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arXiv · 2107.03639

p-refined RBF-FD solution of a Poisson problem

Mitja Jančič·Jure Slak·Gregor Kosec
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Abstract

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain.

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Mitja Jančič, Jure Slak, Gregor Kosec. 2021-07-08. p-refined RBF-FD solution of a Poisson problem. https://doi.org/10.23919/splitech52315.2021.9566401

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