A numerical study for the homogenisation of one-dimensional models describing the motion of dislocations
Mohamed-Amin Ghorbel, Philippe Hoch, Régis Monneau · International Journal of Computing Science and Mathematics · 2008
In this paper we are interested in the collective motion of dislocations defects in crystals. Mathematically, we study the homogenisation of a non-local Hamilton-Jacobi equation. We prove some qualitative properties on the effective Hamiltonian and we provide a numerical scheme which is proved to be monotone under some suitable CFL conditions. Using this scheme, we compute numerically the effective Hamiltonian. Furthermore, we provide numerical computations of the effective Hamiltonian for several models corresponding to the dynamics of dislocations where no theoretical analysis is available.