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A Fast Multipole Accelerated Singular Boundary Method for Potential Problems

W. Chen1,2, C. J. Liu1, Y. Gu2,3
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.
Corresponding author. E-mail:;
College of Mathematics, Qingdao University, Qingdao 266071, PR China.

Computer Modeling in Engineering & Sciences 2015, 105(4), 251-270.


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.


Singular boundary method, method of fundamental solutions, fast multipole method, meshless boundary collocation method, potential problem.

Cite This Article

Chen, W., Liu, C. J., Gu, Y. (2015). A Fast Multipole Accelerated Singular Boundary Method for Potential Problems. CMES-Computer Modeling in Engineering & Sciences, 105(4), 251–270.

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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