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Dissertation Rene Heinzl
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Organization
2 Theoretical Concepts
Subsections
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
2.1.3.1 Field Function Reconstruction and Projection
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
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Dissertation Rene Heinzl
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Organization
R. Heinzl
: Concepts for Scientific Computing
