384 RWTH Publication No: 230298        2014        IGPM384.pdf
TITLE Truncated Nonsmooth Newton Multigrid Methods for Simplex-Constrained Minimization Problems
AUTHORS Carsten Gräser, Oliver Sander
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 con- vergence rate is independent from the temperature parameter and the number of components.
KEYWORDS multigrid, simplex constraints, phase-field models, convex minimization