Mamadou N’Diaye

PhD in Applied Mathematics, Inria Team MAGIQUE-3D
email : mamadou.ndiaye@inria.fr
Tel : +33 5 40 17 51 55

Locally implicit time schemes

Implicit time integration methods are known to have a good stability properties, but they are expensive in terms of memory space consumption. Explicit time schemes which are cheap in memory space usage have a time step restriction regarding the stability. For these reasons I am working on the development of high-order locally implicit schemes which combine explicit and implicit schemes. This allows to take advantage of the good stability properties of implicit time schemes and the less memory consuming process of explicit schemes.

Optimized CFL explicit time integration schemes

I am interested in the development of explicit schemes with optimal CFL number. After space discretization of a PDE, I construct explicit time scheme which stability domain contains a typical profile of spectrum.

A-stable high-order implicit time integration methods

I am working in the development of unconditionally stable ( or A-stable) implicit time schemes for ODEs. The aim is to develop numerical time schemes which have no CFL constraint and have low-dissipation and low-dispersion errors.

Key words:
Runge-Kutta schemes, SDIRK, Padé approximation, dispersion and dissipation
Movie : Scattering of a 2D resonant cavity while solving the acoustic wave equation.

The simulation is performed using the high-order finite element C++ code Montjoie, in which I have implemented the A-stable implicit time schemes.

 

Movie : Simulation of the acoustic wave equation on a regular square mesh.

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