MPI-Projekt
Schnelle Löser für Phasenfeldmodelle
Projektleiter:
- Dr. Martin Stoll
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg
Tel: +49 (0)391-6110-805
E-mail: stollm@mpi-magdeburg.mpg.de
- Jessica Bosch
Max Planck Institut for Dynamics Complex Technical Systems Magdeburg,
Computational Methods in Systems and Control Theory,
Sandtorstr. 1, 39106 Magdeburg
Tel: +49 (0)391-6110-384
E-mail: bosch@mpi-magdeburg.mpg.de
- Projektbeschreibung:
-
Phasenfeldmodelle besitzen ein breites Anwendungsspektrum, zum Beispiel in der Materialwissenschaft zur Modellierung von Entmischungen in Legierungen, in der Bildverarbeitung für das Image Inpainting oder in der Polymerwissenschaft. Die Modelle beruhen im Allgemeinen auf einem Energiefunktional, welches von der Phasenfeldvariable abhängt. Das Cahn-Hilliard Modell ist ein Beispiel eines Phasenfeldmodells mit stetigem Phasenübergang. Das zugrundeliegende Energiefunktional enthält ein Hindernispotential. Das Modell wird üblicherweise als Variationsungleichung von vierter Ordnung formuliert. Wir untersuchen das effiziente Lösen von verschiedenen Cahn-Hilliard Systemen. - Veröffentlichungen:
- @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 = {https://dx.doi.org/10.1137/15M101405X},
eprint = {https://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 = {https://dx.doi.org/10.1137/14M0973633},
eprint = {https://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 = {https://dx.doi.org/10.1016/j.jcp.2013.12.053},
url = {https://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 = {https://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.