%0 Journal Article
	%A Maatoug Hassine and  Mourad Hrizi
	%D 2017
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 121, 2017
	%T Topological Sensitivity Analysis for Reconstruction of the Inverse Source Problem from Boundary Measurement
	%U https://publications.waset.org/pdf/10006334
	%V 121
	%X In this paper, we consider a geometric inverse source
problem for the heat equation with Dirichlet and Neumann boundary
data. We will reconstruct the exact form of the unknown source
term from additional boundary conditions. Our motivation is to
detect the location, the size and the shape of source support.
We present a one-shot algorithm based on the Kohn-Vogelius
formulation and the topological gradient method. The geometric
inverse source problem is formulated as a topology optimization
one. A topological sensitivity analysis is derived from a source
function. Then, we present a non-iterative numerical method for the
geometric reconstruction of the source term with unknown support
using a level curve of the topological gradient. Finally, we give
several examples to show the viability of our presented method.
	%P 26 - 32