Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Jan 30, 2014, 02:00 pm

Numerical solution of binary and multicomponent phase field models

Dr. Carsten Gräser (FU Berlin)

Abstract:
Phase field models are a widely used approach to describe transition and separation processes of two or more different species by gradient flows for non-convex energy functionals. Physically motivated energies
often incorporate singular terms leading to degenerate nonlinear pdes or nonsmooth complementarity problems. While it is common to replace those terms by smooth approximations to avoid numerical difficulties, numerical examples show that this has a strong impact on coarsening rates of solutions.

We present numerical methods for phase field models under the presence of singular or nonsmooth terms. Combining nonsmooth Newton and multigrid techniques those methods are robust with respect to the nonlinearity and exhibit mesh independence and global convergence. Efficiency and robustness are illustrated for binary
and multicomponent Cahn--Hilliard and Allen--Cahn equations with logarithmic and obstacle potentials.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen