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.

Arandiga, F., Donat, R., Romani, L., Rossini, M. (2020). On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques. MATHEMATICS AND COMPUTERS IN SIMULATION, 176, 4-24 [10.1016/j.matcom.2020.01.018].

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

Rossini M.
2020

Abstract

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.
Articolo in rivista - Articolo scientifico
Adaptive parameter; Approximation order; Jump discontinuity; Local multiquadric radial basis function (RBF) interpolation; Weighted Essentially Non-Oscillatory (WENO) interpolation
English
5-feb-2020
2020
176
4
24
none
Arandiga, F., Donat, R., Romani, L., Rossini, M. (2020). On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques. MATHEMATICS AND COMPUTERS IN SIMULATION, 176, 4-24 [10.1016/j.matcom.2020.01.018].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/292966
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