A separating oscillation method of recovering the G-limit in standard and non-standard homogenization problems. (11th January 2016) - Gulliksson, Mårten; Holmbom, Anders; Persson, Jens; Zhang, Ye
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.