Leibner, Tobias: Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition. 2021
Inhalt
- Abstract
- Contents
- List of Figures
- Introduction
- First-order finite element moment models
- Angular bases in slab geometry
- Full moments
- Continuous piecewise linear angular basis (hat functions)
- Partial moments (discontinuous-Galerkin ansatz)
- Angular bases in three dimensions
- Realizability
- Structure of the realizable sets
- Slab geometry (one dimension)
- Three dimensions
- Numerically realizable set
- Numerical results
- Realizability-preserving finite volume schemes
- First-order realizability-preserving finite volume scheme
- Second-order realizability-preserving splitting scheme
- Implementation details
- Solving the optimization problem
- Solving the eigenvalue problems
- Realizability limiting
- Implementation of quadrature rules
- Numerical results
- New numerical scheme based on variable transformation
- Hierarchical approximate proper orthogonal decomposition
- Related work
- Reduced basis methods
- Proper orthogonal decomposition
- Definition of the HAPOD
- Special cases: distributed and incremental HAPOD
- Main theorems
- Algorithmic benefits
- Proofs of main theorems
- Reduction of a large linear moment model
- Conclusion and Outlook
- First-order finite element-based moment models
- Transformed numerical scheme
- Reduced-basis methods for moment models
- Appendix
- Bibliography
- Glossaries