Application of the meshless generalized finite difference method to inverse heat source problems

The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems.