| Introduction |
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11 | (6) |
| Symbols and Notations |
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17 | (2) |
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19 | (20) |
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Covering-up and triangulation |
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20 | (4) |
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Mesh, mesh element, finite element mesh |
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24 | (7) |
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31 | (8) |
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Control space and neighborhood space |
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39 | (56) |
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Mesh quality and mesh optimality |
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41 | (4) |
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Basic Structures and Algorithms |
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45 | (1) |
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46 | (2) |
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48 | (5) |
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Basic notions about complexity |
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53 | (3) |
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56 | (6) |
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One-dimensional data structures |
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62 | (7) |
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Two and three-dimensional data structures |
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69 | (5) |
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Topological data structures |
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74 | (3) |
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77 | (3) |
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Optimality of an implementation |
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80 | (3) |
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Examples of generic algorithms |
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83 | (12) |
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A Comprehensive Survey of Mesh Generation Methods |
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95 | (38) |
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96 | (1) |
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Structured mesh generators |
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97 | (7) |
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Algebraic interpolation methods |
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98 | (2) |
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100 | (1) |
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101 | (2) |
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Product method (topology-based method) |
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103 | (1) |
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Unstructured mesh generators |
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104 | (18) |
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Spatial decomposition methods |
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106 | (3) |
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109 | (5) |
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114 | (3) |
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Tentative comparison of the three classical methods |
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117 | (2) |
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119 | (3) |
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122 | (6) |
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Mesh generation via a parametric space |
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122 | (2) |
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Implicit surface triangulation |
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124 | (1) |
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125 | (1) |
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126 | (2) |
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128 | (1) |
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Parallel unstructured meshing |
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129 | (4) |
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Algebraic, PDE and Multiblock Methods |
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133 | (30) |
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133 | (16) |
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Trivial mapping functions |
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134 | (1) |
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Quadrilateral or triangular analogy |
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135 | (8) |
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143 | (1) |
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Hexahedral, pentahedral or tetrahedral analogy |
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144 | (3) |
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Other algebraic methods and alternative methods |
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147 | (2) |
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149 | (4) |
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149 | (4) |
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Surface meshing and complex shapes |
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153 | (1) |
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153 | (10) |
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153 | (1) |
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154 | (1) |
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Computational issues and application examples |
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155 | (8) |
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Quadtree-octree Based Methods |
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163 | (38) |
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Overview of spatial decomposition methods |
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164 | (7) |
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Classical tree-based mesh generation |
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171 | (18) |
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Governed tree-based method |
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189 | (3) |
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192 | (3) |
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195 | (6) |
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Advancing-front Technique for Mesh Generation |
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201 | (34) |
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A classical advancing-front technique |
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203 | (17) |
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Governed advancing-front method |
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220 | (5) |
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225 | (2) |
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227 | (3) |
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230 | (5) |
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Delaunay-based Mesh Generation Methods |
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235 | (40) |
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Voronoi diagram and Delaunay triangulation |
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236 | (9) |
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Constrained triangulation |
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245 | (5) |
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Maintaining a constrained entity |
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245 | (1) |
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246 | (4) |
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Classical Delaunay meshing |
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250 | (11) |
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Simplified Delaunay type triangulation method |
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252 | (2) |
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Boundary integrity and domain identification |
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254 | (1) |
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255 | (2) |
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257 | (1) |
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258 | (1) |
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259 | (2) |
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261 | (3) |
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262 | (1) |
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262 | (1) |
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263 | (1) |
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Isotropic governed Delaunay meshing |
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264 | (3) |
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267 | (8) |
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Weighted Delaunay triangulation |
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268 | (1) |
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Anisotropic Delaunay meshing |
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268 | (5) |
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273 | (2) |
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Other Types of Mesh Generation Methods |
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275 | (28) |
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276 | (4) |
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Grid or pattern-based methods |
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280 | (3) |
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Optimization-based method |
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283 | (7) |
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Quads by means of triangle combination |
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290 | (6) |
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Quads by means of a direct method |
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296 | (2) |
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298 | (2) |
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300 | (3) |
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Delaunay Admissibility, Medial Axis and Applications |
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303 | (28) |
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Delaunay-admissible set of segments in R2 |
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304 | (6) |
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Delaunay-admissible set of segments in R3 |
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310 | (2) |
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Delaunay-admissible set of triangular faces |
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312 | (6) |
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318 | (7) |
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325 | (1) |
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326 | (5) |
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Quadratic Forms and Metrics |
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331 | (30) |
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Bilinear and quadratic forms |
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332 | (5) |
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337 | (5) |
