The simple boundary element method for transient heat conduction in functionally graded materials Original Research Article

This paper presents a “simple” boundary element method for transient heat conduction in functionally graded materials, which leads to a boundary-only formulation without any domain discretization. For a broad range of functional material variation (quadratic, exponential and trigonometric) of thermal conductivity and specific heat, the non-homogeneous problem can be transformed into the standard homogeneous diffusion problem. A three-dimensional boundary element implementation, using the Laplace transform approach and the Galerkin approximation, is presented. The time dependence is restored by numerically inverting the Laplace transform by means of the Stehfest algorithm. A number of numerical examples demonstrate the efficiency of the method. The results of the test examples are in excellent agreement with analytical solutions and finite element simulation results.