Identification of the heterogeneous conductivity in an inverse heat conduction problem

Abstract

AbstractThis work deals with the problem of determining a nonhomogeneous heat conductivity profile in a steady‐state heat conduction boundary‐value problem with mixed Dirichlet–Neumann boundary conditions over a bounded domain in , from the knowledge of the state over the whole domain. We develop a method based on a variational approach leading to an optimality equation which is then projected into a finite dimensional space. Discretization yields a linear although severely ill‐posed equation which is then regularized via appropriate ad‐hoc penalizers resulting a in a generalized Tikhonov–Phillips functional. No smoothness assumptions are imposed on the conductivity. Numerical examples for the case in which the conductivity can take only two prescribed values (a two‐materials case) show that the approach is able to produce very good reconstructions of the exact solution.