Contents

• List of Tables
• List of Figures
• 1 Introduction
• 2 Theoretical Concepts
  • 1. Mathematical Concepts
    • 1.1 Introduction
    • 1.2 Physical Fields and Electromagnetics
    • 1.3 Topological Toolkit
      • 1.3.1 Order Theory and Sets
      • 1.3.2 Cell Topology
      • 1.3.3 Complex Topology
    • 1.4 Computational Topology
      • 1.4.1 Chains
      • 1.4.2 Cochains
      • 1.4.3 Homology and Cohomology
      • 1.4.4 Duality between Chains and Cochains
    • 1.5 Fiber Bundles
    • 1.6 Fiber Bundles and Chains/Cochains
    • 1.7 Discrete Electromagnetics
    • 1.8 Overview of Theoretical Concepts
  • 2. Numerical Discretization Schemes
    • 2.1 Generic Discretization Concepts
      • 2.1.1 Domain Discretization
      • 2.1.2 Topological Equations
      • 2.1.3 Constitutive Relation Discretization
    • 2.2 Finite Volumes
      • 2.2.1 Basic Concepts
    • 2.3 Finite Elements
      • 2.3.1 Basic Concepts for a Galerkin Method
    • 2.4 Finite Differences
      • 2.4.1 Basic Concepts
      • 2.4.2 Analysis of the Finite Difference Method
      • 2.4.3 Further Analysis
  
  
• 3 Practical Concepts
  • 3. Overview
  • 4. Programming Concepts
    • 4.1 Data Model for Scientific Computing
    • 4.2 Evolution of Programming Paradigms
      • 4.2.1 Object-Orientation Programming
      • 4.2.2 Functional Programming
      • 4.2.3 Generic Programming
      • 4.2.4 Meta-Programming
    • 4.3 Domain-Specific Embedded Language
    • 4.4 Concept Development and Related Work
      • 4.4.1 STAP, SCAP
      • 4.4.2 Minimos-NT
      • 4.4.3 AMIGOS, FEDOS
      • 4.4.4 Wafer-State Server
      • 4.4.5 Boost Graph Library
      • 4.4.6 Computational Geometry Algorithm Library
      • 4.4.7 Grid Algorithms Library
      • 4.4.8 Further Related Work
  • 5. Application Concepts
    • 5.1 Generic Data Structures
    • 5.2 Boundary Operation
    • 5.3 Data Structure Storage Mechanism
    • 5.4 Separation of Base and Fiber Space
    • 5.5 Library-Centric Software Design
  
  
• 4 Applied Concepts
  • 6. Overview
  • 7. A Generic Scientific Simulation Environment
    • 7.1 The Generic Topology Library
      • 7.1.1 The 0-Cell Complex
      • 7.1.2 The 1-Cell Complex
      • 7.1.3 The 2-Cell Complex
      • 7.1.4 Higher-Dimensional Cell Complexes
      • 7.1.5 Data Access
    • 7.2 The Generic Functor Library
      • 7.2.1 Traversal Operators
      • 7.2.2 Data Accessors
      • 7.2.3 Arithmetic Functors
      • 7.2.4 Domain-Specific Embedded Language
    • 7.3 Additional Generic Components
      • 7.3.1 Generic Solver Interface, GSI
      • 7.3.2 Generic Orthogonal Range Queries
      • 7.3.3 Generic File Interface, GFI
      • 7.3.4 Finite Element Components
    • 7.4 Performance Analysis
      • 7.4.1 GTL's Performance
      • 7.4.2 GFL's Performance
  • 8. Generic Application Design
    • 8.1 Visual Programming
    • 8.2 Wave Equation
    • 8.3 Diffusion Simulation
      • 8.3.1 The Equations
      • 8.3.2 Transformation into the GSSE 
      • 8.3.3 Results
    • 8.4 Device Simulation
      • 8.4.1 The Equations
      • 8.4.2 Transformation into the GSSE 
      • 8.4.3 Results
  • 9. Smart Analysis Package
    • 9.1 Structure Modeling
    • 9.2 Basic Equations and Discretization
      • 9.2.1 Capacitance Analysis
      • 9.2.2 Resistance Analysis
      • 9.2.3 Finite Element Solution Procedure
      • 9.2.4 Transformation into GSSE 
    • 9.3 Applications
      • 9.3.1 Capacitance Analysis
      • 9.3.2 Resistance Analysis for Cu-DD Architecture
    • 9.4 Performance Analysis
    • 9.5 Application Design Concepts
• 10. Summary and Outlook
• Appendix A: Common Mathematical Terms
• Appendix B: STL Iterator Analysis
• Appendix C: Cell Properties of Discretization Schemes
  
• Bibliography