AN INTERPOLATING BOUNDARY ELEMENT-FREE METHOD WITH NONSINGULAR WEIGHT FUNCTION FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

In this paper, an improved interpolating moving least-squares (IIMLS) method with nonsingular weight function is presented. The shape function of the IIMLS method satisfies the property of Kronecker delta function. The IIMLS method can overcome the difficulties caused by the singularity of the weight function in the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas. By combining the boundary integral equation (BIE) method with the IIMLS method, an improved interpolating boundary element-free (IIBEF) method is presented for two-dimensional potential problems. The IIBEF method is a direct meshless boundary integral equation method in which the basic unknown quantities are the real solutions to the nodal variables, and the boundary conditions can be applied directly and easily. Thus, it gives greater computational precision. Some numerical examples are presented to demonstrate the IIMLS and IIBEF methods.