A homogenization function method for inverse heat source problems in 3D functionally graded materials

Abstract A simple and effective method is proposed for solving inverse heat source problems in functionally graded materials based on the homogenization function. Making use of given conditions, a homogenization function for the boundary value problem is conceived and a family of homogenization functions is further derived. Then, the superposition of homogenization functions method is developed and used for determining the heat source of the inverse problems. In this new methodology, the inverse heat source problems are directly solved by calculating a linear matrix system. Importantly, this scheme does not involve mesh generation, numerical integration, iteration, regularization and fundamental solutions, and it is easy to program and implement on the existing software. Four numerical examples defined on the cuboid domains are presented to demonstrate the accuracy and efficiency of the presented tool.