TY - EJOU
AU - Chen, Wen
AU - Fu, Zhuojia
AU - Wei, Xing
TI - Potential Problems by Singular Boundary Method Satisfying Moment Condition
T2 - Computer Modeling in Engineering \& Sciences
PY - 2009
VL - 54
IS - 1
SN - 1526-1506
AB - This study investigates the singular boundary method (SBM), a novel boundary-type meshless method, in the numerical solution of potential problems. Our finding is that the SBM can not obtain the correct solution in some tested cases, in particular, in the cases whose solution includes a constant term. To remedy this drawback, this paper presents an improved SBM formulation which is a linear sum of the fundamental solution adding in a constant term. It is stressed that this SBM approximation with the additional constant term has to satisfy the so-called moment condition in order to guarantees the uniqueness of the solution. The efficiency and accuracy of the present SBM scheme are demonstrated through detailed comparisons with the exact solution, the method of fundamental solutions and the regularized meshless method.
KW - Singular boundary method
KW - fundamental solution
KW - singularity at the origin
KW - moment condition
KW - potential problem
DO - 10.3970/cmes.2009.054.065