In finite element software one has to solve a system of non-linear equations, which is commonly simplified to a sequence of linear system. We research the possibility to solve these systems on a GPU to improve the solve time. We are particularly interested in systems arising from geotechnical models. We compare several combinations of Krylov methods, parallel preconditioners and deflation methods and present a suitable combination. This solver is then compared with existing CPU based solvers in PLAXIS 3D. We show that compared to the current iterative solver, the iteration time can be reduced by 50% up to 85% depending on the problem. While compared to the current direct solver, the memory consumption and initialization time can be reduced significantly.

The aim of this research is to develop an N -dimensional adaptive sampling algorithm to efficiently sample functions, meaning that with fewer samples the same accuracy is achieved compared to what homogeneously spaced samples would achieve. This algorithm is based on an existing Python package called Adaptive. The developed algorithm is applied to find and plot the Fermi surface of crystals with a higher resolution than homogeneous sampling would with the same number of points.