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Titel: Sequential Subspace Optimization for Recovering Stored Energy Functions in Hyperelastic Materials from Time-Dependent Data
VerfasserIn: Klein, Rebecca
Schuster, Thomas
Wald, Anne
HerausgeberIn: Kaltenbacher, Barbara
Schuster, Thomas
Wald, Anne
Sprache: Englisch
Titel: Time-dependent Problems in Imaging and Parameter Identification
Seiten: 165-190
Verlag/Plattform: Springer Nature
Erscheinungsjahr: 2021
DDC-Sachgruppe: 510 Mathematik
Dokumenttyp: Buchbeitrag
Abstract: Monitoring structures of elastic materials for defect detection by means of ultrasound waves (Structural Health Monitoring, SHM) demands for an efficient computation of parameters which characterize their mechanical behavior. Hyperelasticity describes a nonlinear elastic behavior where the second Piola-Kirchhoff stress tensor is given as a derivative of a scalar function representing the stored (strain) energy. Since the stored energy encodes all mechanical properties of the underlying material, the inverse problem of computing this energy from measurements of the displacement field is very important regarding SHM. The mathematical model is represented by a high-dimensional parameter identification problem for a nonlinear, hyperbolic system with given initial and boundary values. Iterative methods for solving this problem, such as the Landweber iteration, are very time-consuming. The reason is the fact that such methods demand for several numerical solutions of the hyperbolic system in each iteration step. In this contribution we present an iterative method based on sequential subspace optimization (SESOP) which in general uses more than only one search direction per iteration and explicitly determines the step size. This leads to a significant acceleration compared to the Landweber method, even with only one search direction and an optimized step size. This is demonstrated by means of several numerical tests.
DOI der Erstveröffentlichung: 10.1007/978-3-030-57784-1_6
URL der Erstveröffentlichung: https://link.springer.com/chapter/10.1007/978-3-030-57784-1_6
Link zu diesem Datensatz: urn:nbn:de:bsz:291--ds-394138
hdl:20.500.11880/35534
http://dx.doi.org/10.22028/D291-39413
ISBN: 978-3-030-57784-1
978-3-030-57783-4
Datum des Eintrags: 30-Mär-2023
Fakultät: MI - Fakultät für Mathematik und Informatik
Fachrichtung: MI - Mathematik
Professur: MI - Prof. Dr. Thomas Schuster
Sammlung:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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