Research Areas
- 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 Thesis
A dimensional reduction approach based on the application of reduced basis methods in the context of hierarchical model reduction
- Betreuer
- Professor Dr. Mario Ohlberger
- Doctoral Subject
- Mathematik
- Doctoral Degree
- Dr. rer. nat.
- Awarded by
- Department 10 – Mathematics and Computer Science
CV
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
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Teaching
- Praktikum: Introduction to Programming with C++ [106231]
- Seminar: Master Seminar Applied Mathematics [108046]
(in cooperation with Prof. Dr. Mario Ohlberger) - Vorlesung: Numerical multiscale methods and model reduction [108037]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Master Seminar Efficient Numerical Methods with Applications to Biology and Medicine [104223]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Bachelor Seminar: Efficient Numerical Methods with Applications to Biology and Medicine [104504]
(in cooperation with Prof. Dr. Mario Ohlberger) - Übung: Lab Course: Model Order Reduction for Partial Differential Equations [102162]
(in cooperation with Julia Brunken) - Vorlesung: Model Reduction for Parametrised Partial Differential Equations [102399]
- Seminar: Biomedical Modellling and Model Reduction [104860]
(in cooperation with Dr. Felix Schindler, Prof. Dr. Mario Ohlberger) - Seminar: Other Courses [100948]
(in cooperation with Prof. Dr. Christian Engwer, Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Programming with MATLab [103585]
(in cooperation with Prof. Dr. Mario Ohlberger) - Übung: Tutorial Numerical Analysis [101244]
(in cooperation with Dr. Christian Himpe, Prof. Dr. Mario Ohlberger) - Praktikum: Introduction to Programming with MATLab [101297]
(in cooperation with Dr. Stephan Rave, Prof. Dr. Mario Ohlberger) - Seminar: Bachelor Seminar: Applied Mathematics [101263]
(in cooperation with Prof. Dr. Christian Engwer, Prof. Dr. Mario Ohlberger, Dr. Frank Wübbeling) - Seminar: Modern Methods in Non linear Analysis [102238]
(in cooperation with Prof. Dr. Angela Stevens) - Praktikum: Introduction to Programming with MATLab [102640]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Model Reduction [102689]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Diplomandenseminar: Numerik partieller Differentialgleichungen [102695]
(in cooperation with Prof. Dr. Mario Ohlberger) - Seminar: Bachelorseminar: Angewandte Mathematik [102676]
(in cooperation with Prof. Dr. Mario Ohlberger) - Übung: Übungen zu den Partiellen Differentialgleichungen [100259]
(in cooperation with Prof. Dr. Christopher Deninger) - Doktorandenseminar: 1.3.1 First academic year [102744]
(in cooperation with Prof. Dr. Mario Ohlberger)
Project
- AdaptHydroMod – Co-operative Project "Adaptive hydrological modeling with application in water resource management", Sub-project "Multi-scale modelling and system reduction for ground water flow" ( – )
participations in bmbf-joint project: Federal Ministry of Education and Research | Project Number: 03OMPAF1
- AdaptHydroMod – Co-operative Project "Adaptive hydrological modeling with application in water resource management", Sub-project "Multi-scale modelling and system reduction for ground water flow" ( – )
Publications
Selection
- 10.1137/15M1009603. . ‘Optimal local approximation spaces for component-based static condensation procedures.’ SIAM J. Sci. Comput. 38, No. 5: A3318––A3356. doi:
- . . ‘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.
- . . ‘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, No. 2: A714–A736. doi: 10.1137/130939122.
Complete List
- . . ‘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, No. 2: 641–677. doi: 10.1051/m2an/2016031.
- . . Randomized Local Model Order Reduction : arXiv:1706.09179, . [submitted / under review]
- 10.1137/15M1009603. . ‘Optimal local approximation spaces for component-based static condensation procedures.’ SIAM J. Sci. Comput. 38, No. 5: A3318––A3356. doi:
- . . ‘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.
- . . ‘Problem adapted hierachical model reduction for the Fokker-Planck equation.’ In ALGORITMY 2016 Proceedings of contributed papers and posters, edited by , 13–22. Bratislava: Slovak University of Technology in Bratislava.
- . . ‘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.
- . . ‘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.
- . . ‘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, No. 2: A714–A736. doi: 10.1137/130939122.
- . . ‘Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions.’ Math. Models and Methods in Appl. Sciences 24, No. 5: 901–936. doi: 10.1142/S0218202513500711.
- . . ‘Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management.’ In Progress in Industrial Mathematics at ECMI 2010, 561––567.: Springer,. doi: 10.1007/978-3-642-25100-9_65.
- . . ‘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 , 343–354.: International Center for Numerical Methods in Engineering (CIMNE), Barcelona.
Supervised Doctoral Study
Brunken, Julia Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations 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, .
Dr. Kathrin Smetana
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)