| Foreword |
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ix | |
| Introduction |
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xi | |
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Chapter 1 Metrics, Definitions and Properties |
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1 | (52) |
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1.1 Definitions and properties |
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2 | (4) |
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1.2 Metric interpolation and intersection |
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6 | (8) |
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1.2.1 Metric interpolation |
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7 | (6) |
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1.2.2 Metric intersection |
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13 | (1) |
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14 | (9) |
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1.3.1 Geometric metric for a curve |
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16 | (1) |
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1.3.2 Geometric metric for a surface |
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17 | (6) |
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1.3.3 Turning any metric into a geometric metric |
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23 | (1) |
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23 | (1) |
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24 | (7) |
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31 | (7) |
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1.6.1 Metric of a simplicial element |
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31 | (6) |
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1.6.2 Metric of a non-simplicial element |
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37 | (1) |
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1.6.3 Metric of an element of arbitrary degree |
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38 | (1) |
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1.7 Element shape and metric quality |
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38 | (8) |
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1.8 Practical computations in the presence of a metric |
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46 | (7) |
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1.8.1 Calculation of the length |
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46 | (3) |
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1.8.2 The calculation of an angle, area or volume |
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49 | (4) |
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Chapter 2 Interpolation Errors and Metrics |
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53 | (40) |
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54 | (1) |
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2.2 Interpolation error of a quadratic function |
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55 | (7) |
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2.3 Bezier formulation and interpolation error |
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62 | (24) |
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2.3.1 For a quadratic function |
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63 | (3) |
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2.3.2 For a cubic function |
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66 | (14) |
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2.3.3 For a polynomial function of arbitrary degree |
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80 | (5) |
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2.3.4 Error threshold or mesh density |
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85 | (1) |
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2.4 Computations of discrete derivatives |
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86 | (7) |
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2.4.1 The L2 double projection method |
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86 | (2) |
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88 | (1) |
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2.4.3 Least square and Taylor |
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89 | (4) |
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93 | (14) |
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3.1 Parametric curve meshing |
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95 | (9) |
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95 | (4) |
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3.1.2 About metrics used and computations of lengths |
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99 | (4) |
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3.1.3 Curve plotted on a patch |
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103 | (1) |
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3.2 Discrete curve meshing |
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104 | (1) |
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3.3 Remeshing a meshed curve |
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104 | (3) |
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Chapter 4 Simplicial Meshing |
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107 | (34) |
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108 | (1) |
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4.2 Variety (surface) meshing |
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109 | (13) |
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4.2.1 Patch-based meshing |
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110 | (9) |
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4.2.2 Discrete surface remeshing |
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119 | (1) |
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4.2.3 Meshing using a volume mesher |
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120 | (2) |
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4.3 The meshing of a plane or of a volume domain |
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122 | (14) |
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123 | (3) |
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126 | (3) |
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4.3.3 Delaunay-based method |
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129 | (5) |
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4.3.4 Remeshing of a meshed domain |
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134 | (2) |
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4.4 Other generation methods? |
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136 | (5) |
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Chapter 5 Non-simplicial Meshing |
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141 | (54) |
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142 | (1) |
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143 | (2) |
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5.3 Construction methods for meshing a planar or volume domain |
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145 | (37) |
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5.3.1 Cylindrical geometry and extrusion method |
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147 | (1) |
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5.3.2 Algebraic methods and block-based methods |
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148 | (24) |
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172 | (2) |
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174 | (2) |
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5.3.5 Polygonal or polyhedral cell meshing |
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176 | (1) |
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5.3.6 Construction of boundary layers |
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177 | (5) |
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5.4 Other generation methods |
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182 | (3) |
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5.4.1 "Q-morphism" or "H-morphism" meshing |
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182 | (1) |
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5.4.2 Meshing using a reference frame field |
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183 | (2) |
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5.5 Topological invariants (quadrilaterals and hexahedra) |
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185 | (10) |
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Chapter 6 High-order Mesh Construction |
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195 | (30) |
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196 | (12) |
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6.1.1 Local node numbering |
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196 | (5) |
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6.1.2 Overall node numeration |
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201 | (3) |
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204 | (3) |
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6.1.4 On filling up matrices according to element degrees |
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207 | (1) |
