#### Title

### A Linear Integral Equation Approach to the Robin Inverse Problem

#### Document Type

Article

#### Publication Date

10-1-2005

#### Abstract

We consider the numerical solution of an inverse problem for the Laplace equation where the Robin coefficient is to be recovered from a partial boundary measurement. We first formulate the problem by integral equations on the boundary. By introducing a new variable, the key integral equation involved becomes linear, and the ill-posedness of the inverse problem is clearly revealed. On the basis of this linearity, we then design linear least-squares-based methods for reconstruction of the Robin coefficient. A proper form of regularization is chosen, and both direct (non-iterative) and iterative methods are investigated. Numerical examples are presented to show the effectiveness of these methods in providing excellent estimates for the Robin coefficient from data with and without noise.

#### Repository Citation

Fang, W.,
& Lin, F.
(2005). A Linear Integral Equation Approach to the Robin Inverse Problem. *Inverse Problems, 21* (5), 1757-1772.

https://corescholar.libraries.wright.edu/math/426

#### DOI

10.1088/0266-5611/21/5/015