Phillips-Tikhonov regularization with a priori information for neutron emission tomographic reconstruction on Joint European Torus

2015 ◽  
Vol 86 (9) ◽  
pp. 093505 ◽  
Author(s):  
J. Bielecki ◽  
L. Giacomelli ◽  
V. Kiptily ◽  
M. Scholz ◽  
K. Drozdowicz ◽  
...  
Keyword(s):  
Tikhonov Regularization ◽  
Neutron Emission ◽  
A Priori ◽  
Tomographic Reconstruction ◽  
A Priori Information ◽  
Priori Information

scholarly journals Identifying Elastic and Viscoelastic Material Parameters by Means of a Tikhonov Regularization

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Stefan Diebels ◽  
Tobias Scheffer ◽  
Thomas Schuster ◽  
Aaron Wewior
Keyword(s):  
Viscoelastic Material ◽  
Tikhonov Regularization ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Material Behavior ◽  
Solution Technique ◽  
A Priori Information ◽  
Noisy Input ◽  
Priori Information ◽  
The One

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.

Sign in / Sign up

Export Citation Format

Share Document