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Adaptive Refinement Techniques for RBF-PU Collocation

  • R. Cavoretto
  • A. De RossiEmail author
Conference paper
  • 84 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

We propose new adaptive refinement techniques for solving Poisson problems via a collocation radial basis function partition of unity (RBF-PU) method. As the construction of an adaptive RBF-PU method is still an open problem, we present two algorithms based on different error indicators and refinement strategies that turn out to be particularly suited for a RBF-PU scheme. More precisely, the first algorithm is characterized by an error estimator based on the comparison of two collocation solutions evaluated on a coarser set and a finer one, while the second one depends on an error estimate that is obtained by a comparison between the global collocation solution and the associated local RBF interpolant. Numerical results support our study and show the effectiveness of our algorithms.

Keywords

Adaptive algorithms Refinement strategies RBF methods Meshless methods Elliptic PDEs 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics “Giuseppe Peano”University of TorinoTorinoItaly

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