A separating oscillation method of recovering the \(G\)-limit in standard and non-standard homogenization problems (Q2794611)

This paper deals with a nonlinear inverse problem concerned with the identification of a macroscopic coefficient in a linear elliptic equation with oscillating coefficients (oscillations are here supposed to come from non-periodic distributions of microstructures). The approach is based on a technique that is able to separate the computation of the deviation of the G-limit from the weak convergence of the parameter-dependent sequence of coefficients. The ill-posedness is treated via a Tikhonov regularisation scheme. Numerical examples illustrate the methodology for both periodic and non-periodic test cases.