TY - JOUR
T1 - An Improved Formulation of Singular Boundary Method
AU - Chen , Wen
AU - Gu , Yan
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 543
EP - 558
PY - 2012
DA - 2012/04
SN - 4
DO - http://doi.org/10.4208/aamm.10-m11118
UR - https://global-sci.org/intro/article_detail/aamm/135.html
KW - Singular boundary method, fundamental solution, singularity, desingularization
technique, meshless.
AB - <p style="text-align: justify;">This study proposes a new formulation of singular boundary method (SBM)
to solve the 2D potential problems, while retaining its original merits
being free of integration and mesh, easy-to-program, accurate and
mathematically simple without the requirement of a fictitious boundary
as in the method of fundamental solutions (MFS). The key idea of the SBM
is to introduce the concept of the origin intensity factor to isolate the
singularity of fundamental solution so that the source points can be placed
directly on the physical boundary. This paper presents a new approach to
derive the analytical solution of the origin intensity factor based on the
proposed subtracting and adding-back techniques. And the troublesome sample
nodes in the ordinary SBM are avoided and the sample solution is also not
necessary for the Neumann boundary condition. Three benchmark problems are
tested to demonstrate the feasibility and accuracy of the new formulation
through detailed comparisons with the boundary element method (BEM), MFS,
regularized meshless method (RMM) and boundary distributed source (BDS)
method.</p>