TY  - EJOU
AU  - Chen, W.  
AU  - Liu, C. J.  
AU  - Gu, Y.  

TI  - A Fast Multipole Accelerated Singular Boundary Method for Potential Problems
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2015
VL  - 105
IS  - 4
SN  - 1526-1506

AB  - 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 <i>O(N<sup>2</sup>)</i> 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.
KW  - Singular boundary method
KW  -  method of fundamental solutions
KW  -  fast multipole method
KW  -  meshless boundary collocation method
KW  -  potential problem

DO  - 10.3970/cmes.2015.105.251