A meshless collocation scheme for inverse heat conduction problem in three-dimensional functionally graded materials

This short communication documents the first attempt to apply the generalized finite difference method (GFDM) for inverse heat conduction analysis of functionally graded materials (FGMs). The fact that the GFDM is a meshless collocation method makes it particularly attractive in solving problems with complex geometries and high dimensions. By employing the Taylor series expansion and the moving least-squares technique, the method produces sparse and banded matrix which makes it possible to perform large-scale simulations. Three benchmark examples are provided to demonstrate the accuracy and adaptability of the GFDM approach in solving the inverse Cauchy problems. The convergence and stability of the method with respect to the amount of noise added into the input data are analyzed.