Title: Approximating partial differential equations with missing input data Abstract We consider the problem of numerically approximating the solution of partial differential equations for which not all the input data are known. A situation of particular interest is when the boundary conditions are unknown, or only partially known. To alleviate…
Title: Hilbertian degenerations Abstract We study problems involving entities to which a “mass” is attached. This quantity can actually be a mass in the usual sense for systems of particles, but it can also be a thermal capacity in the context of heat transfer, or a kind of charisma in…
Title: Towards trustworthy use of scientific machine-learning in large-scale numerical simulations Abstract Recently, scientific machine learning (SciML) has expanded the capabilities of traditional numerical approaches by simplifying computational modeling and providing cost-effective surrogates. However, SciML models suffer from the absence of explicit error control, a computationally intensive training phase, and…
Title: A semi-implicit numerical scheme based on moving Voronoi cells Abstract In this talk, I will explain how moving Voronoi grids can be used in computational fluid dynamics. Following the papers of Bruno Després [1] and Volker Springel [2], we pursue a method for compressible Navier-Stokes equations that is as…
Title: Explicit local time-stepping methods for wave propagation Abstract Adaptivity and mesh refinement are certainly key for the efficient numerical simulation of wave phenomena in complex geometry. Locally refined meshes, however, severely constrain the time-step of any explicit time-marching scheme due to the CFL stability condition governed by the smallest…
Title: Unique continuation for the wave equation: The stability landscape Abstract Inverse and ill-posed problems subject to the wave equation occur in a variety of applications ranging from seismology to medicine. Among these problems, the task of unique continuation is perhaps one of the simplest: Given measurements of the solution…