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6.2 Construction of curved meshes |
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208 | (7) |
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209 | (1) |
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209 | (1) |
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6.2.3 Deformation and validation |
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210 | (1) |
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211 | (4) |
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6.3 Curved meshes on a variety, curve or surface |
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215 | (10) |
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Chapter 7 Mesh Optimization |
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225 | (40) |
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7.1 Toward a definition of quality |
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226 | (7) |
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233 | (15) |
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233 | (1) |
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7.2.1.1 Optimization of a cost function |
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233 | (1) |
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7.2.1.2 Iterative relaxation of the position of vertices by duality (simplices) |
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234 | (1) |
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7.2.1.3 Global optimization of the position of vertices (quadrilaterals and hexahedra) |
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235 | (1) |
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7.2.2 Local operators and local methods |
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236 | (1) |
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7.2.2.1 Vertex moves by barycentering |
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236 | (1) |
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7.2.2.2 Vertex moves and Laplacian operator |
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237 | (4) |
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7.2.2.3 Moving or removing vertices and flips by insertion or reinsertion |
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241 | (1) |
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241 | (2) |
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7.2.2.5 Cluster of edge flips |
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243 | (1) |
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7.2.2.6 Edge or face flip by reinsertion |
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244 | (1) |
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244 | (1) |
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7.2.2.8 Removal of an edge by merging |
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245 | (1) |
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7.2.2.9 Metric field update |
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246 | (1) |
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7.2.2.10 Topological and metric criteria |
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246 | (1) |
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246 | (2) |
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248 | (2) |
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250 | (1) |
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251 | (3) |
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254 | (11) |
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Chapter 8 Mesh Adaptation |
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265 | (38) |
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8.1 Generic framework for adaptive computation, the continuous mesh |
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266 | (6) |
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8.1.1 Duality between discrete and continuous geometric entities |
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267 | (2) |
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8.1.2 Duality between discrete and continuous interpolation error |
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269 | (3) |
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8.1.3 Discrete-continuous duality in one diagram |
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272 | (1) |
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8.2 Optimal control of the interpolation error in Lp-norm |
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272 | (7) |
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8.3 Generic scheme of stationary adaptation |
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279 | (10) |
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282 | (5) |
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8.3.2 Interpolation of solution fields |
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287 | (2) |
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289 | (8) |
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8.4.1 Space-time error estimators based on the characteristics of the solution |
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290 | (1) |
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8.4.2 Extension of the error analysis for the fixed-point algorithm for unsteady mesh adaptation |
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291 | (1) |
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8.4.3 Mesh adaptation for unsteady problems |
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292 | (2) |
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8.4.4 Unsteady mesh adaptation targeted at a function of interest |
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294 | (1) |
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8.4.5 Conservative interpolation of solution fields |
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295 | (2) |
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8.5 Mobile geometry with or without deformation |
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297 | (6) |
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8.5.1 General context of the adaptation for mobile and/or deformable geometries |
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297 | (1) |
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8.5.2 ALE continuous optimal mesh minimizing the interpolation error in Lp-norm |
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298 | (2) |
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8.5.3 Space-time error estimator for moving geometry problems |
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300 | (3) |
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Chapter 9 Meshing and Parallelism |
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303 | (28) |
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9.1 Renumbering via a filling curve |
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304 | (3) |
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9.2 Parallelism: two memory paradigms and different strategies |
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307 | (5) |
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9.3 Algorithm parallelization for mesh construction |
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312 | (12) |
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9.4 Parallelization of a mesh construction process, partition then meshing |
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324 | (2) |
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9.5 Mesh parallelization, meshing then partition |
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326 | (5) |
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331 | (22) |
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332 | (2) |
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10.2 In computational fluid dynamics |
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334 | (7) |
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10.3 Computational solid mechanics |
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341 | (4) |
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10.4 Computational electromagnetism |
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345 | (1) |
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10.5 Renumbering and parallelism |
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346 | (3) |
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10.6 Other more exotic applications |
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349 | (4) |
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Chapter 11 Some Algorithms and Formulas |
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353 | (20) |
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11.1 Local numbering of nodes of high-order elements |
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354 | (10) |
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11.2 Length computations etc., in the presence of a metric field |
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364 | (5) |
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369 | (4) |
| Conclusions and Perspectives |
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373 | (2) |
| Bibliography |
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375 | (12) |
| Index |
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387 | |
Lisainfo e-raamatute kohta