TY - JOUR

T1 - A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids

AU - Min, Chohong

AU - Gibou, Frédéric

AU - Ceniceros, Hector D.

PY - 2006/10/10

Y1 - 2006/10/10

N2 - We introduce a method for solving the variable coefficient Poisson equation on non-graded Cartesian grids that yields second order accuracy for the solutions and their gradients. We employ quadtree (in 2D) and octree (in 3D) data structures as an efficient means to represent the Cartesian grid, allowing for constraint-free grid generation. The schemes take advantage of sampling the solution at the nodes (vertices) of each cell. In particular, the discretization at one cell's node only uses nodes of two (2D) or three (3D) adjacent cells, producing schemes that are straightforward to implement. Numerical results in two and three spatial dimensions demonstrate supra-convergence in the L∞ norm.

AB - We introduce a method for solving the variable coefficient Poisson equation on non-graded Cartesian grids that yields second order accuracy for the solutions and their gradients. We employ quadtree (in 2D) and octree (in 3D) data structures as an efficient means to represent the Cartesian grid, allowing for constraint-free grid generation. The schemes take advantage of sampling the solution at the nodes (vertices) of each cell. In particular, the discretization at one cell's node only uses nodes of two (2D) or three (3D) adjacent cells, producing schemes that are straightforward to implement. Numerical results in two and three spatial dimensions demonstrate supra-convergence in the L∞ norm.

UR - http://www.scopus.com/inward/record.url?scp=33748524485&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2006.01.046

DO - 10.1016/j.jcp.2006.01.046

M3 - Article

AN - SCOPUS:33748524485

SN - 0021-9991

VL - 218

SP - 123

EP - 140

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -