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A new reconstruction method for a parabolic inverse source problem. (English) Zbl 1423.35444

Summary: 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.

MSC:

35R30 Inverse problems for PDEs
35A15 Variational methods applied to PDEs
35B20 Perturbations in context of PDEs
49K40 Sensitivity, stability, well-posedness
65R32 Numerical methods for inverse problems for integral equations
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