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A novel radial basis function method for 3D linear and nonlinear advection diffusion reaction equations with variable coefficients

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Abstract

The radial basis function method for 3D advection diffusion reaction equations with variable coefficients is presented. The proposed method implements the linear combination of radial basis functions which impose boundary conditions in advance, and thus such a combination with weighted parameters can be used to construct the final approximation. Furthermore, the weighted parameters are solved by substituting the approximation into governing equations. This method leads to crucial improvements in the feasibility and accuracy which can now be easily applied to general 3D nonlinear problems through linearized techniques. Finally, accuracy and efficiency of the proposed method are verified by several examples.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Nos. U1765204, 11772068), the Natural Science Foundation of Jiangsu Province (No. BK20190073), the Fundamental Research Funds for the Central Universities (No. B200202126), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (No. SKLA202001), the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University (No. KF2020-22), and the China Postdoctoral Science Foundation (Nos. 2017M611669, 2018T110430)

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  1. College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

    Xia Tian & Ji Lin

  2. State Key Laboratory of Acoustic, Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China

    Ji Lin

  3. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Ji Lin

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  1. Xia Tian
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Correspondence to Ji Lin.

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Tian, X., Lin, J. A novel radial basis function method for 3D linear and nonlinear advection diffusion reaction equations with variable coefficients. Engineering with Computers 38 (Suppl 1), 475–488 (2022). https://doi.org/10.1007/s00366-020-01161-1

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