Liu, Ji-Chuan2022-04-202022-04-202017-05-04Liu, J. C. (2017). An inverse source problem of the Poisson equation with Cauchy data. <i>Electronic Journal of Differential Equations, 2017</i>(119), pp. 1-19.1072-6691https://hdl.handle.net/10877/15673In 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalInverse source problemGradient descent methodTrust-region-reflective algorithmPoisson equationIll-posed problemArticle