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We study a multi-scale model for growth of malignant gliomas in the human brain.
Interactions of individual glioma cells with their environment determine the gross tumor shape.
We connect models on different time and length scales to derive a practical description of tumor growth that takes these microscopic interactions into account.
From a simple subcellular model for haptotactic interactions of glioma cells with the white matter we derive a microscopic particle system, which leads to a meso-scale model for the distribution of particles, and finally to a macroscopic description of the cell density.
The main body of this work is dedicated to the development and study of numerical methods adequate for the meso-scale transport model and its transition to the macroscopic limit.
On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials
(2015)
This thesis is concerned with the extended finite element method (XFEM) for deformation analysis of three-dimensional heterogeneous materials. Using the "enhanced abs enrichment" the XFEM is able to reproduce kinks in the displacements and therewith jumps in the strains within elements of the underlying tetrahedral finite element mesh. A complex model for the micro structure reconstruction of aluminum matrix composite AMC225xe and the modeling of its macroscopic thermo-mechanical plastic deformation behavior is presented, using the XFEM. Additionally, a novel stabilization algorithm is introduced for the XFEM. This algorithm requires preprocessing only.