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The Boundary Element Method with a Fast Multipole Accelerated Integration Technique for 3D Elastostatic Problems with Arbitrary Body Forces

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Abstract

A line integration boundary element method (LIBEM) is proposed for three-dimensional elastostatic problems with body forces. The method is a boundary-only discretization method like the traditional boundary element method (BEM), and the boundary elements created in BEM can be used directly in the proposed method for constructing the integral lines. Finally, the body forces are computed by summing one-dimensional integrals on straight lines. Background cells can be used to cut the lines into sub-lines to compute the integrals more easily and efficiently. To further reduce the computational time of LIBEM, the fast multipole method is applied to accelerate the method for large-scale computations and the details of the fast multipole line integration method for 3D elastostatic problems are given. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

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Acknowledgements

Financial support for the project from the National Natural Science Foundation of China (No. 51609181), National Natural Science Funds for Excellent Young Scholars (No. 51322905) and the National Key Research and Development Program of China (No. 2016YFC0401900) are acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, 430072, China

    Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma, Xiaolin Chang & Qiang Huang

  2. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, 430072, China

    Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma, Xiaolin Chang & Qiang Huang

Authors
  1. Qiao Wang
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  2. Wei Zhou
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  3. Yonggang Cheng
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  4. Gang Ma
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  5. Xiaolin Chang
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  6. Qiang Huang
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Correspondence to Qiao Wang.

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Wang, Q., Zhou, W., Cheng, Y. et al. The Boundary Element Method with a Fast Multipole Accelerated Integration Technique for 3D Elastostatic Problems with Arbitrary Body Forces. J Sci Comput 71, 1238–1264 (2017). https://doi.org/10.1007/s10915-016-0335-1

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  • DOI: https://doi.org/10.1007/s10915-016-0335-1

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