HPC@Maths

Loïc Gouarin, Marc Massot

January 30, 2026

Team composition

  • 5 researchers
  • 6 research engineers in scientific computing
  • 3 post-docs
  • 9 phd students
  • Several external collaborators (~10)

Scientific topics

Computer assisted proof in PDEs

Maxime Breden, Matthieu Cadiot, Hugo Chu
  • Existence of specific solutions (overall dynamics of the system - limit cycles / travelling waves…)
  • Certification of the result of a numerical simulation
  • Based on a fixed point argument in the vicinity of the approximate solution
  • Numerical analysis and computations

emerging topics

  • Navier-Stokes
  • Cost reduction of proofs
  • Bifurcations
  • Connexions in parabolic PDEs
  • Beyond Fourier Series standard tools

Computational linear algebra

Élise Fressart, Lucien Gontier, Loïc Gouarin, Pierre Matalon, Nicole Spillane
  • Applied and computational linear algebra
  • High-performance computing in the sense of massively parallel computing,
  • Domain decomposition,
  • Preconditioning,
  • Krylov solvers (Conjugate gradient, GMRES, etc.),
  • PDEs with stochastic coefficients

applications

  • Solid Mechanics
  • Development of code and libraries

Kinetic theory and moment methods

Remy Annunziata, Daniele Biasone, Vincent Giovangigli, Ward Haegeman, Josselin Massot, Marc Massot, Giuseppe Orlando, Teddy Pichard, Zoubaïr Tazzakati
  • Derivation of fluid equation from kinetic theory
  • Cohesive and Interfacial fluid derivation
  • Multi-scale Chapman Enskog and Hilbert expansion
  • Method of moments (Closure)
  • Limits of approach and link with SAP
  • Geometric Method of Moments
  • Large phase space description - semi-kinetic method

applications

  • Gas-surface interaction
  • Two-phase flows
  • Hybrid fluid-rarefied flows
  • Plasma physics
  • Countrail formation and pollution modelling
  • Nuclear Engineering

New numerical schemes

Sébastien Dubois, Vincent Giovangigli, Loïc Gouarin, Alexandre Hoffmann, Josselin Massot, Marc Massot, Pierre Matalon, Teddy Pichard, Laurent Séries, Antoine Simon, Zoubaïr Tazzakati
  • Dynamic spatial and temporal adaptation with error control (wavelet/splitting/ImEx)
  • Code coupling - high-order multi-step
  • DG methods and high-order wavelets
  • Well-balanced / AP schemes / time-space approach

applications

  • Combustion
  • Lithium Battery
  • Plasma physics
  • Two-phase flows
  • Biomedical Engineering
  • Propulsion and reentry at high altitude

Variational approch (SAP)

Ward Haegeman, Marc Massot, Giuseppe Orlando
  • Derivation of PDEs wihtout dissipation
  • Extended Thermodynamics - Dissipation
  • Analysis of mathematical properties
  • Two-scale unified modeling - all topology model
  • Link with microscopic - geometrical moments
  • Lin constraint - Geometry
  • Sources terms / Relaxation and numerical schemes

applications

  • Two-phase flows
  • Fluid Mechanics
  • Nuclear Engineering

Lattice Boltzmann methods

Loïc Gouarin, Marc Massot
  • Numerical Analysis of LB schemes
  • Treatment of boundary conditions
  • Dynamic mesh adaption with erroir control
  • High order schemes
  • Hyperbolic/parabolic scaling

applications

  • Two-phase flows
  • Fluid Mechanics
  • Aerospace Engineering - Hypersonic flows

Turbulence, processes and particles

Clément Morhain, Marc Massot
  • Low-regularity stochastic processes (Intermittency)
  • Kinetic Simulation of Turbulence based on wavelets
  • Numerical simulation based on OU processes
  • Kinetic approach / FP / Moment methods
  • Link with SPDEs in fluid mechanics

applications

  • Two-phase flows
  • Fluid Mechanics and Turbulence
  • LES of two-way coupled particle-laden turbulence

Quantum computing

Sébastien Dubois, Élise Fressart, Loïc Gouarin, Nicole Spillane
  • Quantum algorithm for PDE simulation
  • Mesh adaptation and error control
  • Linear Algebra
  • FE programming with DOLFINx and PETSc (Python + MPI),
  • Quantum computer emulation with Qiskit (Python).

applications

  • ElectroMagnetism : Maxwell Equations

Emerging topics : SciML

Loïc Gouarin, Rémy Hosseinkhan, Marc Massot
  • Simulation of high-dimensional PDEs
  • Closure for moment methods

applications

  • Plasma physics
  • Two-phase flows
  • Financial Engineering (collab.)

Technical skills

open source software

samurai

  • C++ 20 header only
  • Adaptive mesh refinement techniques
  • New data structure: intervals + algebra of sets
  • Finite volume and lattice Boltzmann methods
  • MPI and GPU soon


ponio

  • C++ 20 header only
  • time integrators for solving differential equations
  • A large collection of methods: eRK, DIRK, LRK, expRK, RKC, Lie or Strang splitting
  • Highly flexible

open source software

pylbm

  • Python
  • lattice Boltzmann methods
  • Analysis tools
  • Sympy
  • Source code generator
  • MPI and GPU


SCoPI

  • C++ code
  • Simulation of interacting particle collections
  • 2D and 3D simulations
  • Convex regular shape
  • Contact models: inelastic, with or without friction or viscous

open source software

GenEO

  • linear elasticity
  • Finite element
  • GenEO algorithm
  • Python
  • New preconditioner implementation using petsc4py
  • Fenics for matrix assembling

software engineering

  • Version control
  • Tests
  • Documentation
  • Packaging (conda, spack, guix)
  • GitHub Actions
  • AI agents (beginner)

Training

Scientific partnership

  • CEA
  • MdlS
  • EDF
  • ONERA
  • TotalEnergies
  • Thales
  • Safran
  • NASA

Technical partnership

  • CEA
  • QuantStack
  • NVIDIA

Interactions

  • Alexandre H., Philippe M. (HJB simulation with samurai)
  • Sébastien I. (code-coupling / mesh adaptation / DG)
  • GT Fixed-point resolution improvement (Visit Y. Saad 1st and 2nd of June)
  • Kinetic theory and fluid equations (Flash Workshop next Monday)
  • SAP : workshop before Ward’s defense (8th of June - defense 9th of June)

Thank you for your attention