Welcome to my personal page!

Since December 2022 I am a post-doctoral researcher in applied mathematics, member of the team EDP et Physique mathématique at Institut de Mathématiques de Bordeaux. This research project is funded by the CNRS.

Between October 2019 and November 2022, I was a Ph.D. candidate at Sorbonne University in the Jacques-Louis Lions laboratory. This work was supervised by Nina Aguillon and Nathalie Ayi, and was funded by the DIM MathInnov. You can find the manuscript of the thesis on the HAL portal.

My research focuses on the design, study and implementation of efficient numerical schemes for simulating complex geophysical flows. In particular I am interested in the following topics:

• In the Boussinesq regime: nonlocal dispersive boundary layer, bathymetry impact, extreme waves formation;
• In the nonlinear shallow water regime:
  • Asymptotic preserving implicit-explicit schemes for the low Froude limit;
  • Fully implicit and iterative kinetic schemes admitting a discrete entropy inequality;

You can contact me at mathieu.rigal[AT]math.u-bordeaux.fr

Education

2019-2022
Ph.D. degree in applied mathematics, Sorbonne University

2016-2019
Engineering degree in applied mathematics and scientific computing (equivalent to a Master degree), Sup Galilée

2018-2019
Exchange semester at the Technical University of Munich

Publications

Upcoming

• A low Froude accurate implicit-explicit scheme for the shallow water system
  M. Rigal
• Implicit kinetic scheme for the Saint-Venant system
  C. El Hassanieh, M. Rigal, J. Sainte-Marie

Proceeding CEMRACS 2019

• Adaptive wavelet schemes and finite volumes
  Daniele Del Sarto, Erwan Deriaz, Xavier Lhebrard, Mathieu Rigal
  ESAIM: ProcS 70 107-123 (2021)

Thesis manuscript

• Low Froude regime and implicit kinetic schemes for the Saint-Venant system

Talks and presentations

Amiens, October 10, 2022
Low Froude regime and implicit kinetic schemes for the Saint-Venant system
Seminar of the LAMFA laboratory, Université de Picardie
Slides

Évian-les-Bains, June 15, 2022
Fully implicit kinetic scheme for the 1D Saint-Venant system
Congrès national d’Analyse NUMérique (CANUM)
Slides

Pornichet, March 10, 2022
Schémas bas Froude IMEX pour les équations de Saint-Venant
Pornichet, MoHyCon conference
Poster

Paris, December 2, 2021
Designing accurate and efficient schemes for the low Froude regime
Inria Paris, team ANGE seminar
Slides

Strasbourg, November 9, 2021
Preserving nearly incompressible states at low Froude number
University of Strasbourg, seminar
Slides

Online, November 16, 2020
Kinetic schemes and wave splitting for the shallow water system in low Froude regime
MathInnov day
Slides

Online, June 16, 2020
Schémas cinétiques et splitting d'ondes pour les équations de Saint-Venant en régime bas Froude
Inria Paris, team ANGE seminar
Slides

Paris, November 18, 2019
Schéma de reconstruction exact sur les chocs isolés
Inria Paris, team ANGE seminar
Slides

Teaching (fr)

• TD d'Analyse hilbertienne, intégration et topologie, niveau L3 (2019-2021) ;
• Cours et révisions d'Analyse vectorielle, niveau L2 (2020)
• TD d'Analyse vectorielle, niveau L2 (2019-2020)
• TP d'introduction à Matlab, niveau L1 (2019-2021)

Code

The program swimpy-1d provides solvers for the one dimensionnal shallow water system in a Python framework. It features explicit and implicit kinetic solvers alongside hydrostatic reconstruction for preserving the lakes at rest and the positivity.