On a PDE-based material parameter identification problem with contact constraints

TL;DR

This paper investigates a PDE-based parameter estimation problem with contact constraints, analyzing uniqueness issues and testing reconstruction algorithms through numerical examples.

Contribution

It introduces a benchmark model for contact problems, discusses uniqueness challenges, and develops reconstruction methods tested on numerical simulations.

Findings

Demonstrates both uniqueness and non-uniqueness in parameter identification.

Provides numerical examples illustrating the effectiveness of reconstruction approaches.

Analyzes the impact of contact constraints on inverse problem solvability.

Abstract

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.