Eric Sonnendrücker

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Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we perform in this paper a homogenization of the Vlasov equation and the Vlasov-Poisson system which yield approximate(More)
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Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the(More)
In this paper, we study high order methods for solving the time domain Maxwell equations using spline finite elements on domains defined by NURBS. Convenient basis functions for the discrete exact sequence of spaces introduced by Buffa et al [4] are exhibited which provided the same discrete structure as for classical Whitney Finite Elements. An analysis of(More)
In this work, a new discretization scheme of the gyrokinetic quasi-neutrality equation is proposed. It is based on Isogeometric Analysis; the IGA which relies on NURBS functions, seems to accommodate arbitrary coordinates and the use of complicated computation domains. Moreover, arbitrary high order degree of basis functions can be used. Here, this approach(More)
A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r, h, z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exhibits(More)
We introduce here a new method for the numerical resolution of the Vlasov equation on a phase space grid using an adaptive semi-Lagrangian method. The adaptiv-ity is obtained through a multiresolution analysis which enables to keep or remove grid points from the simulation depending on the size of their associated coefficients in a multiresolution(More)
A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semi-Lagrangian algorithm that approaches the Vlasov equation on a grid of phase space. As this kind of method requires a huge computational(More)
This paper deals with the numerical simulations of the Vlasov-Poisson equation using a phase space grid in the quasi-neutral regime. In this limit, explicit numerical schemes suffer from numerical constraints related to the small Debye length and large plasma frequency. Here, we propose a semi-Lagrangian scheme for the Vlasov-Poisson model in the(More)