Numerical solution of potential problems using radial basis reproducing kernel particle method

Abstract

The paper presents the radial basis reproducing kernel particle method (RRKPM) for potential problems. The proposed RRKPM can eliminate the negative effect of different reproducing kernel functions (RKF) on computational stability and accuracy. The integral weak form is used to derive a discretized system equation for potential problem, and the essential boundary condition is imposed by the Lagrange interpolation method, the corresponding governing equations of RRKPM are investigated and obtained. Compared with the conventional RKPM, the RRKPM has higher computational stability and accuracy. Finally, the RRKPM is applied to numerical simulation of potential problems, and the accuracy and stability of the RRKPM can be illustrated by the two numerical results. Keywords: Radial basis functions, Meshless methods, Reproducing kernel particle method, The Lagrange interpolation method, Potential problems