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Numerical Methods for Multiscale Problems

Course Coordinator
Dr. Iryna Rybak
Begin 12.10.2015
Period 12.10.2015 - 06.02.2016
Time and place
Monday, 11:30 -- 13:00 (weekly), Pfaffenwaldring 57, 7.122
Tuesday, 14:00 -- 15:30 (every 2nd week), Pfaffenwaldring 57, 7.122
Practice sessions
Tuesday, 14:00 -- 15:30 (every 2nd week), Pfaffenwaldring 57, 7.122
Excercises
Modelling flows in heterogeneous porous media
Homogenization
Parameter calculation, homogenization
Numerical upscaling, MsFEM
Finite volumes
MsFVEM, domain decomposition
Contents
  • Mathematical models for flow and transport processes in porous media, surface flows und flows in coupled systems;
  • Development of macroscale models using averaging theories;
  • Numerical methods for multiscale problems (in space and time): finite volumes, multiscale finite elements, numerical upscaling, multigrid, domain decomposition and time-splitting schemes.
Modelling Numerical methods Numerical simulations
Modelling Numerical methods Numerical simulations
Literature J.-L. Auriault, C. Boutin, C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, 2009.
U. Hornung, Homogenization and Porous Media, 1996.
W. E, Principles of Multiscale Modeling, 2011.
Y. Efendiev, T. Hou, Multiscale Finite Element Methods: Theory and Applications, 2009.
B. Smith, P. Bjorstad, W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, 2004.
S. Whitaker, The Method of Volume Averaging, 1999.
Learning goals
  • Knowledge of classical models for fluid dynamics, flows in porous media and averaging techniques;
  • Ability to develop macroscale models and efficient numerical methods for multiscale problems.
Curricula M.Sc. Mathematics, M.Sc. SimTech, Dipl., LA.
Prerequisites
Basic knowledge of partial differential equations
ECTS 6
Examination

Oral exam (30 min)

Module assignment
67250 Numerical Methods for Multiscale Problems