Repository: Freie Universit├Ąt Berlin, Math Department

On multigrid methods for vector-valued Allen-Cahn equations

Kornhuber, R. and Krause, R. (2003) On multigrid methods for vector-valued Allen-Cahn equations. In: Proceedings of the fourteenth international conference on domain decomposition methods. National Autonomous University of Mexico (UNAM), Mexico City, Cocoyoc, Mexico, pp. 307-314. ISBN 970-32-0859-2


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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. Similar multigrid techniques have been applied in a different context. Numerical experiments illustrate the reliability and efficiency of our method

Item Type:Book Section
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1834
Deposited By: Ekaterina Engel
Deposited On:06 Mar 2016 12:37
Last Modified:03 Mar 2017 14:42

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