On a PDE-based material parameter identification problem with contact constraints
It provides a benchmark for analyzing contact problems in PDE-based parameter estimation, but the results are incremental and lack concrete performance numbers.
The paper tackles parameter identification in PDEs with contact constraints, analyzing uniqueness and non-uniqueness issues and testing reconstruction algorithms on numerical examples.
We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability.