Maatoug Hassine and Mourad Hrizi Topological Sensitivity Analysis for Reconstruction of the Inverse Source Problem from Boundary Measurement
26 - 32
2017
11
1
International Journal of Mathematical and Computational Sciences http://waset.org/publications/10006334
http://waset.org/publications/121
World Academy of Science, Engineering and Technology
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 oneshot algorithm based on the KohnVogelius
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 noniterative 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.
International Science Index 121, 2017