 132
5.3 Field points (creation) 136
5.3.1 Several methods for field point creation 136
5.4 Control space 138
5.5 Creation along the edges, classical case 140
5.6 Creation along the edges, isotropic case 143
5.7 Creation along the edges, anisotropic case 147
5.8 Advancing front type creation 149
5.9 Field points (insertion) 151
5.10 Optimization 151
5.11 General scheme for the mesh generator 152
5.12 Some results 154
5.13 Notes 159
6 Parametric surface meshing 161
6.1 Introduction 161
6.2 The fundamental forms and related metrics 163
6.2.1 Metric of the tangent plane 164
6.2.2 Metric related to the main curvatures 166
6.2.3 Physically based metric 172
6.3 Surface meshing 173
6.3.1 General scheme 174
6.3.2 Construction of a metric in fi 174
6.3.3 Classification of the useful metrics 175
6.3.4 Boundary meshing 176
6.3.5 Domain meshing 176
6.3.6 Surface mapping 177
6.4 Some results 177
6.5 Applications 187
6.5.1 Cylindrical meshing 187
6.5.2 Sampled surface meshing 190
6.5.3 Arbitrary surface meshing 190
6.5.4 Adaptive meshing 192
6.6 Notes 192
IV CONTENTS
7 Meshing in three dimensions 195
7.1 Introduction 195
7.2 The empty mesh construction 196
7.3 Field points (creation) 199
7.3.1 Several methods for field points creation 199
7.4 Control space 201
7.5 Creation along the edges, classical case 201
7.6 Creation along the edges, isotropic case 203
7.7 Creation along the edges, anisotropic case 203
7.8 Advancing front type creation 204
7.9 Field points (insertion) 206
7.10 Specified internal edges and faces 207
7.11 Optimization 207
7.12 General scheme of the mesh generator 208
7.13 About some results 209
7.14 Notes 213
8 Optimizations 215
8.1 Introduction 215
8.2 Mesh quality 215
8.2.1 Shape and size qualities 216
8.2.2 Classification 220
8.2.3 Other (isotropic) quality measures 221
8.3 Topological operators 222
8.3.1 Edge swapping in two dimensions 223
8.3.2 Ball remeshing in two dimensions 223
8.3.3 Shell transformation in three dimensions 223
8.3.4 Entity suppression by local remeshing 227
8.3.5 Suppression by means of reduction 227
8.3.6 Edge splitting 229
8.3.7 Valance relaxation 229
8.4 Geometric operators 230
8.4.1 Local geometric operator 230
8.4.2 Global geometric operators 234
8.5 Remarks on surface optimization 234
8.6 Algorithmic aspects 235
8.6.1 How to use an optimization operator 236
8.6.2 How to control an optimization operator 236
8.6.3 How to control an optimization process 237
8.7 Some results 238
8.8 Applications 242
CONTENTS V
8.9 Notes 242
9 Mesh adaptation 243
9.1 Introduction 243
9.2 Mesh adaptivity methods 244
9.2.1 The r method 244
9.2.2 The ft method 245
9.2.3 The p method 245
9.2.4 The hp method 247
9.3 Modification versus reconstruction 247
9.3.1 Adaptivity based on local modifications 248
9.3.2 Adaptivity based on a complete reconstruction . . . 250
9.4 General scheme for an adaptation loop 251
9.5 Control space 252
9.5.1 Definition of the successive control spaces 252
9.5.2 Control space construction 253
9.6 Boundary meshing (or remeshing) 256
9.6.1 Curve meshing (or remeshing) 256
9.6.2 Surface meshing (or remeshing) 256
9.7 Domain meshing 256
9.8 Solution interpolation 259
9.9 General scheme of an adaptive loop 264
9.10 Some results 265
9.10.1 An isotropic example 266
9.10.2 An anisotropic example 272
9.11 Notes 276
10 Data structures 277
10.1 Introduction 277
10.2 Useful information (tentative list) 278
10.2.1 Recalling the notion of a mesh 278
10.2.2 For a (static) problem using a P1 approximation . . 278
10.2.3 For a (static) problem using a F2 approximation . . 283
10.2.4 For an adaptive computational process 286
10.2.5 Constraining a mesh 287
10.3 A general data structure 288
10.3.1 A general data structure 288
10.4 A geometric data structure 296
10.4.1 The two dimensional case 296
10.4.2 A few remarks about three dimensions 299
10.5 Geometric representation 302
Vi CONTENTS
10.5.1 The two dimensional case 302
10.5.2 The three dimensional case 304
10.6 Mesh data structure 311
10.6.1 The two dimensional case 311
10.6.2 The three dimensional case 313
10.7 Notes 315
11 Boundary meshing 317
11.1 Introduction 317
11.2 Boundary meshing in two dimensions 317
11.2.1 CAD definition of a boundary 318
11.2.2 Related (discrete) data base 318
11.2.3 Construction of a polygonal discrete line 318
