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A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains

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Abstract

High-dimensional space-fractional PDEs are topics of special focus in applied disciplines, but solving them on irregular domains is challenging and deserves particular attention in scientific computing. In response to this issue, we establish a family of differential quadrature (DQ) methods for the space-fractional diffusion equations on 3D irregular domains. The fractional derivatives in space are represented by weighted linear combinations based on the functional values at scattered nodes with their weights determined by using radial basis functions (RBFs) as trial functions. The resulting system of ordinary differential equations (ODEs) are discretized by the weighted average scheme. The presented DQ methods have the virtues which are shared by the classical DQ methods. Several benchmark problems on typical irregular domains are solved to illustrate their advantages in flexibility and accuracy.

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Acknowledgements

The authors are very grateful to the anonymous referees for their constructive suggestions. This research was supported by the Scientific Research Funds of Hunan Provincial Education Department (Nos. 19C1643 and 19B509) and National Natural Science Foundations of China (Nos. 11471262 and 11601432).

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Authors and Affiliations

  1. School of Science, Shaoyang University, Shaoyang, 422000, Hunan, People’s Republic of China

    X. G. Zhu

  2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’ an, 710129, Shaanxi, People’s Republic of China

    Y. F. Nie, Z. B. Yuan & J. G. Wang

  3. School of Mathematics and Statistics, Henan University, Kaifeng, 475000, Henan, People’s Republic of China

    Z. H. Ge

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  1. X. G. Zhu
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  2. Y. F. Nie
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Zhu, X.G., Nie, Y.F., Ge, Z.H. et al. A class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domains. Comput Mech 66, 221–238 (2020). https://doi.org/10.1007/s00466-020-01848-8

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