Minimal positive stencils in meshfree finite difference methods for the Poisson equation
Abstract
Meshfree finite difference methods for the Poisson equation approximate the Laplace operator on a point cloud. Desirable are positive stencils, i.e. all neighbor entries are of the same sign. Classical least squares approaches yield large stencils that are in general not positive. We present an approach that yields stencils of minimal size, which are positive. We provide conditions on the point cloud geometry, so that positive stencils always exist. The new discretization method is compared to least squares approaches in terms of accuracy and computational performance.
 Publication:

Computer Methods in Applied Mechanics and Engineering
 Pub Date:
 December 2008
 DOI:
 10.1016/j.cma.2008.09.001
 arXiv:
 arXiv:0802.2674
 Bibcode:
 2008CMAME.198..592S
 Keywords:

 Mathematics  Numerical Analysis;
 65N06;
 65N50;
 90C05
 EPrint:
 26 pages, 20 figures