Inverse Problems
In 2005, the topological asymptotic expansion for the Laplace equation with respect to the insertion of a short crack inside a plane domain has been found. It allows to detect and locate cracks for a simple model problem: the steady-state heat equation with the heat flux imposed and the temperature measured on the boundary.
In 2009, the topological gradient method has been applied to tomographic reconstruction.
Read more about this topic: Topological Derivative, Applications
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