IMLPG Method For Transient Heat Conduction Analysis Based On Precise Integration Method

Meshless method is a new numerical method for solving the partial differential equations. Different from the finite element method, the meshless method requires only nodes to construct approximation function. In recent years, a lot of important pioneering effort has been done on the meshless methods.The improved meshless local Petrov-Galerkin (IMLPG) method is a new numerical method, which is obtained from the local weak formulation of the weighted residual method and the natural neighbour interpolation (NNI). The shape functions constructed from the NNI possess Kronecker delta function property and therefore essential boundary conditions can be easily imposed. In addition, the system stiffness matrix in the IMLPG method is banded and sparse.The precise integration method is a mature numerical algorithm to solve the ordinary differential equation. It has many notable merits such as large time step, higher accuracy and unconditional stability. The improved meshless local Petrov-Galerkin in conjunction with the modified precise time step integration method in the time domain is proposed for transient heat conduction analysis in this paper for homogeneous materials and functionally graded materials. In addition, the FORTRAN programs of the above methods have been written. The availability and accuracy of the present method for transient heat conduction analysis are tested through numerical examples.