Improved meshless local Petrov-Galerkin method for two-dimensional potential problems

In this paper, combining the moving Kriging interpolation method and meshless local Petrov-Galerkin method, an improved meshless local Petrov-Galerkin method is presented, in which the Heaviside step function is used as test function over the local weak form. The present method is applied to two-dimensional potential problems and the corresponding discrete equations are derived. Because the shape functions so-obtained possess the Kronecker delta property, the essential boundary conditions can be enforced as the FEM; furthermore, the Heaviside step function is used as the test function, there is no domain integral, and only a regular boundary integral is involved. In this paper, the choice of the important parameters is studied. Numerical examples show that the present method has simpler numerical procedures and lower computation cost, in addition, the essential boundary conditions can be implemented directly.