Numerical modelling plays an increasingly important role in the solid earth geosciences as a crucial tool to understand geological processes. Yet, the numerical schemes and computational models that are currently in use have a number of shortcomings, particularly when it comes to the manner in which nonlinearities are dealt with and to solving the governing equations in 3D using iterative and multigrid methods. As a result, we are currently not yet able to perform 3D simulations with the correct physics and at the desired resolutions. In this project, the PhD student will address these issues starting with improving the manner in which nonlinearities are dealt with in our 2D and (parallel) 3D codes. This will allow us to address many geodynamic scientific questions and also pave the way for some of the sub-projects within geocycles, related to volatile cycles within the Earth.