Study of A RPIM Method Independent of Shape Parameters

Generally, the value of a shape parameter will affect the accuracy of the radial point interpolation method (RPIM). However, a small shape parameter will cause this meshless method become unstable. In this paper, we expand the Gaussian basis function with a polynomial. Therefore, the calculation based on Gaussian is converted into the calculation of the corresponding feature vector, thereby eliminating the influence of the shape parameters on the performance of the algorithm. The numerical experiments prove the efficiency of the algorithm.