Recovering the Initial and Boundary Data in the Two-Dimensional Inverse Heat Conduction Problems Using the Novel Space-Time Collocation Meshfree Approach

Abstract

The novel meshfree approach based on the space-time collocation scheme for dealing with the two-dimensional inverse heat conduction problem (IHCP) is presented in this study. Numerical solutions obtained in the space-time collocation scheme are approximated by linear combinations of basis functions exactly satisfying the two-dimensional heat equation. We can then describe the approximated solutions of the two-dimensional heat conduction problems as a series by utilizing the addition theorem. Several numerical implementations including three cases with the consideration of the different combinations of absent initial or boundary conditions are carried out to verify the proposed numerical approach. The results reveal that highly accurate initial and boundary heat distribution with an accuracy of the order of 10−6 can be recovered, even when the data are absent on the initial as well as boundary condition and only final time data are specified. It may be concluded that the proposed numerical approach is able to provide promising approximations for solving two-dimensional IHCP.