Numerical solution of partial differential equations using a fictitious domain method

Abstract

The thesis deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the effective solvers based on the discrete Fourier transform or the Total-FETI domain decomposition. We discuss the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on a model benchmark. The main goals of this thesis are the extension of the modified fictitious domain approach for solving elliptic boundary value problems of linear elasticity and the comparison of two above mentioned solvers. The thesis formed the basis of the papers, also presented during several domestic and international conferences.