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