11.2.4 Meshing 319
11.3 Boundary meshing in three dimensions 327
11.3.1 Curve meshing 328
11.3.2 Meshing of a surface consisting of several patches . . 328
11.3.3 Surface remeshing using optimization 335
11.4 Results 336
11.4.1 Planar curve mesh 336
11.4.2 Mesh of a surface defined by several patches 339
11.4.3 Surface mesh (remeshing via optimization) 341
11.5 Notes 342
12 Finite element applications 345
12.1 Introduction 345
12.2 Metric definition and metric construction 345
12.2.1 Hessian computation 348
12.2.2 Remark about the metric computation 349
12.2.3 Metric associated with the usual norms 349
12.2.4 Relative error metric 350
12.2.5 Intersection of several metrics 350
12.2.6 Transfer of the solution from one mesh to the other 351
12.3 Three CFD examples 352
12.3.1 General presentation 352
12.3.2 Supersonic scramjet 354
12.3.3 Viscous transonic flow for a Naca 0012 357
12.3.4 Viscous supersonic flow around a cylinder 360
12.4 Notes 365
CONTENTS VII
13 Other applications 367
13.1 Introduction 367
13.2 Medial axis and medial surface 367
13.2.1 Medial axis 367
13.2.2 Medial surface 368
13.2.3 Several applications based on the skeleton 369
13.3 Parallel computing 370
13.3.1 A posteriori partitioning 370
13.3.2 A priori partitioning 371
13.3.3 Partitioning by inductive Delaunay triangulation . . 371
13.3.4 Partitioning a set of points by induction from the
Delaunay triangulation of the convex hull 373
13.3.5 Partitioning from the domain boundary 374
13.4 Minimal roughness of a surface 380
13.5 Notes 381
Appendix 383
. Bibliography 393
. Index 411
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:24:12Z |
| institution | BVB |
| isbn | 2866016920 |
| language | English |
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| spelling | George, Paul-Louis Verfasser aut Delaunay triangulation and meshing applications to finite elements Paul-Louis George ; Houman Borouchaki Paris Hermes 1998 VII 413 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Eindige-elementenmethode gtt Numerieke wiskunde gtt Triangulation ram Trigonometrie gtt Éléments finis, Méthode des ram Algorithms Finite element method Numerical grid generation (Numerical analysis) Triangulation Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Anwendung (DE-588)4196864-5 s DE-604 Borouchaki, Houman Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008298094&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | George, Paul-Louis Borouchaki, Houman Delaunay triangulation and meshing applications to finite elements Eindige-elementenmethode gtt Numerieke wiskunde gtt Triangulation ram Trigonometrie gtt Éléments finis, Méthode des ram Algorithms Finite element method Numerical grid generation (Numerical analysis) Triangulation Finite-Elemente-Methode (DE-588)4017233-8 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4017233-8 (DE-588)4196864-5 |
| title | Delaunay triangulation and meshing applications to finite elements |
| title_auth | Delaunay triangulation and meshing applications to finite elements |
| title_exact_search | Delaunay triangulation and meshing applications to finite elements |
| title_full | Delaunay triangulation and meshing applications to finite elements Paul-Louis George ; Houman Borouchaki |
| title_fullStr | Delaunay triangulation and meshing applications to finite elements Paul-Louis George ; Houman Borouchaki |
| title_full_unstemmed | Delaunay triangulation and meshing applications to finite elements Paul-Louis George ; Houman Borouchaki |
| title_short | Delaunay triangulation and meshing |
| title_sort | delaunay triangulation and meshing applications to finite elements |
| title_sub | applications to finite elements |
| topic | Eindige-elementenmethode gtt Numerieke wiskunde gtt Triangulation ram Trigonometrie gtt Éléments finis, Méthode des ram Algorithms Finite element method Numerical grid generation (Numerical analysis) Triangulation Finite-Elemente-Methode (DE-588)4017233-8 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Eindige-elementenmethode Numerieke wiskunde Triangulation Trigonometrie Éléments finis, Méthode des Algorithms Finite element method Numerical grid generation (Numerical analysis) Finite-Elemente-Methode Anwendung |
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