A Second-Order-Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains

• DOI: 10.1006/jcph.2001.6977
• Publication Date: 2002-10-06T15:11:21Z
• Authors: Frederic Gibou; Ronald P. Fedkiw; Li-Tien Cheng; Myungjoo Kang
• Keywords: Poisson's equation; Matrix (chemical analysis)

In this paper, we consider the variable coefficient Poisson equation with Dirichlet boundary conditions on an irregular domain and show that one can obtain second-order accuracy with a rather simple discretization. Moreover, since our discretization matrix is symmetric, it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second-order-accurate discretizations of this problem. Multidimensional computational results are presented to demonstrate the second-order accuracy of this numerical method. In addition, we use our approach to formulate a second-order-accurate symmetric implicit time discretization of the heat equation on irregular domains. Then we briefly consider Stefan problems.