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

Summary: A supra-convergent finite difference scheme for the
variable coefficient Poisson equation on non-graded grids
Chohong Min a
, FreŽdeŽric Gibou b,*, Hector D. Ceniceros a,1
a
Mathematics Department, University of California, Santa Barbara, CA 93106, USA
b
Department of Mechanical and Environmental Engineering, University of California at Santa Barbara,
Santa Barbara, CA 93106-5070, USA
Received 2 May 2005; received in revised form 7 October 2005; accepted 29 January 2006
Abstract
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 advan-
tage 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 L1
norm.
Ó 2006 Elsevier Inc. All rights reserved.
1. Introduction

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics