Improved complex variable moving least squares approximation for three-dimensional problems using boundary integral equations

The improved complex variable moving least squares approximation is an efficient method to generate meshless approximation functions. In the past, the approximation has been used only for 2D problems. In this paper, the approximation is developed to solve 3D problems. Theoretical error estimation of the approximation is given. Then, incorporating the approximation into boundary integral equations, a symmetric and boundary-only meshless method, the complex variable Galerkin boundary node method, is developed and analyzed theoretically for 3D potential, Helmholtz and Stokes problems. Numerical results demonstrate the accuracy and efficiency of the developed method.