Kornhuber, R. and Krause, R. (2003) On multigrid methods for vectorvalued AllenCahn equations. In: Proceedings of the fourteenth international conference on domain decomposition methods. National Autonomous University of Mexico (UNAM), Mexico City, Cocoyoc, Mexico, pp. 307314. ISBN 9703208592

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Abstract
In this paper, we consider multicomponent phase transitions as described by a vectorvalued AllenCahn equation with obstacle potential. Semiimplicit discretization in time is unconditionally stable but, after finite element discretization in space, leads to large nonsmooth 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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