The meshless method for a two-dimensional inverse heat conduction problem with a source parameter

Inverse problems are difficult to be solved in scientific research. And theyare widely applied in the aerospace, nuclear physics, metallurgyand other fields. The finite difference method and the finite element methodare main numerical methods to obtain numerical solutions of inverseproblems. The finite point method is one of meshless methods. Comparing withthe numerical methods based on mesh, such as finite element method andboundary element method, the finite point method only needs the scatterednodes instead of meshing the domain of the problem when the shape functionare formed. For problems with complicated domain which need to be re-meshed,the finite point method has the advantage of that no mesh is needed. In thispaper, the finite point method is used to obtain numerical solutions oftwo-dimensional inverse heat conduction problems with a source parameter,and the corresponding discretized equations are obtained. The collocationmethod is used to discretize the governing partial differential equations,and boundary conditions can be directly enforced without numericalintegration in the problem domain. This reduces the computation costgreatly. A numerical example is presented to show the method in this paperis effective. The finite point method, which is for two-dimensional inverseheat conduction problems with a source parameter, presented in this paperhas some advantages of arbitrary nodes distribution, simple numericalprocedures and low computation cost. The researches in this paper provide anew numerical method for inverse heat conduct problems, and can be appliedto other inverse problems.