Abstract
Three dimensional functionally graded material is presented. It is assumed that the thermal conductivity varies exponentially along one direction. The heat generation and non-uniform initial distribution can be considered in the simulation. In the process of solving this diffusion problem numerically, the Laplace transform will be used to remove the time dependence of the problem. And the multiple reciprocity formulation of the modified Helmholtz fundamental solutions is used to convert the domain integral into boundary integrals. The results of test calculations are in agreement with exact solutions and finite element method simulations.
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