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Identification of the heterogeneous conductivity in an inverse heat conduction problem
Author(s) -
Ciarbonetti Angel A.,
Idelsohn Sergio,
Spies Ruben D.
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.7156
Subject(s) - thermal conduction , discretization , mathematics , boundary value problem , heat equation , tikhonov regularization , mathematical analysis , bounded function , thermal conductivity , inverse problem , neumann boundary condition , domain (mathematical analysis) , physics , thermodynamics
This 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 inℝ n$$ {\mathbb{R}}^n $$ , 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.