Identification of an internal material boundary

Abstract

The goal of this article is to provide a simple and fast numerical method to estimate an internal shape of a material by exploiting certain measurements performed on its external boundary. This inverse problem is formulated as a least-squares minimization problem. A numerical approach to this minimization problem based on the domain derivation ideas is outlined. Real implementation is achieved with the Freefem software. Numerical tests are provided to demonstrate the efficiency of the proposed method. Special attention is given to the impact of the material thermophysical properties on the quality of the identification. The effect of the errors in the measurements on the identification is also investigated.

Keywords:

• Output least-squares method
• Inverse heat conduction problem
• Domain derivation
• Finite element method

AMS Subject Classifications::

• 80A20
• 80A23
• 65K10