A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures

The goal of this paper is to describe the oscillatory microstructure that can emerge from minimizing sequences for nonconvex energies. We consider integral functionals are defined on real valued (scalar) functions $u(x)$ which in gradient $\nabla u$ and possibly also $u$. To characterize microstructures these energies, we minimize associated relaxed energy using two novel approaches: i) a semi-analytical method based control systems theory, ii) numerical scheme combines convex splitting together with modified version split Bregman algorithm. These solutions then used gain information about original problem spatial distribution microstructure.