Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition
Mathematical Citation Quotient 2013: 0.51
Volume 22 (2014)
Volume 21 (2013)
Volume 20 (2012)
Volume 19 (2011)
Volume 18 (2011)
Volume 17 (2009)
Volume 16 (2008)
Volume 15 (2007)
Volume 14 (2006)
Volume 13 (2005)
Volume 12 (2004)
Volume 11 (2003)
Volume 10 (2002)
Volume 9 (2001)
Volume 8 (2000)
Volume 7 (1999)
Volume 6 (1998)
Volume 5 (1997)
Volume 4 (1996)
Volume 3 (1995)
Volume 2 (1994)
Most Downloaded Articles
- Chemnitz Symposium on Inverse ProblemsChemnitz, Germany, September 27–28, 2007 by Hofmann, B.
- Obituary of Alfredo Lorenzi
- A numerical study of heuristic parameter choice rules for total variation regularization by Kindermann, Stefan/ Mutimbu, Lawrence D. and Resmerita, Elena
- Limited-angle cone-beam computed tomography image reconstruction by total variation minimization and piecewise-constant modification by Zeng, Li/ Guo, Jiqiang and Liu, Baodong
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems by Klibanov, Michael V.
Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
1Bauhaus Universität Weimar, Graduiertenkolleg “Modellqualitäten”, Berkaerstr. 9, 99423 Weimar, Germany. Email: (email)
Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 6, Pages 585–593, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.036, August 2009
- Published Online:
In piezoelectric applications, especially when the devices are used as actuators, the piezoelectric materials are driven under large signals which cause a nonlinear behavior. One way to model the nonlinearities is by functional dependencies of the material parameters on the electric field strength or the mechanical strain, respectively. The focus lies in the inverse problem, namely the identification of the parameter curves by appropriate measurements of charge signals over time. The problem is assumed to be ill-posed, since in general measured data are contaminated with noise. The solution process requires regularizing methods where modified Landweber iterations are in the focus. Implementations of modified Landweber iterations, namely the steepest descent and minimal error method can be shown to perform much faster than classical Landweber iterations due to the flexible handling of the relaxation parameter.
In our application, parameter curve identification in nonlinear piezoelectricity, the sought-for quantities require to be discretized. Therefore, an iterative multilevel algorithm as proposed by Scherzer [Numer. Math.: 579–600, 1998] is investigated where the iterations begin with coarse discretizations of the parameter curves profitting from the inherent regularization property of coarse discretization. At an advanced state of the iterations the algorithm switches according to an inner discrepancy principle to finer levels of discretization. By this, a sufficient smooth resolution of the sought-for quantities can be achieved. Convergence results and the regularizing property of such an iterative multilevel algorithm are proven. Numerical identification results are presented at the end of this article.