On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques

We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2020-10, Vol.176, p.4-24
Main Authors: Aràndiga, Francesc, Donat, Rosa, Romani, Lucia, Rossini, Milvia
Format: Article
Language:English
Subjects:
Adaptive parameter
Approximation order
Jump discontinuity
Local multiquadric radial basis function (RBF) interpolation
Weighted Essentially Non-Oscillatory (WENO) interpolation
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Summary:We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was proposed in Guo and Jung (2017) [12,13]. We present also some numerical examples that confirm the theoretical approximation orders derived in the paper.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2020.01.018