Wenske, Michael: Data-aware methods for the simulation of glioblastoma multiforme. 2020
Inhalt
- Abstract
- Zusammenfassung
- Acknowledgments
- List of Abbreviations
- List of Figures
- List of Tables
- Introduction
- Medical perspective
- Mathematical forward modeling of GBM
- Problems and challenges of the PDE models
- Stationary modeling of GBM
- Existing numerical approaches
- Outline
- Preliminaries
- Notations
- Fully anisotropic advection diffusion reaction equations
- Variational formulation
- Finite-dimensional space and grid
- Matrix expressions
- Matrix exponential and logarithm
- Powers of a matrix
- Artificial inhomogeneous diffusion
- Fractional anisotropy
- Manufactured solutions
- The MPFA-O method
- The Hölder finite volume method
- Problem description
- Diffusivity averaging
- Hölder finite volume method
- Numerical convergence results
- Inhomogeneous isotropic case (eigenvalue)
- Homogeneous anisotropic case
- Inhomogeneus anisotropic case (rotation)
- Inhomogeneus anisotropic case (combined)
- Conclusion
- Stationalization
- Forward tumor models
- Stationalization of Fisher-KPP equation in 1D
- Stationalized tumor models
- Numerical methods
- Numerical results
- Implementation: The DUNE-glio module
- Application to real data sets
- Discussion and outlook
- Bibliography
- Appendix