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 MINGuS).
• 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.

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.

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).