Research Foci
- Adaptive and Hierarchical Model Reduction
- A posteriori error estimates
- A priori error estimates
- Scientific Computing
- Domain Decomposition Methods
- Solid Mechanics
- Surface and subsurface flow
Doctoral AbstractThesis
A dimensional reduction approach based on the application of reduced basis methods in the context of hierarchical model reduction
- Supervisor
- Professor Dr. Mario Ohlberger
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
CV
Academic Education
- PhD in Mathematics, University of Münster
- Studium im Fach Mathematik mit Nebenfach Wissenschaftliche Politik an der Albert-Ludwigs-Universität Freiburg
Positions
- Assistant Professor, Department of Applied Mathematics, University of Twente, Netherlands
- Postdoctoral Research and Teaching Associate, Institute for Computational and Applied Mathematics, University of Münster
- Postdoctoral Research Associate, Department of Mechanical Engineering, Massachusetts Institute of Technology, USA
- Teaching and Research Assistant, Institute for Computational and Applied Mathematics, University of Münster
Honors
- Erstklassig! WWU Mentoring-Programm für Wissenschaftlerinnen – Universität Münster
- Stipendium – e-fellows.net
Teaching
- Lecture: Numerische Mehrskalenmethoden und Modellreduktion [108037]
(in cooperation with Mario Ohlberger)- Seminar: Masterseminar: Numerische Mathematik in den Lebenswissenschaften [108046]
(in cooperation with Mario Ohlberger)- Practical: Einführung in die Programmierung mit C++ [106231]
- Seminar: Masterseminar: Effiziente numerische Methoden mit Anwendungen in der Biologie und Medizin [104223]
(in cooperation with Mario Ohlberger)- Seminar: Bachelorseminar: Effiziente numerische Methoden mit Anwendungen in der Biologie und Medizin [104504]
(in cooperation with Mario Ohlberger)- Lecture: Modellreduktion für partielle Differentialgleichungen [102399]
- Practice: Praktikum zur Modellreduktion für Partielle Differentialgleichungen [102162]
(in cooperation with Julia Brunken)- Seminar: Biomedizinische Modellierung und Modellreduktion [104860]
(in cooperation with Felix Schindler, Patrick Henning and Mario Ohlberger)- Seminar: Biomedizinische Modellierung und Modellreduktion [100948]
(in cooperation with Christian Engwer and Mario Ohlberger)- Practical: Einführung in die Programmierung mit MATLab [103585]
(in cooperation with Mario Ohlberger)- Seminar: Bachelorseminar: Angewandte Mathematik [101263]
(in cooperation with Christian Engwer, Mario Ohlberger, Martin Burger, Frank Wübbeling and Chantal Oberson Ausoni)- Practical: Einführung in die Programmierung mit MATLab [101297]
(in cooperation with Mario Ohlberger and Stephan Rave)- Practice: Übungen zur Numerischen Analysis [101244]
(in cooperation with Christian Himpe and Mario Ohlberger)- Seminar: Moderne Methoden der Nichtlinearen Analysis [102238]
(in cooperation with Angela Stevens)- Seminar: Modellreduktion [102689]
(in cooperation with Mario Ohlberger)- Practical: Einführung in die Programmierung mit MATLab [102640]
(in cooperation with Mario Ohlberger)- Seminar: Bachelorseminar: Angewandte Mathematik [102676]
(in cooperation with Mario Ohlberger)- Seminar: Diplomandenseminar: Numerik partieller Differentialgleichungen [102695]
(in cooperation with Martin Drohmann, Patrick Henning and Mario Ohlberger)- Seminar for PhD students: Gebietszerlegungsmethoden [102744]
(in cooperation with Martin Drohmann and Mario Ohlberger)- Practice: Übungen zu den Partiellen Differentialgleichungen [100259]
(in cooperation with Christopher Deninger) - Seminar: Masterseminar: Numerische Mathematik in den Lebenswissenschaften [108046]
Project
- Co-operative Project "Adaptive hydrological modeling with application in water resource management", Sub-project "Multi-scale modelling and system reduction for ground water flow" – AdaptHydroMod ()
Participation in Federally Funded Joint Project: Bundesministerium für Forschung, Technologie und Raumfahrt | Project Number: 03OMPAF1
Publications
Selection
- Smetana, Kathrin Patera Anthony T. . “Optimal local approximation spaces for component-based static condensation procedures.” SIAM J. Sci. Comput. 38 (5): A3318––A3356.. doi: 10.1137/15M1009603.
