Romain Mottier

PhD student in Applied Mathematics for Computational Physics
romain.mottier@outlook.com
French Alternative Energies and Atomic Energy Commission (CEA)
Teaching and Research Center in Mathematics and Scientific Computing (CERMICS)
French Institute for Research in Numerical Science and Technology (INRIA - SERENA)

Welcome to my academic webpage!

About me

I am a PhD student in applied mathematics for the numerical simulation of physic problems under the direction of Alexandre Ern at CERMICS, École des Ponts ParisTech and Inria. I am also co-supervised by Laurent Guillot at CEA.

As a computational scientist I have a strong background in numerical methods with competencies in numercial analysis for partial differential equations (PDEs) and strong programming skills (Fortran/C++/Python/Matlab) and physics (fluid and solid mechanics, geophysiscs or biology). I am also interested in the optimization and the portability of the numerical methods on high performance computing architectures (HPC).

More specifically, my research is focused on the use of non conforming hybrid high-order finite element methods (HDG/HHO) especially in the context of unfitted methods (also known as embedded or immersed methods). These latter allow the boundary or physical interfaces to cut arbitrarily through the mesh cells. By coupling them with HDG/HHO methods, the idea is to achieve a high-order approximation of our problem while greatly simplifying the mesh generation. In this framework, I am currently working on the numerical simulation of the propagation of elasto-acoustic waves (coupling between the seismic field and atmospheric acoustics or the water), using the methods mentioned above.

Research interests

  • Numerical methods:

    •        -    Unfitted methods
           -    Finite Element Methods (FEM)
           -    Discontinuous (and hybrid) Galerkin methods (DG - HDG - HHO - VEM)

  • Application domains:

    •        -    Solid and Fluid Mechanics
           -    Geophysics (wave propagation - climate modeling)
           -    Biology

    Talks

    Hybrid high-order methods for time-dependent, coupled elasto-acoustic wave propagation - [PDF]
    World Congress on Computational Mechanics (WCCM) - Vancouver (Canada) - July 2024
    European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS) - Lisbon (Portugal) - June 2024

    Unfitted HHO method stabilized by polynomial extension for elliptic interface problems - [PDF]
    National Congress of Numerical Analysis (CANUM) - Ile de Ré (France) - May 2024

    Posters

    Numerical study of energy transfer in sedimentary basins using high-order methods - [PDF]
    American Geophysical Union (AGU) - San Francisco (USA) - December 2023
    Congress of Young Researchers in Applied Mathematics (CJCMA) - Paris (France) - September 2023

    Previous experiences

  • Internships:

    •        -    Implementation of Spectral Differences (SD) and a Compatible Discrete Operator (CDO) scheme to solve Maxwell equations.
                 French Office for Aerospace Studies and Research (ONERA) , Toulouse (France), March - August 2021.
           -    Numerical modeling of the temperature distribution on the surface and in the depths of Mercury.
                 European space agency (ESA), Nordwijck (Nederland), May - August 2020.

    Teaching

  • Spring semester 2023 - Paris Dauphine University:

    •              2nd year of Bachelor's degree in Mathematics and Computer science
                 Course : Numerical methods (Nonlinear equations, polynomial interpolation, quadrature formulas, iterative and direct
                                                                              methods for solving linear systems, eigenvalue and eigenvector computing)
                 Teaching Assistantship: Supervision of theoretical and practical work classes


  • Fall semester 2022 - Paris Sorbonne University:

    •              1st year of Master's degree in Computational Mechanics
                 Course : Numerical methods (Linear systems, Finite differences etc...)
                 Teaching Assistantship: Supervision of practical work sessions and numerical modeling projects