Reduced Basis Methods (RBM)

Reduced Basis Methods are a model reduction tool for parameterized partial differential equations.

Focus:

• RBM for time-periodic problems
• RBM for space-time formulations
• RBM with adaptive offline computations
• RBM using wavelets
• (Time-dependent) parameter functions
• Parameter dependent domains
• Development of rigorous a posteriori error bounds for time-periodic problems

Time-Periodic PDEs

• Space-time formulations
• Existence and uniqueness
• Numerical Solvers: Fixed-point methods, space-time approaches

• K. Steih, Reduced Basis Methods for Time-Periodic Parametric Partial Differential Equations, PhD Thesis, 2014.
• K. Steih and K. Urban, <link fileadmin website_uni_ulm mawi.inst.070 urban papers su-adap-20140505-submitted.pdf download>Reduced Basis Methods based upon Adaptive Snapshot Computations. Preprint (submitted), 2014.
• S. Kestler, K. Steih and K. Urban. An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations. Preprint (submitted), 2013.
• K. Steih und K. Urban. Space-Time Reduced Basis Methods for Time-Periodic Partial Differential Equations. Proceedings MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, February 15-17, 2012.
• K. Steih und K. Urban. Space-Time Reduced Basis Methods for Time-Periodic Parametric Differential Equations. Preprint, University of Ulm (2012).
• K. Steih, Solving Markov Decision Processes by Simulation: a Model-Based Approach, Diploma Thesis, 2008.

• RB Summer School (PhD Workshop), Kopp, August 2013:
  Talk  Adaptive Space-Time Methods in Reduced Basis Methods
• WONAPDE, Fourth Chilean Workshop on Numerical Analysis of PDEs, Concepciòn, Chile, January 2013:
  Talk On Space-Time Approaches in Reduced Basis Methods
• Summer School "A Posteriori Error Control and Adaptivity", Zurich, August 2012
• MATHMOD, Vienna Conference on Mathematical Modelling, Vienna, February 2012:
  Talk Space-Time Approaches for Reduced Basis Methods
• Workshop on Advances in POD and RB Model Order Reduction, Konstanz, November 2011
• RB Summer School (PhD Workshop), Günzburg, October 2011:
  Talk Space-Time RBM for Time-Periodic Problems
• Workshop ''Reduced Basis Methods in High Dimensions'', Paris, June 2011
• Workshop on Reduced Basis Methods, Ulm, December 2010:
  Talk Time-periodic problems with time-dependent parameter functions
• Summer School "Optimal Control of PDEs", Cortona, Italy, July 2010

since 09/2011

Research Assistant in the Institute for Numerical Mathematics, Ulm University

09/2008 - 09/2011

PhD Student in the DFG Research Training Group 1100, Ulm University

10/2010

Research visit with Prof. Dr. Anthony T. Patera, Department for Mechanical Engineering, MIT, USA

10/2002 - 09/2008

Studies of Mathematics and Economics, Ulm University, Degree: Dipl. math. oec.
Diploma Thesis: "Solving Markov Decision Processes by Simulation: a Model-Based Approach"

09/2006 - 06/2007

Study visit (Erasmus) at the Faculté d'Economie appliquée, Université Paul Cézanne, Aix-en-Provence

SS 14

Exercises Numerical Finance
Exercises Programming (with C++, for CSE students)

WS 13/14

Exercises WiMa Praktikum 2
Seminar Modell reduction of linear systems

SS 13

Exercises High Performance Computing
Exercises Programming (with C++, for CSE students)

WS 12/13

Exercises Numerical Finance

SS 12

Exercises Numerics of partial differential equations 2
Exercises Programming (with C++, for CSE students)

WS 11/12

Exercises Numerical Mathematics I

SS 09

Reading Course Numerical Finance

SS 08

Exercises Introduction to Operations Research
(Institute for Optimization and Operations Research)

WS 07/08

Exercises Operations Research I
(Institute for Optimization and Operations Research)

Reduced Basis Methods (RBM)

Reduced Basis Methods are a model reduction tool for parameterized partial differential equations.