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342 | (8) |
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350 | (11) |
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Parametric surface meshing |
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351 | (1) |
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Finite element simulation with error control |
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352 | (9) |
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361 | (34) |
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Metric properties of curves and arcs |
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362 | (15) |
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Metric properties of a surface |
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377 | (10) |
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Computational issues about surfaces |
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387 | (5) |
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392 | (3) |
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395 | (40) |
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Interpolation and smoothing techniques |
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397 | (3) |
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Lagrange and Hermite interpolation |
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400 | (4) |
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Explicit construction of a composite curve |
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404 | (2) |
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Control polygon based methods |
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406 | (3) |
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409 | (5) |
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From composite curves to B-splines |
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414 | (9) |
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423 | (4) |
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Curve definitions and numerical issues |
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427 | (4) |
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Towards a ``pragmatic'' curve definition? |
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431 | (4) |
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435 | (28) |
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436 | (1) |
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Interpolation-based surfaces |
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437 | (5) |
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Tensor product and control polyhedron |
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442 | (4) |
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Triangular patches and Bezier triangles |
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446 | (4) |
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450 | (2) |
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452 | (5) |
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Explicit construction of a composite surface |
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457 | (6) |
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463 | (28) |
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464 | (7) |
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Meshing a parametric curve |
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471 | (12) |
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Curve meshing using a discrete definition |
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483 | (3) |
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486 | (2) |
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488 | (3) |
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Surface Meshing and Re-meshing |
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491 | (36) |
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Curve meshing (curve member of a surface) |
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492 | (1) |
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First steps in surface meshing |
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493 | (10) |
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503 | (10) |
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Multi-patches surface (patch-dependent) |
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513 | (2) |
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Multi-patches surface (patch-independent) |
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515 | (2) |
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Ill-defined multi-patches surface |
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517 | (2) |
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519 | (2) |
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521 | (2) |
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Discrete surface (re-meshing process) |
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523 | (4) |
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Meshing Implicit Curves and Surfaces |
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527 | (32) |
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Review of implicit functions |
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528 | (5) |
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Implicit function and meshing |
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533 | (4) |
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537 | (8) |
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545 | (11) |
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556 | (3) |
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559 | (32) |
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Mesh (geometric) modifications |
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559 | (8) |
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567 | (6) |
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Node creation and node labeling |
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573 | (4) |
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577 | (10) |
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587 | (4) |
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591 | (32) |
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About element measurement |
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592 | (4) |
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Mesh quality (classical case) |
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596 | (6) |
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Mesh quality (isotropic and anisotropic case) |
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602 | (4) |
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Tools for mesh optimization |
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606 | (11) |
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Strategies for mesh optimization |
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617 | (1) |
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618 | (1) |
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619 | (4) |
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Surface Mesh Optimization |
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623 | (40) |
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624 | (8) |
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Discrete evaluation of surface properties |
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632 | (11) |
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Constructing a geometric support |
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643 | (2) |
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645 | (9) |
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654 | (2) |
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656 | (7) |
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A Touch of Finite Elements |
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663 | (30) |
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Introduction to a finite element style computation |
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664 | (4) |
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Definition and first examples of finite elements |
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668 | (4) |
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Error estimation and convergence |
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672 | (5) |
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Stiffness matrix and right-hand side |
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677 | (13) |
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A few examples of popular finite elements |
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690 | (3) |
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Mesh Adaptation and H-methods |
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693 | (42) |
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Control space (background mesh) |
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694 | (7) |
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Adaptation by local modifications |
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701 | (7) |
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Global isotropic adaptation method |
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708 | (8) |
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Global anisotropic adaptation method |
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716 | (6) |
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722 | (5) |
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General framework of a local adaptation method |
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722 | (2) |
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General framework of a global adaptation method |
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724 | (3) |
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727 | (8) |
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Mesh Adaptation and P or Hp-methods |
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735 | (18) |
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736 | (6) |
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742 | (5) |
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Construction of P2 elements |
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747 | (3) |
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Elements of higher degree |
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750 | (1) |
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751 | (2) |
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Moving or Deformable Meshing Techniques |
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753 | (22) |
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754 | (4) |
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758 | (6) |
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764 | (3) |
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767 | (8) |
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Parallel Computing and Meshing Issues |
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775 | (24) |
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776 | (14) |
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790 | (2) |
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Parallel meshing techniques |
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792 | (7) |
| Bibliography |
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799 | (44) |
| Index |
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843 | |
Lisainfo e-raamatute kohta