Identification of a heterogeneous orthotropic conductivity in a rectangular domain

This paper investigates the problem of identifying a heterogeneous transient orthotropic thermal conductivity in a two-dimensional rectangular domain using initial and Dirichlet boundary conditions and fluxes as overdetermination conditions. The measurement data represented by the heat fluxes are shown to ensure the unique solvability of the inverse problem solution. The finite-difference method is employed as the direct solver which is fed iteratively in a nonlinear minimization routine. Exact and noisy input data are inverted numerically. Numerical results indicate that accurate and stable solutions are obtained.