Speaker
Vanessa Llerasas, University of Montpellier
Abstract
The phiFEM method is a numerical technique designed to solve partial differential equations on complex geometries without requiring boundary-fitted meshes. The domain is implicitly described using a level-set function $\phi$, allowing computations on simple background meshes. This approach combines the ease of implementation of immersed methods with the accuracy of classical finite elements.
phiFEM achieves optimal convergence rates for elliptic and parabolic problems such as the Poisson or heat equations and extends naturally to Stokes flow and hyperelasticity.
In this talk, we will present simulations on various applications, including heat transfer, fluid mechanics, and nonlinear elasticity.
We will also show recent developments combining phiFEM with neural networks and multigrid solvers to enhance efficiency and robustness.