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 -