A new reconstruction method for a parabolic inverse source problem

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.

KEYWORDS:

• Inverse source problems
• heat equation
• topology optimization
• topological sensitivty
• Kohn-Vogelius formulation

AMS SUBJECT CLASSIFICATIONS:

• 35A15
• 35B20
• 49K40
• 65R32

Notes

No potential conflict of interest was reported by the authors.