research activities

here you can see some of my project descriptions, attended conferences and other miscellaneous stuff

attended conferences

  • 4th International Conference on Numerical Methods in Multiphase Flows (ICNMMF-4), September 28-30, 2022, Venice. Gave a 15 minute talk (slides)
  • ENUMATH 2023 (ENUMATH), September 4-8, 2023, Lisbon. Gave a 20 minute talk.

project descriptions

  • Conservative cut finite element methods [PhD Project] , with S. Zahedi and T. Frachon

The cut finite element method (CutFEM) is a numerical method for meshes unfitted to the physical domain associated to a partial differential equation. In this paper we present a method which is able to preserve a conservation law - a condition on the divergence - in the setting of the Darcy interface problem, which models flow of porous media. The method introduces stabilization terms which preserve the saddle-point structure of the problem. The same mixed stabilization terms allow us to find methods exhibiting divergence-free velocity solutions also for Stokes flow, see this follow-up paper.

  • Auxiliary space preconditioners for mixed virtual element methods , with W. Boon

In this work we propose nodal auxiliary space preconditioners for facet and edge virtual elements of lowest order, for applications to PDEs approximated using the virtual element method (VEM). Under assumed regularity of the mesh, the preconditioned system is proven to have bounded spectral condition number independent of the mesh size and this is verified by numerical experiments on a sequence of polygonal meshes. Moreover, we observe numerically that the preconditioner is robust on meshes containing elements with high aspect ratios.

  • Can one hear the shape of a flat torus? [~2021] , with J. Rowlett and F. Rydell

Flat tori are particularly simple Riemannian manifolds for which it is in some dimensions possible to discern their isometry class (shape) from simply looking at the list of numbers we call the Laplace eigenvalue spectrum. In which dimensions can we do this? The answer is written in the language of quadratic forms (and also only German - up until now!)

(See here for a less polished introduction. Beware of errors.)