An inverse source problem of the Poisson equation with Cauchy data

Abstract

In this article, we study an inverse source problem of the Poisson equation with Cauchy data. We want to find iterative algorithms to detect the hidden source within a body from measurements on the boundary. Our goal is to reconstruct the location, the size and the shape of the hidden source. This problem is ill-posed, regularization techniques should be employed to obtain the regularized solution. Numerical examples show that our proposed algorithms are valid and effective.

Keywords

• Inverse source problem
• gradient descent method
• trust-region-reflective algorithm
• Poisson equation
• ill-posed problem