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.


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
Full Text: DOI


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