Two-dimensional Inverse Heat Conduction Problem Using a Meshless Manifold Method

Inverse heat conduction problems (IHCP) are widely applied to the aerospace, nuclear physics, metallurgy and other fields. The meshless method and the finite element method are main numerical methods to obtain numerical solutions for IHCP. The meshless manifold method (MMM) is based on moving least-square method and the finite cover approximation theory in the mathematical manifold. Comparing with the numerical methods based on mesh, such as finite element method and boundary element method, the MMM only uses cover nodes without having to mash the domain of the problem when the cover function is formed. In this paper, the MMM is used to obtain numerical solutions of two-dimensional IHCP with a source parameter, and the corresponding discretized equations are obtained. A numerical example is given to show the effectiveness of the method. The MMM can also be applied to other inverse problems.