Meshfree finite difference methods for the Poisson equation approximate theLaplace operator on a point cloud. Desirable are positive stencils, i.e. allneighbor entries are of the same sign. Classical least squares approaches yieldlarge stencils that are in general not positive. We present an approach thatyields stencils of minimal size, which are positive. We provide conditions onthe point cloud geometry, so that positive stencils always exist. The newdiscretization method is compared to least squares approaches in terms ofaccuracy and computational performance.
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