Mi, 13.12.2017, 17:15
Parameter identification for elastic wave equations
Mathematisches Kolloquium

Referent: Prof. Dr. Thomas Schuster, Universität des Saarlandes Saarbrücken
Raum: S2|14 /24

Zuvor findet um 16:45 Uhr die Teerunde in Raum 244 des Mathematikgebäudes (S2/15), Schlossgartenstaße 7, statt.

We start with a short introduction to the world of inverse problems. Subject of such problems is the computation of a quantity, which is not directly ac cessible, from indirect observations (measurements). Usually such problems suffer from an inherent ill-posedness in the sense that already small perturbations in the measurement data cause large errors in the solution making a direct solver meaningless. This is why inverse problems are solved by so-called regularization methods leading to a stable solution. An important class of inverse problems consist of parameter identification problems for partial differential equations. Usually these problems are nonlinear and they are solved by iterative regularization schemes such as the Landweber method.

In the talk we consider identification problems for the linear and the nonlinear, hyperelastic wave equation. The motivation comes from developing Structural Health Monitoring systems. These consist of a number of sensor and actors that are applied to an elastic structure. The actors generate a guided wave that interacts with possible defects and is measured at the sensors. Computing parameters such as volume forces or stored energy functions should give pointers to damages. We consider the linear inverse problem of computing an external volume force and the nonlinear problem of identifying the stored energy function of a hyperelastic material from boundary sensor measurements. In the talk we go all the way from stating the mathematical model, analyzing the forward operators and establishing iterative, numerical solvers. We present numerical results for both setups.



Fachbereich Mathematik
Technische Universität Darmstadt

Schlossgartenstraße 7
64289 Darmstadt

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