Abstract
This paper presents a numerical method for solving a problem usually encountered in thermal imaging. The goal is to estimate an interior boundary of a material by applying a known heat flux and measuring the induced temperature response on its external boundary. The interior boundary is assumed to be under a homogeneous Neumann condition. This boundary is first parameterized by a finite-term of Fourrier series and the corresponding approximate inverse problem is numerically optimized using an iterative Newton method. The required gradient is established using the domain derivative techniques. The system of heat equations is treated using finite element method for space and implicit scheme for time. Some numerical tests are provided to illustrate the performances of the proposed method.
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