Titre : Nathan Rouxelin (INRIA Bordeaux, équipe MAKUTU). A HDG framework for convected acoustics. Applications in helioseismology.
Contact : Jean-François Fritsch  
Date : 21/10/2021
Lieu : 14h, amphi 2329
This work takes place in the context of the scientific collaboration between the Makutu Team (Inria Bordeaux – Sud-Ouest and University of Pau) and the Max-Planck Institute for solar system research in Göttingen. The goal of this collaboration is to build a computational framework to solve inverse problems in helioseismology, which is a branch of solar physics that aims at imaging the solar interior thanks to surface observations. As a first step toward the development of efficient and reliable numerical methods for wave-propagation problems arising in helioseismology, we present three variations of the Hybridizable Discontinuous Galerkin (HDG) method to solve the convected Helmholtz equation. HDG methods are mixed DG methods whose solution is computed thanks to a surfacic auxiliary unknown. This allows for an efficient implementation of the method that relies on a static condensation process, leading to a so-called global problem for this skeleton unknown only. The original unknowns can then be reconstructed locally in a parallel way. As a result of this, HDG methods keep the advantages of the DG methods (eg. hp-adaptivity, high order,...) without incurring their high numerical cost. For the three HDG methods that we have constructed, we present theoretical results including well-posedness of the local and global problems, convergence analysis for regular solutions and a discussion about the choice of penalization parameters. To illustrate the theoretical results, we then provide implementation details and numerical results for both academic and realistic cases.