Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 124, Issue 5, Pages 1128-1145Publisher
WILEY
DOI: 10.1002/nme.7156
Keywords
heat conduction problem; inverse problem; regularization; Tikhonov-Phillips
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This work addresses the problem of determining a nonhomogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem in a bounded domain in Double-struck capital R-n. A method based on variational approach and finite dimensional projection is developed, resulting in a regularized linear equation that can reconstruct the exact solution even when the conductivity can only take two prescribed values.
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 in Double-struck capital 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.
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