Focus:

• RBM for time-periodic problems
• RBM for space-time formulations
• RBM with adaptive offline computations
• RBM using wavelets
• (Time-dependent) parameter functions
• Parameter dependent domains
• Development of rigorous a posteriori error bounds for time-periodic problems

Time-Periodic PDEs

• Space-time formulations
• Existence and uniqueness
• Numerical Solvers: Fixed-point methods, space-time approaches

• K. Steih, Reduced Basis Methods for Time-Periodic Parametric Partial Differential Equations, PhD Thesis, 2014.
• K. Steih and K. Urban, <link fileadmin website_uni_ulm mawi.inst.070 urban papers su-adap-20140505-submitted.pdf download>Reduced Basis Methods based upon Adaptive Snapshot Computations. Preprint (submitted), 2014.
• S. Kestler, K. Steih and K. Urban. An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations. Preprint (submitted), 2013.
• K. Steih und K. Urban. Space-Time Reduced Basis Methods for Time-Periodic Partial Differential Equations. Proceedings MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, February 15-17, 2012.
• K. Steih und K. Urban. Space-Time Reduced Basis Methods for Time-Periodic Parametric Differential Equations. Preprint, University of Ulm (2012).
• K. Steih, Solving Markov Decision Processes by Simulation: a Model-Based Approach, Diploma Thesis, 2008.

• RB Summer School (PhD Workshop), Kopp, August 2013:
  Talk  Adaptive Space-Time Methods in Reduced Basis Methods
• WONAPDE, Fourth Chilean Workshop on Numerical Analysis of PDEs, Concepciòn, Chile, January 2013:
  Talk On Space-Time Approaches in Reduced Basis Methods
• Summer School "A Posteriori Error Control and Adaptivity", Zurich, August 2012
• MATHMOD, Vienna Conference on Mathematical Modelling, Vienna, February 2012:
  Talk Space-Time Approaches for Reduced Basis Methods
• Workshop on Advances in POD and RB Model Order Reduction, Konstanz, November 2011
• RB Summer School (PhD Workshop), Günzburg, October 2011:
  Talk Space-Time RBM for Time-Periodic Problems
• Workshop ''Reduced Basis Methods in High Dimensions'', Paris, June 2011
• Workshop on Reduced Basis Methods, Ulm, December 2010:
  Talk Time-periodic problems with time-dependent parameter functions
• Summer School "Optimal Control of PDEs", Cortona, Italy, July 2010

since 09/2011

Research Assistant in the Institute for Numerical Mathematics, Ulm University

09/2008 - 09/2011

PhD Student in the DFG Research Training Group 1100, Ulm University

10/2010

Research visit with Prof. Dr. Anthony T. Patera, Department for Mechanical Engineering, MIT, USA

10/2002 - 09/2008

Studies of Mathematics and Economics, Ulm University, Degree: Dipl. math. oec.
Diploma Thesis: "Solving Markov Decision Processes by Simulation: a Model-Based Approach"

09/2006 - 06/2007

Study visit (Erasmus) at the Faculté d'Economie appliquée, Université Paul Cézanne, Aix-en-Provence

SS 14

Exercises Numerical Finance
Exercises Programming (with C++, for CSE students)

WS 13/14

Exercises WiMa Praktikum 2
Seminar Modell reduction of linear systems

SS 13

Exercises High Performance Computing
Exercises Programming (with C++, for CSE students)

WS 12/13

Exercises Numerical Finance

SS 12

Exercises Numerics of partial differential equations 2
Exercises Programming (with C++, for CSE students)

WS 11/12

Exercises Numerical Mathematics I

SS 09

Reading Course Numerical Finance

SS 08

Exercises Introduction to Operations Research
(Institute for Optimization and Operations Research)

WS 07/08

Exercises Operations Research I
(Institute for Optimization and Operations Research)