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# The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Elasticity

Qiao Wang1, Yu Miao1,2, Junjie Zheng1

School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
Corresponding Author. Tel: 86 27 87540172; Fax: 86 27 87542231; Yu Miao Email: my_miaoyu@163.com

Computer Modeling in Engineering & Sciences 2010, 70(2), 123-152. https://doi.org/10.3970/cmes.2010.070.123

## Abstract

In this paper, a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving 3D elasticity is presented. Coupling modified variational principle with the Moving Least Squares (MLS) approximation, the Hybrid BNM only requires discrete nodes constructed on the surface of a domain. The preconditioned GMERS is employed to solve the resulting system of equations. At each iteration step of the GMERS, the matrix-vector multiplication is accelerated by the fast multipole method (FMM). The fundamental solution of three-dimensional elasticity problem is expanded in terms of series. An oct-tree data structure is adopted to subdivide the computational domain into well-separated cells hierarchically and to invoke the multipole expansion approximation. Formulations for the local and multipole expansions and conversion of multipole to local expansion are given. Nearly one million of total unknowns can be computed on a PC with 2.67GHz CPU and 2.0GB RAM. All the formulations are implemented in a computer code written in C++. Numerical examples demonstrate the accuracy and efficiency of the proposed approach.

## Cite This Article

Wang, Q., Miao, Y., Zheng, J. (2010). The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3D Elasticity. CMES-Computer Modeling in Engineering & Sciences, 70(2), 123–152.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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