On the fundamental solutions-based inversion of Laplace matrices

The discretisation of the Laplacian results into the well-known Laplace matrix. In the case of a one dimensional problem, an explicit formula for its inverse is derived on the basis of fundamental solutions (Green’s functions) for general boundary conditions. For a linear reaction–diffusion equation, approximations of the inverse are given.

Analysis of Stabilized Finite Element Methods for a Morpho-Poroelastic Model Applied to Tumor Growth

The theory of morpho-poroelasticity is applied to tumor growth. This allows for the modeling of permanent deformation in the tissue as a result of the presence of tumor cells. The work done in this project can be divided into two parts. In the first part we review existing models for elasticity and build corresponding finite element models. The...