Hend Benameur: Thursday 2 November at 11 am, A415 Inria Paris.
We are interested in some inverse problems in porous media: parameter estimation, fracture identification
and wells location. All these problems are formulated as optimization problems. The main and common
tool in the developed techniques is “ the gradient” of a convenient function.
An adaptive parameterization algorithm is developed, implemented and applied for the estimation of
scalar and vector parameters in porous media. Values of parameters and shapes of hydrogeological zones
are unknown. The main tool in the adaptive parameterization approach is a refinement indicator: Once
the identification problem is set as a minimization of an objective function, the question is what is the
effect on this function of allowing discontinuity of the parameter in some candidate location? Refinement
indicators give the answer to this question .
Since fractures are characterized by discontinuities, the idea is to extend previous indicators to locate
fractures. We define fracture indicators and we proceed in an iterative way in order to identify fractures
in porous media.
The topological sensitivity analysis method has been recognized as a promising tool to solve topology
optimization problems. It consists to provide an asymptotic expansion of a shape functional with respect
to the size of a small hole created inside the domain. To solve the inverse problem where both parametrization and well’s location are unknown, we incorporate the topological gradient approach in the adaptive parametrization algorithm; results are promising.
