Transient heat transfer analysis of functionally graded materials using adaptive precise time integration and graded finite elements

In this article, the precise time integration (PTI) method in conjunction with the finite-element method is applied to conduct the heat transfer analysis of functionally graded materials. Two techniques are introduced to improve the computational efficiency and accuracy. The first one is an adaptive algorithm of PTI, which can determine the algorithm parameters according to the problem characteristics and the prescribed computational error tolerance. The second one is the isoparametric graded finite-elements method, which can be compatible with the problem of spatially varying material properties. Numerical examples are presented to demonstrate the advantages of the present method.