A VARIATIONAL PENALIZED APPROACH FOR IDENTIFYING HETEROGENEOUS CONDUCTIVITY IN AN INVERSE HEAT CONDUCTION PROBLEM

ANGEL CIARBONETTI; IDELSOHN, SERGIO; RUBEN SPIES

Santa Fe

Congreso; IX CONGRESO DE MATEMÁTICA APLICADA, COMPUTACIONAL E INDUSTRIAL, MACI 2023; 2023

ASAMACI

This work deals with the problem of determining the non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in Rn, 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 leading to generalized Tikhonov-Phillips functionals. No smoothness assumptions are imposed on the conductivity. In fact profiles with jump discontinuities are allowed. 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.