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Localized space–time method of fundamental solutions for three-dimensional transient diffusion problem

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Abstract

A localized space–time method of fundamental solutions (LSTMFS) is extended for solving three-dimensional transient diffusion problems in this paper. The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems. In the LSTMFS, the whole space–time domain with nodes arranged is divided into a series of overlapping subdomains with a simple geometry. In each subdomain, the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined. By calculating a combined sparse matrix system, the value at any node inside the space–time domain can be obtained. Numerical experiments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS, even for the problems defined on a long-time and quite complex computational domain.

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (Grants B200203009 and B200202126), the Natural Science Foundation of Jiangsu Province (Grant BK20190073), the State Key Laboratory of Acoustics, Chinese Academy of Sciences (Grant SKLA202001), the State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University (Grant KF2020-22), and the China Postdoctoral Science Foundation (Grants 2017M611669 and 2018T110430).

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Authors and Affiliations

  1. International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, 210098, China

    L. Qiu, J. Lin & W. Chen

  2. College of Engineering and Computer Science, Australian National University, Canberra, ACT, 2601, Australia

    L. Qiu & Q.-H. Qin

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

    J. Lin

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

    J. Lin

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  1. L. Qiu
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  2. J. Lin
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  3. Q.-H. Qin
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  4. W. Chen
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Correspondence to J. Lin.

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Qiu, L., Lin, J., Qin, QH. et al. Localized space–time method of fundamental solutions for three-dimensional transient diffusion problem. Acta Mech. Sin. 36, 1051–1057 (2020). https://doi.org/10.1007/s10409-020-00979-8

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  • DOI: https://doi.org/10.1007/s10409-020-00979-8

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