On the numerical solution of an inverse boundary value problem for the heat equation
- 1 August 1998
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 14 (4), 853-867
- https://doi.org/10.1088/0266-5611/14/4/006
Abstract
We consider the inverse problem of reconstructing the interior boundary curve of an arbitrary-shaped annulus from overdetermined Cauchy data on the exterior boundary curve. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton method based on a boundary integral equation approach for the initial boundary value problem for the heat equation. A theoretical foundation for this Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the interior boundary curve in the sense of a domain derivative. Numerical examples indicate the feasibility of our method.Keywords
Other Versions
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