A meshless local Petrov-Galerkin method with the universal Kriging interpolation for heat conduction problems

摘要

A meshless local Petrov-Galerkin method (MLPG) based on the universal Kriging interpolation is employed for solving two-dimensional linear and nonlinear heat conduction problems. Here the trigonometric functions are chosen as basis functions. The essential boundary conditions can be implemented directly as the shape functions derived from the universal Kriging interpolation possess the Kronecker Delta property. In constructing the weak form of heat conduction equations, the Heaviside step function is used as the test function in each sub-domain and the two-point difference method is selected for the time discretization scheme. In solving the nonlinear heat conduction problems, the quasi-linearization scheme is adopted to avoid the iteration for nonlinear solution. This method does not involve the sub-domain integral in generating the global stiffness matrix except for the boundary integral. The result of numerical examples is presented to show this method is effective.