Institute of Mathematics


Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

The X-MESH method for capturing interfaces

Talk by Prof. Dr. Jean-François Remacle

Speaker invited by: Prof. Dr. Rémi Abgrall

Date: 19.10.22  Time: 16.15 - 17.15  Room: ETH HG E 1.2

In this presentation, we develop an innovative approach - X-MESH - to overcome a major difficulty associated with numerical simulation in engineering: we aim to provide a revolutionary way to track physical interfaces in finite element simulations. The idea is to use so-called extreme mesh deformations. This new approach should allow low computational cost simulations as well as high robustness and accuracy. X-MESH is designed to avoid the pitfalls of current ALE methods by allowing topological changes on fixed mesh. The key idea of X-MESH is to allow elements to deform until they reach a zero measure. For example, a triangle can deform into an edge or even a point. This idea is rather extreme and completely revisits the interaction between the meshing community and the computational community, which for decades have been trying to interact through beautiful meshes.

In this talk, we will focus on both the mathematical issues related to the use of zero-measure elements and the X-MESH resolution scheme. Several applications will be targeted: the Stefan model of phase change, two-phase flows and contact between deformable solids.