Research interests

My research focusses on the following topics:

Solvers for Isogeometric Analysis

I am currently working on efficient solvers for linear systems arising within Isogeometric Analysis. In particular, my work focusses on p-multigrid methods, which can be used as a stand-alone solver or preconditioner. The key idea of p-multigrid methods is to obtain the coarse grid correction on a low-order level to update the solution at the high-order level. In recent publications, p-multigrid methods have shown to be a robust and efficient solver for a variety of benchmark problems, including single patch and multipatch geometries in two and three dimensions.

Recently, I have been working on solvers for the discretized Helmholtz equation as well. Here, the well known Complex Shifted Laplacian Preconditioner (CSLP) has been combined with deflation to obtain a scalable solver when applying Isogeometric Analysis for the spatial discretization

A high-order Material Point Method

Another field of interest is particle-mesh methods, in particular the Material Point Method (MPM). Throughout the years, I adopted concepts from the field of IgA to improve MPM. The use of high-order B-spline basis functions has shown to lead to more accurate solutions, while enabling high-order spatial convergence.

Furthermore, I have investigated the use of alternative basis functions with higher continuity (i.e. Powell-Sabin splines) within MPM. Finally, I worked on the comparison of MPM with Optimal Transportation Meshfree (OTM) methods.