Truncated nonsmooth Newton multigrid methods for simplex-constrained minimization problems

Abstract

We present a multigrid method for the minimization of strongly convex functionals defined on a finite product of simplices. Such problems result, for example, from the discretization of multi-component phase-field problems. Our algorithm is globally convergent, requires no regularization parameters, and achieves multigrid convergence rates. We present numerical results for the vector-valued Allen--Cahn equation and observe that the convergence rate is independent from the temperature parameter and the number of components.