Convergence rates of Tikhonov regularization for parameter identification in a Maxwell system

Abstract

In this paper, we investigate the convergence rates of the widely used output least squares method with Tikhonov regularization for the identification of the magnetic permeability in a Maxwell system. By introducing some new techniques, we derive a simple and easily interpretable source condition and guarantee the usual convergence rate O( ) for the regularized solutions, where is assumed to be the noise level of the data. More importantly, we finally construct the source functions successfully in two-dimensional spaces.

Keywords:

• parameter identification
• Maxwell system
• permeability
• source condition

AMS Subject Classifications:

• MSC 2010
• 41A25
• 65M32

Acknowledgement

The authors would like to thank Professor Jun Zou (Chinese University of Hong Kong) for his valuable discussions and two anonymous referees for their constructive comments.

Notes

1 The work was supported by National Natural Science Foundation of China [grant number 91130022], [grant number 10971159] and [grant number 11161130003]; NCET of China; China Postdoctoral Science Foundation [grant number 2012M521444]; National Natural Science Foundation of China [grant number 11326233].