Critical length for a Beurling type theorem

In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem

A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem

Marseille, France, 19 Juillet - 27 Août 2010In this paper, we test an innovative numerical scheme for the simulation of the guiding-center model, of interest in the domain of plasma physics, namely for fusion devices. We propose a 1D Discontinuous Galerkin (DG) discretization, whose basis are the Lagrange polynomials interpolating the Gauss points inside each cell, coupled to a conservative semi-Lagrangian (SL) strategy. Then, we pass to the 2D setting by means of a second-order Strangsplitting strategy. In order to solve the 2D Poisson equation on the DG discretization, we adapt the spectral strategy used for equally-spaced meshes to our Gauss-point-based basis. The 1D solver is validated on a standard benchmark for the nonlinear advection; then, the 2D solver is tested against the swirling deformation ow test case; nally, we pass to the simulation of the guiding-center model, and compare our numerical results to those given by the Backward Semi-Lagrangian method

An Ingham type proof for the boundary observability of a N-d wave equation

International audienceThe boundary observability of the wave equation has been studied by many authors. A method of choice is to use the multiplier method. Recently, a first Fourier based proof is given in the case where the domain is a square, thanks to a new Hautus type test. We give here a new self-contained proof with an Ingham type approach in the more general case where the domain is a product of intervals; this leads to explicit time and constants. However, we do not reach the optimal time which can be obtained for this problem by the multiplier method

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation

About recurrence time for a semi-Lagrangian discontinuous Galerkin Vlasov solver

International audienc

Semi-Lagrangian simulations of the diocotron instability

We consider a guiding center simulation on an annulus. We propose here to revisit this test case by using a classical semi-Lagrangian approach. First, we obtain the conservation of the electric energy and mass for some adapted boundary conditions. Then we recall the dispersion relation and discussions on diff erent boundary conditions are detailed. Finally, the semi-Lagrangian code is validated in the linear phase against analytical growth rates given by the dispersion relation. Also we have validated numerically the conservation of electric energy and mass. Numerical issues/diffi culties due to the change of geometry can be tackled in such a test case which thus may be viewed as a fi rst intermediate step between a classical guiding center simulation in a 2D cartesian mesh and a slab 4D drift kinetic simulation

Optimal decay rates for the stabilization of a string network

We study the decay of the energy for a degenerate network of strings, and obtain optimal decay rates when the lengths are all equal. We also de ne a classical space semi-discretization and compare the results with the exact method