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Fast multipole accelerated dual reciprocity boundary element method for diffusion problems

  • Original Article
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Annals of Solid and Structural Mechanics

Abstract

A fast multipole boundary element method (FMBEM) is presented for diffusion problems based on a dual reciprocity formulation. In the dual reciprocity formulation, domain integrals that arise from solving the time-dependent boundary value problems are transformed into boundary integrals by constructing particular solutions. The time-derivatives in the governing differential equation are approximated with a first-order finite difference time-stepping scheme. Discontinuous linear elements, which are known to give more accurate results than constant or linear elements, are used in the implementation to discretize the boundary integral equations, in combination with the fast multipole method for speeding up the solution. Three numerical examples of diffusion are presented. The performance of the developed FMBEM is compared with that of a conventional BEM and a commercial finite element program. The results show that the developed FMBEM can be a reliable and efficient tool for solving diffusion problems.

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Acknowledgments

The authors would like to thank Professor Whye-Teong Ang at Nanyang Technological University in Singapore and Professor Yijun Liu at the University of Cincinnati for their valuable discussions on the topic of DR-BEM and the fast multipole BEM.

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Authors and Affiliations

  1. Mechanical Engineering, School of Engineering and Computer Science, Washington State University, Vancouver, WA, 98686, USA

    Bo Wang & Xiaolin Chen

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  1. Bo Wang
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  2. Xiaolin Chen
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Correspondence to Xiaolin Chen.

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Wang, B., Chen, X. Fast multipole accelerated dual reciprocity boundary element method for diffusion problems. Ann. Solid Struct. Mech. 7, 45–58 (2015). https://doi.org/10.1007/s12356-015-0041-y

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  • DOI: https://doi.org/10.1007/s12356-015-0041-y

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