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 *O(N*^{2}) 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