A new reconstruction method for a parabolic inverse source problem |
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Authors: | M. Hrizi M. Hassine R. Malek |
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Affiliation: | 1. Faculty of Sciences, Department of Mathematics, Monastir University, Monastir, Tunisia.mourad-hrizi@hotmail.fr;3. Faculty of Sciences, Department of Mathematics, Monastir University, Monastir, Tunisia. |
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Abstract: | In this paper, we focus on the detection of the shape and location of a discontinuous source term from the knowledge of boundary measurements. We propose a non-iterative reconstruction algorithm based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from an energy-like cost function. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. The efficiency of our algorithm is illustrated by some numerical simulations. |
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Keywords: | Inverse source problems heat equation topology optimization topological sensitivty Kohn-Vogelius formulation |
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