|Preprint-No.:||< 384 >||Published in:||March 2014||PDF-File:||IGPM384.pdf|
|Title:||Truncated Nonsmooth Newton Multigrid Methods for Simplex-Constrained Minimization Problems|
|Authors:||Carsten Gräser, Oliver Sander|
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|