Contents

• List of Figures
• 1 Introduction and Motivation
• 2 Geometries and Meshes
  • 2.1 Geometries
    • 2.1.1 Implicit Representation
    • 2.1.2 Boundary Representation and Piecewise Linear Complexes
    • 2.1.3 Constructive Solid Geometries
  • 2.2 Meshes
    • 2.2.1 Geometry-Conformity
    • 2.2.2 Mesh Element Quality and Mesh Quality
  • 2.3 Delaunay Elements and Meshes
  • 2.4 Data Structure for Meshes
  
  
• 3 Related Work
  • 3.1 Mesh Generation
    • 3.1.1 Simplex Mesh Generation
    • 3.1.2 Quadrilateral and Hexahedral Mesh Generation
    • 3.1.3 Mesh Generation Software
  • 3.2 Mesh Adaptation Algorithms
    • 3.2.1 Topological Operations
    • 3.2.2 Geometrical Operations
    • 3.2.3 Mixed Operations
    • 3.2.4 Mesh Quality Improvement
    • 3.2.5 Mesh Adaptation Software
  • 3.3 Symmetry and Similarity
    • 3.3.1 Symmetry Detection
    • 3.3.2 Similarity Detection
    • 3.3.3 Symmetry-Aware Mesh Processing
  
  
• 4 Templated Geometries and Meshes
  • 4.1 Decomposition of Geometries and Meshes, Templated Structures
  • 4.2 Instance Interfaces and Conformity
  • 4.3 Boundary Patch Partition
  • 4.4 Template-Aware Delaunay
  • 4.5 Mesh Data Structures for Templated Meshes
  
  
• 5 Algorithms for Templated Geometries and Meshes
  • 5.1 Mesh Generation
    • 5.1.1 Independent Mesh Generation and Interface Merging
    • 5.1.2 Templated Mesh Generation Based on the Boundary Patch Partition
  • 5.2 Mesh Adaptation
    • 5.2.1 Template Cloning, Merging, and Splitting
    • 5.2.2 Vertex Smoothing
    • 5.2.3 Flips
    • 5.2.4 Vertex Insertion and Refinement
    • 5.2.5 Adapt to Delaunay Mesh
    • 5.2.6 Quality Improvement
  
  
• 6 Decompositions and Symmetries
  • 6.1 Decomposition Identification
  • 6.2 Reflective Symmetries
  • 6.3 Rotational Symmetries
    • 6.3.1 Finding Optimal Slicing Positions
    • 6.3.2 Handling Small Angles
  • 6.4 Combined Symmetries
    • 6.4.1 Combination of Reflective Symmetries
    • 6.4.2 Combination of Reflective Symmetry and Rotational Symmetry
  
  
• 7 Results and Applications
  • 7.1 Benchmark Setup
  • 7.2 Reflective Symmetries
  • 7.3 Rotational Symmetries
  • 7.4 General Similarities
  • 7.5 FEM-based Symmetry Analysis using a Five-pointed Star
  • 7.6 Memory and Runtime Benefits in FEM applications
  
  
• 8 Conclusion and Outlook
  • 8.1 Conclusion
  • 8.2 Outlook
  
  
• A Mathematical and Geometrical Background
• Bibliography