An interpolating boundary element-free method for three-dimensional potential problems

This paper begins by discussing an improved interpolating moving least-square (IIMLS) method and the properties of its shape function. In the IIMLS method, the shape function is of delta function property and the weight function is nonsingular, so it overcomes the drawbacks in both the moving least-square approximation and the interpolating moving least-square method. Then combining boundary integral equations with the IIMLS method, an interpolating boundary element-free method (IBEFM) is developed for three-dimensional potential problems. In the IBEFM, only a nodal data structure on the boundary face of a domain is required. Unlike the boundary node method (BNM), the IBEFM is a direct meshless method in which the primary unknown quantities are real solutions of nodal variables, and boundary conditions can be imposed directly and easily, which leads to a greater computational precision. Besides, the number of both unknowns and system equations in the IBEFM is only half of that in the BNM, and thus the computing speed and efficiency are increased. Numerical examples on curve/surface fittings and potential problems indicate that the efficiency and convergence rate of the present methods is high.