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doi:10.22028/D291-28321
Title: | Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization |
Author(s): | Diebels, Stefan Scheffer, Tobias Schuster, Thomas Wewior, Aaron |
Language: | English |
Title: | Mathematical problems in engineering : theories, methods and applications |
Volume: | 2018 |
Publisher/Platform: | Hindawi |
Year of Publication: | 2018 |
Publikation type: | Journal Article |
Abstract: | For studying the interaction of displacements, stresses, and acting forces for elastic and viscoelastic materials, it is of utmost importance to have a decent mathematical model available. Usually such a model consists of a coupled set of nonlinear differential equations together with appropriate boundary conditions. However, since the different material classes vary significantly with respect to their physical and mechanical behavior, the parameters which appear in these equations are unknown and therefore have to be determined before the equations can be used for further investigations or simulations. It is this very step which is addressed in this article where we consider elastic as well as viscoelastic material behavior. The idea is to compute the parameters as solutions of a minimization problem for Tikhonov functionals. Tikhonov regularization is a well-established solution technique for tackling inverse problems. On the one hand, it assures a computation that is stable with respect to noisy input data, and on the other hand, it involves desired a priori information on the solution. In this article we develop problem adapted Tikhonov functionals and prove that a Tikhonov regularization improves the accuracy especially when the underlying system is ill-conditioned. |
DOI of the first publication: | 10.1155/2018/1895208 |
URL of the first publication: | https://www.hindawi.com/journals/mpe/2018/1895208/ |
Link to this record: | hdl:20.500.11880/27599 http://dx.doi.org/10.22028/D291-28321 |
ISSN: | 1563-5147 1024-123X |
Date of registration: | 3-Aug-2019 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Professorship: | MI - Prof. Dr. Thomas Schuster |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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