Evaluating the Origin Intensity Factor in the Singular Boundary Method for Three-Dimensional Dirichlet Problems (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, a new formulation is proposed to evaluate the origin intensityfactors (OIFs) in the singular boundary method (SBM) for solving 3D potentialproblems with Dirichlet boundary condition. The SBM is a strong-form boundarydiscretization collocation technique and is mathematically simple, easy-to-program,and free of mesh. The crucial step in the implementation of the SBM is to determinethe OIFs which isolate the singularities of the fundamental solutions. Traditionally,the inverse interpolation technique (IIT) is adopted to calculate the OIFs on Dirichletboundary, which is time consuming for large-scale simulation. In recent years, thenew methodology has been developed to efficiently calculate the OIFs on Neumannboundary, but the Dirichlet problem remains an open issue. This study employsthe subtracting and adding-back technique based on the integration of the fundamentalsolution over the whole boundary to develop a new formulation of the OIFs on3D Dirichlet boundary. Several problems with varied domain shapes and boundaryconditions are carried out to validate the effectiveness and feasibility of the proposedscheme in comparison with the SBM based on inverse interpolation technique, themethod of fundamental solutions, and the boundary element method.