IDENTIFICATION OF A SPATIAL FIELD OF MATERIAL PROPERTIES WITH ADAPTIVE REGULARIZATION AND MESHES

摘要

It is well known that the solution of an inverse problem is unstable and not unique. In order to avoid these difficulties when solving such a problem, a Tikhonov's regularization term is usually added to the norm quantifying the discrepancy between the model's predictions and experimental data. However, this regularization term is often insufficient to deal with the identification of a spatially variable field of material properties.rnHere is discussed a general strategy using classical adaptive meshing methods in order to improve the regularization of the inverse problem in such cases. The first step consists in using two distinct meshes: one associated with the discretization of the sought spatial field, and one associated with the resolution of the mere mechanical problems. Then the introduction of usual local error estimators in a second step can drive the refinement of the coarse mesh associated with the sought parameters.rnThis general strategy is then applied to a practical case of study: the detection of subterranean cavities using experimental data obtained by an interferometric device on a satellite.