Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy

Abstract

We present efficient and robust multigrid methods for the solution of large, nonlinear, non-smooth systems as resulting from implicit time discretization of vector-valued Allen-Cahn equations with isotropic interfacial energy and logarithmic potential. The algorithms are shown to be robust in the sense that convergence is preserved for arbitrary values of temperature, including the deep quench limit. Numerical experiments indicate that the convergence speed as well is independent of temperature.