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MPI Project

Fast solvers for phase field models




Project leader:
  • Dr. Martin Stoll
    Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg, Germany
    Tel: +49 (0)391-6110-805
    E-mail: stollm@mpi-magdeburg.mpg.de
Researcher:
  • Jessica Bosch
    Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
    Computational Methods in Systems and Control Theory,
    Sandtorstr. 1, 39106 Magdeburg, Germany
    Tel: +49 (0)391-6110-384
    E-mail: bosch@mpi-magdeburg.mpg.de
Duration: since January 2012

Project description:
Phase field models have a wide area of application such as in materials science to model coarsening in alloys, in image processing for image inpainting or in polymer science. These models are usually based on an energy functional depending on the phase field variable. The Cahn-Hilliard model is an example of a phase field model based on a diffuse interface. The underlying energy includes an obstacle potential. The model is usually formulated as a variational inequality of fourth order. We consider the efficient solution of various Cahn-Hilliard systems.



Related publications:

@TECHREPORT{BosS15b,
author = {Bosch, J. and Stoll, M.},
title = {A fractional inpainting model based on the vector-valued {C}ahn--{H}illiard equation},
journal = {SIAM J. Imaging Sci.},
volume = {8},
number = {4},
pages = {2352--2382},
year = {2015},
doi = {10.1137/15M101405X},
URL = {http://dx.doi.org/10.1137/15M101405X},
eprint = {http://dx.doi.org/10.1137/15M101405X} }
A fractional inpainting model based on the vector-valued Cahn--Hilliard equation;
Jessica Bosch, Martin Stoll;
SIAM Journal on Imaging Sciences  :  Vol. 8, No. 4, pp. 2352-2382;
2015.
@TECHREPORT{BosS15a,
author = {Bosch, J. and Stoll, M.},
title = {Preconditioning for vector-valued {C}ahn--{H}illiard equations},
journal = {SIAM J. Sci. Comput.},
volume = {37},
number = {5},
pages = {S216--S243},
year = {2015},
doi = {10.1137/14M0973633},
URL = {http://dx.doi.org/10.1137/14M0973633},
eprint = {http://dx.doi.org/10.1137/14M0973633} }
Preconditioning for vector-valued Cahn-Hilliard equations;
Jessica Bosch, Martin Stoll;
SIAM Journal on Scientific Computing  :  Vol. 37, No. 5, pp. S216-S243;
2015.
@article{BosSB14,
author = {Bosch, J. and Stoll, M. and Benner, P.},
title = {Fast solution of {C}ahn--{H}illiard variational inequalities using implicit time discretization and finite elements},
journal = {J. Comput. Phys.},
volume = {262},
pages = {38--57},
year = {2014},
doi = {http://dx.doi.org/10.1016/j.jcp.2013.12.053},
url = {http://www.sciencedirect.com/science/article/pii/S0021999114000084} }
Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements;
Jessica Bosch, Martin Stoll, Peter Benner: ;
Journal of Computational Physics  :  Vol. 262, pp. 38-57;
2014.
@article{BosKSetal14,
author = {Bosch, J. and Kay, D. and Stoll, M. and Wathen, A.~J.},
title = {Fast Solvers for {C}ahn--{H}illiard Inpainting},
journal = {SIAM J. Imaging Sci.},
volume = {7},
number = {1},
pages = {67--97},
year = {2014},
doi = {10.1137/130921842},
url = {http://dx.doi.org/10.1137/130921842} }
Fast Solvers for Cahn-Hilliard Inpainting;
Jessica Bosch, David Kay, Martin Stoll, Andrew J. Wathen;
SIAM Journal on Imaging Sciences  :  Vol. 7, No. 1, pp. 67-97;
2013.
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Jessica Bosch, bosch@mpi-magdeburg.mpg.de