An immersed interface method for anisotropic elliptic problems on irregular domains in 2D

✍ Scribed by Miguel A. Dumett; James P. Keener

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 418 KB
• Volume: 21
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20051

✦ Synopsis

Abstract

This work is a generalization of the immersed interface method for discretization of a nondiagonal anisotropic Laplacian in 2D. This first‐order discretization scheme enforces weakly diagonal dominance of the numerical scheme whenever possible. A necessary and sufficient condition depending on the mesh size h for the existence of this scheme at an interior grid point is found in terms of the anisotropy matrix. A linear programming approach is introduced for finding the weights of the schemes. The method is tested with a parametrized family of anisotropic Poisson equations. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005