AN INTERPOLATING LOCAL PETROV-GALERKIN METHOD FOR POTENTIAL PROBLEMS

作者：Chen, L.; Liu, C.; Ma, H. P.; Cheng, Y. M.^*

来源：International Journal of Applied Mechanics, 2014, 6(1): 1450009.

DOI：10.1142/S1758825114500094

• Meshless local Petrov-Galerkin method
• moving Kriging interpolation
• Heaviside step function
• interpolating local Petrov-Galerkin method
• potential problem

In this paper, based on the moving Kriging interpolation (MKI), the meshless interpolating local Petrov-Galerkin (ILPG) method is presented to solve two- and three-dimensional potential problems. In the present method, the shape function constructed by the MKI has the property of the Kronecker delta function. Then in the ILPG method the essential boundary conditions can be implemented directly. The discrete equations are obtained using the local symmetric weak form. The Heaviside step function is used as the test function in each sub-domain to avoid some domain integral in the symmetric weak form, which will greatly improve the effectiveness of the present method. The ILPG method in this paper is a truly meshless method, which does not require a mesh either for obtaining shape function or for numerical integration in the local weak form. Several numerical examples of potential problems show that the ILPG method has higher computational efficiency and convergence rate than the MLPG method.

• 出版日期2014-2
• 单位上海大学; 长安大学