TY - JOUR
T1 - Evaluating the Origin Intensity Factor in the Singular Boundary Method for Three-Dimensional Dirichlet Problems
AU - Sun , Linlin
AU - Chen , Wen
AU - Cheng , Alexander H.-D.
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1289
EP - 1311
PY - 2017
DA - 2017/09
SN - 9
DO - http://doi.org/10.4208/aamm.2015.m1153
UR - https://global-sci.org/intro/article_detail/aamm/10179.html
KW - Origin intensity factors, singular boundary method, boundary-type meshless method, potential problem, fundamental solution.
AB - <p style="text-align: justify;">In this paper, a new formulation is proposed to evaluate the origin intensity
factors (OIFs) in the singular boundary method (SBM) for solving 3D potential
problems with Dirichlet boundary condition. The SBM is a strong-form boundary
discretization collocation technique and is mathematically simple, easy-to-program,
and free of mesh. The crucial step in the implementation of the SBM is to determine
the OIFs which isolate the singularities of the fundamental solutions. Traditionally,
the inverse interpolation technique (IIT) is adopted to calculate the OIFs on Dirichlet
boundary, which is time consuming for large-scale simulation. In recent years, the
new methodology has been developed to efficiently calculate the OIFs on Neumann
boundary, but the Dirichlet problem remains an open issue. This study employs
the subtracting and adding-back technique based on the integration of the fundamental
solution over the whole boundary to develop a new formulation of the OIFs on
3D Dirichlet boundary. Several problems with varied domain shapes and boundary
conditions are carried out to validate the effectiveness and feasibility of the proposed
scheme in comparison with the SBM based on inverse interpolation technique, the
method of fundamental solutions, and the boundary element method.</p>