Abstract
This paper describes the application of Trefftz method to the steady-state heat conduction problem on the functionally gradient materials. Since the governing equation is given as the Poisson equation, it is difficult to apply the ordinary Trefftz method to this problem. For overcoming this difficulty, we will present the combination scheme of the Trefftz method with the computing point analysis method. The non-homogeneous term of the Poisson equation is approximated by the polynomials of the Cartesian coordinates to determine the particular solution related to the non-homogeneous term. The solution of the problem is approximated with the linear combination of the particular solution and the T-complete functions of the Laplace equation. The unknown parameters are determined so that the approximate solutions will satisfy the boundary conditions by means of the collocation method. Finally, the scheme is applied to some numerical examples.
