April 9, 202513:30-17:30

K. Johnson, building 1R3, Institut de mathématiques

13h30 - Francesco Bonaldi Université de Perpignan)

Numerical simulation of elasto-acoustic wave propagation

This talk addresses the numerical approximation of coupled elastic-acoustic wavepropagation, a key problem in seismic modeling, geophysical exploration, and ultrasoundapplications. Given the complexity of computational domains, we employ a discontinuousGalerkin (dG) method on polyhedral meshes to balance geometric accuracy and computationalefficiency. We establish existence, uniqueness, and stability results using Hille-Yosida theoryand derive error estimates in an energy norm. Numerical experiments, including 3D simulationsof seismic sources and marine exploration, validate our theoretical findings. These simulationswere conducted using the SPEED code, developed at the Polytechnic University of Milan..

15h00 - Radu Ignat (Institut de Mathématiques de Toulouse)

Maximum principle and applications

The maximum principle started from the following idea: in dimension one, a convex continuousfunction on a segment achieves its maximum at the boundary. This idea has been generalizedin higher dimension to solutions u of certain elliptic partial differential equations (PDEs), inparticular, for harmonic functions : unless u is a constant function, the maximum of u cannotbe achieved in the interior. The aim of this lecture is to state and prove the main resultsconcerning the maximum principle for elliptic PDEs. As consequences, we will review thefollowing applications: uniqueness of solutions to elliptic PDEs, symmetry results (the movingplane method), Liouville's theorem...

16h00 - Coffee Break

https://indico.math.cnrs.fr/event/14063/