Efficient Numerical Methods for Strongly Anisotropic Elliptic Equations

Authors:
Christophe Besse;Fabrice Deluzet;Claudia Negulescu;Chang Yang
Affiliations:
Laboratoire Paul Painlevé (UMR 8524), Université Lille 1, Villeneuve d'Ascq Cedex, France 59655;UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Université de Toulouse, Toulouse, France 31062 and CNRS, Institut de Mathématiques de Toulouse UMR 5219, Toulouse, France ...;CMI/LATP (UMR 6632), Université de Provence, Marseille Cedex, France 13453;Laboratoire Paul Painlevé (UMR 8524), Université Lille 1, Villeneuve d'Ascq Cedex, France 59655
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

In this paper, we study an efficient numerical scheme for a strongly anisotropic elliptic problem which arises, for example, in the modeling of magnetized plasma dynamics. A small parameter 驴 induces the anisotropy of the problem and leads to severe numerical difficulties if the problem is solved with standard methods for the case 0驴驴1. An Asymptotic-Preserving scheme is therefore introduced in this paper in a 2D framework, with an anisotropy aligned to one coordinate axis and an 驴-intensity which can be either constant or variable within the simulation domain. This AP scheme is uniformly precise in 驴, permitting thus the choice of coarse discretization grids, independent of the magnitude of the parameter 驴.