MLS-based numerical manifold method based on IPIM for 3D transient heat conduction of FGMs

In this study, the moving least squares based numerical manifold method (MLS-NMM) is presented to solve threedimensional (3D) transient heat conduction problems of functionally graded materials (FGMs), where the increment dimensional precise integration method (IPIM) is applied to integrate the ordinary differential equations derived from the semi-discrete form. In the 3D MLS-NMM, the influence domains of the MLS-nodes are taken as the mathematical patches which are used to construct the mathematical cover (MC), and the shape functions of the MLS-nodes are employed as the weight functions subordinate to the MC. MLS-NMM is utilized for spatial discretization of the weak form of the problem. The IPIM overcomes the shortcomings of traditional backward difference scheme dependent on the time step and greatly improves the computing efficiency. Meanwhile, a mass lumping technique is proposed for the 3D MLS-NMM. Furthermore, a number of numerical experiments on transient thermal conduction are conducted, suggesting that the 3D MLS-NMM based on IPIM and the proposed mass lumping has excellent accuracy, absolutely stable and high computing efficiency.