List of Figures

  1. Objects with symmetries used in CAE
  2. A sketch of a bridge$ ^3$ with similarities
  3. Re-construction of objects with symmetries
  4. Symmetric geometry and exemplary non-symmetric mesh
  5. Templated meshes
  6. Multi-region geometry
  7. Implicit geometries
  8. Reconstruction process of a boundary representation
  9. Reconstruction process of a multi-region boundary representation
  10. CSG set operations of two sets
  11. CSG tree
  12. Mesh intersection
  13. 2D multi-region mesh
  14. Respect property
  15. Inballs for a rectangle, for a triangle, and for a tetrahedron
  16. Delaunay property
  17. Constrained Delaunay property
  18. Mesh data structure layout
  19. Advancing front mesh generation
  20. Delaunay refinement mesh generation
  21. Overlaying grid mesh generation
  22. Edge flipping operation for triangles
  23. Laplacian smoothing
  24. 2D simplex refinement
  25. Instancing
  26. Decomposition of a multi-region mesh
  27. Templated mesh
  28. Templated structure with non-conforming structure instance
  29. Non-trivial interface of a template with itself
  30. Instance graph
  31. Indirect neighbors
  32. Template boundary mapping
  33. Composition of template boundary mappings
  34. Boundary patch partition
  35. Issues due to boundary template mapping incompatibility
  36. Issues with the Delaunay property of templated meshes
  37. Templated mesh stored with and without SVB
  38. Eliminating non-conformities by vertex merging
  39. Vertex merging fails to fix all non-conformities
  40. Eliminating vertex-in-facet non-conformities
  41. Non-conformity induced by a line-line intersection
  42. Templated mesh generation using surface meshes
  43. Non-locality of operations in the structure instance
  44. Conformity issues with operations performed on template boundaries
  45. The template cloning operation
  46. The template splitting operation
  47. Combination of template splitting and cloning
  48. Examples of vertices which cannot be moved
  49. Valid vertex movements visualized using the boundary patch partition
  50. Issues with element flips across instances
  51. Vertex insertion in the interior of a template
  52. Conformity issues with insertion of multiple vertices
  53. A templated mesh is made template-aware Delaunay
  54. The ping-pong encroachment effect near small angles
  55. Two different templated meshes with same structure instance
  56. Boundary dependencies in a templated geometry
  57. Grid slicing decomposition
  58. Reflective symmetry
  59. Boundary patch partition of a set with reflective symmetry
  60. A slice of a set with a rotational symmetry
  61. Boundary patch partition of a set with rotational symmetry
  62. Boundary patch partition of a multi-region geometry with rotational symmetry
  63. Examples for possible slice positions
  64. Piecewise linear slice starting angle
  65. Issues with small angles
  66. Small angle optimization for rotational symmetries
  67. Small angle optimization for high rotational symmetry orders $ n$.
  68. Combination of reflective symmetries
  69. Combination of reflective and rotational symmetries
  70. Benchmark objects with reflective symmetries and their templates
  71. Benchmark results for objects with reflective symmetries
  72. Memory benchmark results of structure instance
  73. Element qualities
  74. Element quality issues due to sharp angles in the 2D aircraft geometry
  75. Benchmark objects with rotational symmetries
  76. Benchmark results for the 2D $ n$-polygon
  77. Smallest angle quality histograms for $ n$-polygon benchmarks
  78. Quality comparison of meshes generated for a $ 16$-polygon
  79. Benchmark results for the 3D open TSV structure
  80. Benchmark objects with similarities
  81. Benchmark results for the 2D bridge beam construction
  82. Benchmark results for the multiple open TSV structure
  83. The Gummel Star with non-symmetric boundary conditions
  84. Non-symmetric and symmetric example meshes of the Gummel Star
  85. All rotations of the non-symmetric Gummel Star boundaries
  86. Memory benchmark results including the FEM system matrix
  87. Memory benchmark results using the templated CSR matrix
  88. Runtime benchmark results for templated CSR matrix-vector product
  89. Connected property of sets
  90. Element faces are not minimal
  91. Affine and convex hull
  92. Simplices
  93. Faces
  94. Non-simplex elements
  95. The intersection of manifolds is not a manifold



florian 2016-11-21