63 research outputs found
Numerical study of a nonlinear heat equation for plasma physics
This paper is devoted to the numerical approximation of a nonlinear
temperature balance equation, which describes the heat evolution of a
magnetically confined plasma in the edge region of a tokamak. The nonlinearity
implies some numerical difficulties, in particular long time behavior, when
solved with standard methods. An efficient numerical scheme is presented in
this paper, based on a combination of a directional splitting scheme and the
IMEX scheme introduced in [Filbet and Jin
An asymptotic preserving scheme for strongly anisotropic elliptic problems
In this article we introduce an asymptotic preserving scheme designed to
compute the solution of a two dimensional elliptic equation presenting large
anisotropies. We focus on an anisotropy aligned with one direction, the
dominant part of the elliptic operator being supplemented with Neumann boundary
conditions. A new scheme is introduced which allows an accurate resolution of
this elliptic equation for an arbitrary anisotropy ratio.Comment: 21 page
Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
The present paper introduces an efficient and accurate numerical scheme for
the solution of a highly anisotropic elliptic equation, the anisotropy
direction being given by a variable vector field. This scheme is based on an
asymptotic preserving reformulation of the original system, permitting an
accurate resolution independently of the anisotropy strength and without the
need of a mesh adapted to this anisotropy. The counterpart of this original
procedure is the larger system size, enlarged by adding auxiliary variables and
Lagrange multipliers. This Asymptotic-Preserving method generalizes the method
investigated in a previous paper [arXiv:0903.4984v2] to the case of an
arbitrary anisotropy direction field
Effcient numerical methods for strongly anisotropic elliptic equations
In this paper, we study an effcient numerical scheme for a strongly anisotropic elliptic problem which arises in the modeling of ionospheric plasma dynamics. A small parameter \varepsilon induces the anisotropy of the problem, which leads to severe numerical diffculties for 0 < \varepsilo
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