Open Access

ARTICLE

A Fast Multipole Accelerated Singular Boundary Method for Potential Problems

W. Chen^1,2, C. J. Liu¹, Y. Gu^2,3

1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China.
2 Corresponding author. E-mail: chenwen@hhu.edu.cn; guyan1913@163.com
3 College of Mathematics, Qingdao University, Qingdao 266071, PR China.

Computer Modeling in Engineering & Sciences 2015, 105(4), 251-270. https://doi.org/10.3970/cmes.2015.105.251

Abstract

The singular boundary method (SBM) is a recently-developed meshless boundary collocation method. This method overcomes the well-known fictitious boundary issue associated with the method of fundamental solutions (MFS) while remaining the merits of the later of being truly meshless, integral-free, and easy-to-program. Similar to the MFS, this method, however, produces dense and unsymmetrical coefficient matrix, which although much smaller in size compared with domain discretization methods, requires O(N²) operations in the iterative solution of the resulting algebraic system of equations. To remedy this bottleneck problem for its application to large-scale problems, this paper makes the first attempt to develop a fast multipole SBM (FM-SBM) formulation for two-dimensional (2D) potential problems. The proposed strategy can solve large-scale problems with several millions boundary discretization nodes on a desktop computer.

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Keywords

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