A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems. (11th January 2016)

• Record Type: Journal Article
• Authors: Gulliksson, Mårten; Holmbom, Anders; Persson, Jens; Zhang, Ye
• Is Part Of: Inverse problems. Volume 32:Number 2(2016:Feb.)
• Publication Date: 2016-01-11
• Subjects: homogenization -- inverse problems -- regularization -- G-limit; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/2/025005
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Reconstructing the homogenized coefficient, which is also called the G -limit, in elliptic equations involving heterogeneous media is a typical nonlinear ill-posed inverse problem. In this work, we develop a numerical technique to determine G -limit that does not rely on any periodicity assumption. The approach is a technique that separates the computation of the deviation of the G -limit from the weak -limit of the sequence of coefficients from the latter. Moreover, to tackle the ill-posedness, based on the classical Tikhonov regularization scheme we develop several strategies to regularize the introduced method. Various numerical tests for both standard and non-standard homogenization problems are given to show the efficiency and feasibility of the proposed method.