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RBF–DQ algorithms for elliptic problems in axisymmetric domains

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Abstract

A radialbasis function (RBF)–differentialquadrature (DQ) method is applied for the numerical solution of elliptic boundary value problems (BVPs) in three-dimensional axisymmetric domains. By appropriately selecting the collocation points, for any choice of RBF, the proposed discretization leads to linear systems in which the coefficient matrices possess block circulant structures. Matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs) are employed for the efficient solution of these systems. Three types of BVPs are considered, namely ones governed by the Poisson equation, the inhomogeneous biharmonic equation, and the inhomogeneous Cauchy–Navier equations of elasticity. The high accuracy of the proposed technique as well as its ability to solve large-scale problems is demonstrated on several numerical examples.

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Acknowledgements

The first author gratefully acknowledges the financial support of the Ministry of Science and Technology of Taiwan (MOST) under the recruitment of visiting science and technology personnel with subsidies (109-2811-E-002-516 and 110-2811-E-002-518). The work of the second author was supported by the Poznan University of Technology (Poland) through Grant No. 0612/SBAD/3567.

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Authors and Affiliations

  1. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

    C. S. Chen

  2. School of Mathematics and Natural Sciences, University of Southern Mississippi, Hattiesburg, MS, 39406, USA

    C. S. Chen

  3. Institute of Applied Mechanics, Faculty of Mechanical Engineering, Poznan University of Technology, Jana Pawla II 24, Poznan, 60–965, Poland

    Malgorzata A. Jankowska

  4. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia, 1678, Cyprus

    Andreas Karageorghis

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  1. C. S. Chen
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  2. Malgorzata A. Jankowska
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  3. Andreas Karageorghis
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Correspondence to Andreas Karageorghis.

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Chen, C.S., Jankowska, M.A. & Karageorghis, A. RBF–DQ algorithms for elliptic problems in axisymmetric domains. Numer Algor 89, 33–63 (2022). https://doi.org/10.1007/s11075-021-01105-w

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  • DOI: https://doi.org/10.1007/s11075-021-01105-w

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