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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
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