TY  - EJOU
AU  - Li, Weiwei  
AU  - Chen, Wen  

TI  - Boundary Layer Effect in Regularized Meshless Method for Laplace Equation
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2014
VL  - 100
IS  - 5
SN  - 1526-1506

AB  - This paper presents an efficient strategy for the accurate evaluation of near-boundary solutions in the regularized meshless method (RMM), also known as the boundary layer effect associated with the boundary element method. The RMM uses the double layer potentials as its interpolation basis function. When the field point is close to the boundary, the basis function will present nearly strongand hyper-singularities, respectively, for potentials and its derivative. This paper represents the first attempt to apply a nonlinear transformation, based on sinh function, to the accurate evaluation of nearly singular kernels associated with the RMM. The accuracy and efficiency of the proposed strategy are demonstrated through several numerical examples, where the solutions at as close as 1.0E–6 distance to the boundary are accurately evaluated.
KW  - Regularized meshless method
KW  -  Double layer potentials
KW  -  Near singularity
KW  -  Boundary layer effect
KW  -  nonlinear transformation

DO  - 10.3970/cmes.2014.100.347