Minimal positive stencils in meshfree finite difference methods for the Poisson equation

Details Minimal positive stencils in meshfree finite difference methods for the Poisson equation Minimal positive stencils in meshfree finite difference methods for the Poisson equation

2008-02-19

arxiv.org/abs/0802.2674v2

Comput. Methods Appl. Mech. Engrg., Vol. 198 (3-4), 2008, pp. 592-601

Mathematics

Numerical Analysis

26 pages, 20 figures

Scientific paper

10.1016/j.cma.2008.09.001

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.

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