A Fast Multipole Accelerated Singular Boundary Method for Potential Problems
W. Chen, C. J. Liu and Y. Gu

doi:10.3970/cmes.2015.105.251
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 105, No. 4, pp. 251-270, 2015
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Keywords Singular boundary method, method of fundamental solutions, fast multipole method, meshless boundary collocation method, potential problem.
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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