Dr. Anna Lena Gerner

Dr. Anna Lena Gerner

Advisor / Co. Advisor

Prof. Karen Veroy-Grepl/ Prof. Arnold Reusken

Dissertation

Certified Reduced Basis Methods for Parametrized Saddle Point Problems

Contact

Anna-Lena Gerner, Dipl.-Math.
AICES Graduate School
RWTH Aachen University
Schinkelstr. 2
52062 Aachen
Germany

Phone: + 49 (0) 241 80 99 147
Fax: + 49 (0) 241 80 628 498
Email: gerner@aices.rwth-aachen.de

Education

08/2009 - 10/2012 Doctoral student at AICES Graduate School, RWTH Aachen University, Germany
10/2003 - 06/2009 Student of Mathematics at RWTH Aachen University, Germany
01/2008 - 06/2008 Student of Mathematics at The University of York, United Kingdom

Research Interests

Reduced Basis Methods
The reduced basis (RB) method is a model order reduction approach that permits the efficient yet reliable approximation of input-output relationships induced by a parametrized partial differential equation (PDE). As the method recognizes, the solutions to a parametrized PDE are not arbitrary members of the infinite-dimensional solution space, but rather reside or evolve on a much lower-dimensional manifold. Exploitation of this low-dimensionality is the key idea of the RB approach.

Project Outline
Although there are many existing examples of reduced order models for the Stokes and incompressible Navier-Stokes equations, only the RB method is endowed with practicable and rigorous a posteriori error bounds. Indeed, the development of rigorous RB error estimators presents the main methodological challenge, and has been the focus of recent research. The goal of the project is to further extend the RB method to deal with more generally parametrized incompressible fluid flow problems. Although such problems present additional difficulties in both theory and implementation, addressing these problems permits the use of the RB method for a wider, more relevant class of applications. For further details, please visit the project website.

Publications

Journal Publications

A-L Gerner, K Veroy, Reduced basis a posteriori error bounds for symmetric parametrized saddle point problems, submitted, preprint here.

A-L Gerner, K Veroy, Reduced basis a posteriori error bounds for the instationary Stokes equations, submitted, preprint here.

A-L Gerner, K Veroy, Certified reduced basis methods for parametrized saddle point problems, SIAM J. Sci. Comput., accepted, final preprint here.

A-L Gerner, K Veroy, Reduced basis a posteriori error bounds for the Stokes equations in parametrized domains: A penalty approach, Math. Models Methods Appl. Sci., 21 (2011), pp. 2103-2134. doi:10.1142/S0218202511005672 | final preprint here.

Other Publications

A-L Gerner, K Veroy, Reduced basis a posteriori error bounds for the instationary Stokes equations: A penalty approach, MATHMOD 2012 Conference Proceedings, accepted, final preprint here.

Presentations

ECCOMAS 2012, European Congress on Computational Methods in Applied Sciences and Engineering,
Vienna, Austria (Sep 10-14, 2012)

Reduced Basis Methods Workshop 2012,
Freudenstadt, Germany (Aug 28-31, 2012)

FEM2012, The 11th International Workshop on Finite Elements for Microwave Engineering,
Estes Park, CO, US (Jun 4-6, 2012)

HPSC 2012, 5th International Conference on High Performance Scientific Computing,
Hanoi, Vietnam (Mar 5-9, 2012)

MATHMOD 2012, 7th Vienna International Conference on Mathematical Modelling,
Vienna, Austria (Feb 15-17, 2012)

Workshop on Advances in POD and RB Model-Order Reduction,
University of Konstanz, Germany (Nov 21-25, 2011)

ICIAM 2011, 7th International Congress on Industrial and Applied Mathematics,
Vancouver, Canada (Jul 18-22, 2011)

CSC-Aachen Workshop on Parametric Model Order Reduction,
MPI Magdeburg, Germany (Jul 4-6, 2011)

Arbeitsgruppe Numerik Seminar,
University of Konstanz, Germany (Mar 28 - Apr 1, 2011)

SIAM CSE11, SIAM Conference on Computational Science and Engineering,
Reno, NV, US (Feb 28 - Mar 4, 2011)

Workshop on Reduced Basis Methods,
Ulm University, Germany (Dec 7-8, 2010)

ICNAAM 2010, 8th International Conference of Numerical Analysis and Applied Mathematics,
Rhodes, Greece (Sep 19-25, 2010)