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

Inverse problems are widely found in the aerospace, nuclear physics, metallurgy and other fields. The finite difference method and the finite element method are main numerical methods to obtain numerical solutions for inverse problems. The finite point method is a meshless method. Comparing with the numerical methods based on mesh, such as finite element method and boundary element method, the finite point method only uses scattered nodes without having to mesh the domain of the problem when the shape function is formed. In this paper, the finite point method is used to obtain numerical solutions of two-dimensional inverse heat conduction problems with a source parameter, and the corresponding discretized equations are obtained. The collocation method is used to discretize the governing partial differential equations, and boundary conditions can be directly enforced without numerical integration in the problem domain. This reduces the computation cost greatly. A numerical example is given to show the effectiveness of the method. The finite point method can also be applied to other inverse problems.