Dr. Mark Kärcher

Dr. Mark Kärcher

Member

AICES

Research

Model Reduction and A Posteriori Error Estimation for Variational Data Assimilation (4D-Var)

Advisor / Co. Advisor

Prof. Grepl / Prof. Volkwein

Dissertation

Reduced Basis A Posteriori Error Estimation for PDE-Constrained Optimization

Contact

AICES Graduate School
RWTH Aachen University
Schinkelstr. 2a
D-52062 Aachen
Germany

Office: 202
Phone: +49 (0) 241 80 99 746
Email: kaercher@aices.rwth-aachen.de

Education

  • since 11/2016: Post-doctoral researcher, AICES, RWTH Aachen
  • 05/2011 - 10/2016: PhD in applied mathematics, AICES & IGPM, RWTH Aachen
  • 10/2005 - 04/2011: Diploma in applied mathematics, TU München, KTH Stockholm

Research Interests

  • Reduced Basis Methods
  • PDE-Constrained Optimization
  • Variational Data Assimilation (4D-Var)

Publications

Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation
M. Kärcher, S. Boyaval, M.A. Grepl, and K. Veroy
(submitted)
preprint available

Certified Reduced Basis Methods for Parametrized Distributed Optimal Control Problems with Control Constraints
E. Bader, M. Kärcher, M.A. Grepl, and K. Veroy
SIAM Journal on Scientific Computing, Volume 38, Issue 06, 2016, pp. A3921-A3946.
preprint available | http://dx.doi.org/10.1137/16M1059898

Certified Reduced Basis Methods for Parametrized Distributed Optimal Control Problems
M. Kärcher, M.A. Grepl, and K. Veroy
(submitted)
preprint available

A Posteriori Error Estimation for Reduced Order Solutions of Parametrized Parabolic Optimal Control Problems
M. Kärcher and M.A. Grepl
ESAIM: Mathematical Modelling and Numerical Analysis, Volume 48, Issue 06, 2014, pp. 1615-1638.
preprint available | http://dx.doi.org/10.1051/m2an/2014012

A Certified Reduced Basis Method for Parametrized Elliptic Optimal Control Problems
M. Kärcher and M.A. Grepl
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20, Issue 02, 2014, pp. 416-441.
preprint available | http://dx.doi.org/10.1051/cocv/2013069

Reduced Basis A Posteriori Error Bounds for Parametrized Linear-Quadratic Elliptic Optimal Control Problems
M.A. Grepl and M. Kärcher
C. R. Acad. Sci. Paris, Ser. I 349, 2011, pp. 873-877.
preprint available | http://dx.doi.org/10.1016/j.crma.2011.07.010

Dissertation

Certified reduced basis methods for parametrized PDE-constrained optimization problems
PDF | publication record

Presentations

OCIP 2014, Workshop on Numerical Methods for Optimal Control and Inverse Problems,
Technische Universität München, Germany (Mar 3-5, 2014)

Reduced Basis Summer School 2013,
Kopp, Germany (Aug 20-23, 2013)

SIAM CSE 2013, SIAM Conference on Computational Science and Engineering,
Boston, USA (Feb 25 - Mar 1, 2013)

WONAPDE 2013, Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations,
Concepción, Chile (Jan 14-18, 2013)

Oberseminar: Mathematische Optimierung,
Technische Universität München, Germany (Nov 12, 2012)

MoRePas 2, Second International Workshop on Model Reduction for Parametrized Systems,
Guenzburg, Germany (Oct 2-5, 2012)

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)

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

PhD Summer School on Reduced Basis Methods,
University of Ulm, Germany (Oct 25-28,2011)

IFIP 2011, 25th IFIP TC 7 Conference on System Modeling and Optimization,
Berlin, Germany (Sep 12-16, 2011)

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