MATHEON-ICM WORKSHOP on Free Boundaries and Materials Modeling - Abstract

Gräser, Carsten

Multigrid methods for phase field models

The discretization of phase field models leads to large systems of coupled nonlinear equations. Unfortunately usual Newton methods fail in general for these problems since the nonlinearties are nonsmooth or degenerate to nonsmooth operators for small temperatures. We show that nonsmooth Newton and multigrid techniques based on problem inherent energies can be used to construct fast, robust, and globally convergent algorithms even for the degenerate nonsmooth case.