Analysis

There are three research groups working in analysis: Numerical Analysis, Partial Differential Equations and Mechanics.

Some thematics studied by research groups in analysis
  1. Numerical Analysis
  2. Partial Differential Equations
  3. Mechanics

Numerical Analysis

The mathematicians in this group (fr) work on the following topics:

  • Development and analysis of numerical methods. Finite element methods, integral equations, nonlinear hyperbolic problems, kinetic equations, Lattice-Boltzmann methods, optimisation problems with equilibrium constraints, Krylov methods, approximation.
  • Scientific computing, code designs, numerical simulations. In particular design and maintenance of the finite element library MELINA++ (fr), then XLiFE++; of the advection-reaction-diffusion equations integrator PIROCK, and more generally the modelling and numerical simulations interplaying with other fields.​
  • High-frequency problems, confinement and quantum models. Schrödinger operators with magnetic fields, quantum waveguides, nonlinear Schrödinger equation and quantum confinement, high-frequency Helmholtz equation or Maxwell system, superconductivity.
  • Hamiltonian PDEs. Stability, large time behavior, geometric integrators, highly oscillatory problems and averaging, gravitational Vlasov-Poisson system (INRIA team IPSO).
  • Elliptic Problems. Homogenization, boundary conditions, singular perturbations.
  • Shape optimization and control.
  • Transient phenomena and front propagation. Reaction-diffusion equations, front propagation, Hamilton-Jacobi equations, nonlinear parabolic problems, gradient fields identification, modelling ecological networks.
  • Operators and applied functional analysis. Singular integral operators, numerical range of operators, Taylorian fields.

Partial Differential Equations

The mathematicians in this group (fr) work on the following topics:

  • Spectral theory. Scattering theory, quantum diffusion, quantum fields theory, non self-adjoint operators.
  • Phase-space analysis. Microlocal analysis, semiclassical methods, symplectic geometry and quantification, integrable systems, mean fields evolution in quantum fields theory.
  • Multiscale analysis. WKB method, nonlinear geometrical optics, semi-quantum models, homogenization, Dirichlet forms, fractal structures, turbulence theory.
  • Analysis of nonlinear PDEs. Hyperbolic systems, stability of dispersive waves, nonlinear quantum mechanics, fluid mechanics and oceanography.

Mechanics

The mathematicians in this group (fr) work on the following topics:

  • Generalized continuum mechanics.
  • Biomechanics. Analysis of brain-CSF-skull and cardiovascular systems during shocks. Diagnosis and orthopedic treatment of idiopathic scoliosis. Biological tissue and artificial transplant thermodynamics.
  • Vibration and wave propagation. Structure vibration through Timoshenko beam theory. Vibro-acoustic analysis. Waves and fluid-structure coupling.
  • Homogenization. Multi-diffusion, mathematical homogenization.
  • Modelling and analysis of turbulence models of incompressible flows (INRIA team Fluminance).