- Smetana, Kathrin. . “A new certification framework for the port reduced static condensation reduced basis element method.” Computer Methods in Applied Mechanics and Engineering 283: 352–383. doi: 10.1016/j.cma.2014.09.020.
- Ohlberger, M, and Smetana, K. . “A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.” SIAM Journal on Scientific Computing 36 (2): A714–A736.. doi: 10.1137/130939122.
Complete List
- Smetana, K, and Ohlberger, M. . “Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques.” M2AN Math. Model. Numer. Anal. 51 (2): 641–677. doi: 10.1051/m2an/2016031.
- Buhr, Andreas Smetana Kathrin. . “Randomized Local Model Order Reduction.” arXiv:1706.09179.
- Smetana, Kathrin Patera Anthony T. . “Optimal local approximation spaces for component-based static condensation procedures.” SIAM J. Sci. Comput. 38 (5): A3318––A3356.. doi: 10.1137/15M1009603.
- Ohlberger, M, and Smetana, K. . “Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approach.” J. Comp. Phys. 321: 1185–1205. doi: 10.1016/j.jcp.2016.06.021.
- Brunken, Julia Leibner Tobias, and Ohlberger, Mario Smetana Kathrin. . “Problem adapted hierachical model reduction for the Fokker-Planck equation.” in ALGORITMY 2016 Proceedings of contributed papers and posters, edited by Angela Handlovicova and Daniel Sevcovic. Bratislava: Publishing House of Slovak University of Technology.
- Ohlberger, Mario Smetana Kathrin. . “A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.” Oberwolfach Reports 2/2015: 141–144. doi: 10.4171/OWR/2015/2.
- Smetana, Kathrin. . “A new certification framework for the port reduced static condensation reduced basis element method.” Computer Methods in Applied Mechanics and Engineering 283: 352–383. doi: 10.1016/j.cma.2014.09.020.
- Ohlberger, M, and Smetana, K. . “A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.” SIAM Journal on Scientific Computing 36 (2): A714–A736.. doi: 10.1137/130939122.
- Berninger, H, Ohlberger, M, Sander, O, and Smetana, K. . “Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions.” Math. Models and Methods in Appl. Sciences 24 (5): 901–936. doi: 10.1142/S0218202513500711.
- Bastian, P, Berninger, H, Dedner, A, Engwer, C, Henning, P, Kornhuber, R, Kröner, D, Ohlberger, M, Sander, O, Schiffler, G, Shokina, N, and Smetana, K. . “Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management.” in Progress in Industrial Mathematics at ECMI 2010, Vol. 17 of Mathematics in Industry, Springer. doi: 10.1007/978-3-642-25100-9_65.
- Ohlberger, M, and Smetana, K. . “A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems.” in Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011, edited by Aubry D. et al.. CIMNE.
Supervised Doctoral Study
Scientific Talks
- Smetana, Kathrin : “Localized Model Order Reduction”. Absolventenseminar Numerical Mathematics University of Ulm, University of Ulm, Ulm, Germany, .
- Smetana, Kathrin : “A Posteriori Error Estimation for Localized Model Order Reduction”. WCCM XII and APCOM VI. Minisymposium: A Posteriori Estimation and Adaptive Control of Discretization and Modeling Errors in Computational Sciences and Engineering (J. Lang, S. Prudhomme, K. Van der Zee), Seoul, South Korea, .
- Smetana, Kathrin : “Efficient approximation of optimal local approximation spaces for localized model order reduction”. ECCOMAS Congress 2016. Minisymposium: Reduced Basis, POD and PGD Model Order Reduction Techniques (F. Chinesta, E. Cueto, A. Huerta, P. Ladeveze, G. Rozza), Crete Island, Greece, .
- Smetana, Kathrin : “Localized Model Order Reduction”. Seminar Numerische Mathematik und Mechanik, University of Cologne, Cologne, Germany, .
- Smetana, Kathrin : “Optimal Local Approximation Spaces for Component-based Static Condensation Procedures”. Joint annual meeting of GAMM and DMV 2016, Braunschweig, Germany, .
- Smetana, Kathrin : “Localized Model Order Reduction”. Seminar Applied Mathematics Münster, University of Münster, Münster, Germany, .