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IGPM384.pdf March 2014 
TITLE 
Truncated Nonsmooth Newton Multigrid Methods for SimplexConstrained 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 multicomponent phaseﬁeld problems. Our algorithm is globally convergent, requires no regularization parameters, and achieves multigrid convergence rates. We present numerical results for the vectorvalued 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, phaseﬁeld models, convex minimization 