Preprint No.
A-02-04
Ralf Kornhuber, Rolf Krause
On multigrid methods for vector-valued Allen-Cahn equation with
obstacle potential
Abstract:
Phase field models provide a well-established
framework for the mathematical description to free
boundary problems for phase transitions.
In this paper, we consider multicomponent phase transitions as described by
a vector-valued Allen-Cahn equation with obstacle potential.
Semi-implicit discretization in time is unconditionally stable but,
after finite element discretization in space,
leads to large non-smooth algebraic systems.
So far, fast solvers for such kind of
problems were not available. As a consequence,
explicit schemes are applied,
in spite of severe stability restrictions on the time step.
We present a new class of multigrid methods
based on successive minimization in the direction of
well selected search directions and prove global convergence.
Numerical experiments illustrate the
reliability and efficiency of our method.
Keywords: multigrid methods, constrained minimization, phase fields models
Mathematics Subject Classification (MSC00): 65K10, 65M55, 65N55, 65N22
Language: ENG
Available: Pr-A-02-04.ps,
Pr-A-02-04.ps.gz
Contact: Ralf Kornhuber, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (kornhube@math.fu-berlin.de)
[Home Page] - [Up] - [Search] - [Help] - Created: 20020821 -