Two-dimensional nonlinear inverse heat conduction problem

Y and T: Temperatures. Y: Solution of the direct problem, in K. T: Solution of the inverse problem, in K. k: Iteration of the conjugate gradient method. The inverse problem is solved using this method. x: Space. t: Time. Inverse problem in Case 1.1: Temperatures on the inner boundary of an annulus are estimated from data (namely, temperatures and heat fluxes) on the outer boundary of the annulus. Inverse problem in Case 2.1: Temperatures on the outer boundary of an annulus are estimated from data (namely, temperatures and heat fluxes) on the inner boundary of the annulus. In both cases, the initial condition is known. In both cases, the redundant boundary data and initial conditions for the inverse problem are perturbed with Gaussian noise. Case_1.1/DHCP: Y(x, t) for Case 1.1. Case_1.1/11: T(x, t) for Case 1.1 at k = 11. Case_1.1/Case_1.1_vid.mp4: Y(x, t) for Case 1.1 is compared with T(x, t) for Case 1.1 at k = 11. Upper-left corner: t, in s. Case_2.1/DHCP: Y(x, t) for Case 2.1. Case_2.1/3: T(x, t) for Case 2.1 at k = 3. Case_2.1/Case_2.1_vid.mp4: Y(x, t) for Case 2.1 is compared with T(x, t) for Case 2.1 at k = 3. Upper-left corner: t, in s. Y(x, t) is saved to file T.*. T(x, t) is saved to file dir_IHCP.*. HDF5 files (*.h5) can be read using, for example, the h5py package in Python. XDMF files (*.xdmf) can be read using, for example, ParaView. MP4 files (*.mp4) can be played using, for example, VLC.