Dr. Bernhard Wieland  

CONTACT

  • Postal Address
  • Institut für Numerische Mathematik
  • Universität Ulm
  • D-89069 Ulm
    Germany

 

FIELD OF RESEARCH

REDUCED BASIS METHODS (RBM)
for parameterized PDEs with stochastic influences

  • PDEs with stochastic influences
    • stochasticity in coefficients, right-hand side, domain
    • linear and nonlinear, stationary and instationary PDEs
  • Affine decompositions of stochastic processes for application within the RBM
    • connection of the Karhunen-Loeve expansion with the RBM
    • modifications of the empirical interpolation method (EIM)
    • implicit partitions of probability spaces
  • Efficient and rigorous a-posteriori error analysis
    • error bounds for reduced random solutions
    • error bounds for output functionals (linear and quadratic)
    • error bounds moments and variance (quadratic output problems)
  • Mini-introduction to RBM (1 page, in German) 

 

PUBLICATIONS

2013-10Bernhard Wieland
Implicit Partitioning Methods for Unknown Parameter Domains - in the Context of the Reduced Basis Method 
Preprint, Universität Ulm, October 2013
2013-04Bernhard Wieland
Reduced Basis Methods for Partial Differential Equations with Stochastic Influences
PhD Thesis, Ulm University, April 2013
2013-02Bernard Haasdonk, Karsten Urban and Bernhard Wieland
Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences using the Karhunen-Loève Expansion 
SIAM/ASA J. Uncertainty Quantification, 1:79–105, 2013.
Press release: launch of SIAM/ASA JUQ Volume 1
2012-09 Karsten Urban and Bernhard Wieland
Reduced Basis Methods for Quadratically Nonlinear Partial Differential Equations with Stochastic Influences 
CD-ROM Proceedings ECCOMAS 2012, Vienna, Austria (BibTex)
Available as Preprint, Universität Ulm, July 2012 
2012-06Karsten Urban and Bernhard Wieland
Affine Decompositions of Parametric Stochastic Processes for Application within Reduced Basis Methods 
Proceedings MATHMOD 2012, 7th Vienna International Conference on Mathematical Modelling, 2012
2012-04 Bernard Haasdonk, Karsten Urban and Bernhard Wieland
Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences using the Karhunen-Loève Expansion 
Preprint, Universität Ulm, April 2012

  

SELECTED TALKS

2013-01-23Reduced Basis Methods for parametrized PDEs with stochastic influences 
@ 29th GAMM-Seminar Leipzig on Numerical Methods for Uncertainty Quantification, Max Planck Institute for Mathematics in the Sciences, January 21-23, 2013
2012-10-03An Implicit Partitioning Method for Unknown Parameter Domains
@ Second International Workshop on Model Reduction for Parametrized Systems (MoRePaS II), Schloss Reisensburg, Günzburg, October 2-5, 2012
2012-09-11Reduced Basis Methods for quadratically nonlinear PDEs with stochastic influences
@ ECCOMAS 2012, 6th European Conference on Computational Methods in Applied Science and Engineering, Vienna, September 10-14, 2012
2012-08-29An Implicit Partitioning Method for Unknown Parameter Domains (in the context of RBMs with stochastic influences)
@ Workoshop on Reduced Basis Methods, Freudenstadt, August 28-31, 2012
2012-02-15Affine Decompositions of Parametric Stochastic Processes for Application within Reduced Basis Methods 
@ MathMod, Vienna Conference on Mathematical Modelling, Vienna, February 14 - 17, 2012
2011-11-21Affine Decompositions of Parametric Stochastic Processes for Application within RBM
@ Workshop on Advances in POD and RB Model Order Reduction, Konstanz
2011-10-25Reduced Basis Methods for PDEs on Stochastic Domains
@ Summer School on Reduced Basis Methods, Günzburg Reisensburg, October 25-28, 2011
2011-02-08Reduced Basis Methods for PDEs with Stochastic Influences
@SimTech Network Seminar Model Reduction, Control and Real Time Simulation, Stuttgart
2010-12-08Reduced Basis Methods for PDEs with Stochastic Influences 
@ Workshop on Reduced Basis Methods, Ulm, December 7-8, 2010
2010-07-12Reduced Basis Methods for Parametric PDEs with Stochastic Influences
@ Summer School Optimal Control of PDEs, Cortona, July 12-17, 2010

  

SHORT CV

12/2009 to 06/2013

Doctoral Student at the Institute for Numerical Mathematics at Ulm University
Supported by the German federal state of Baden-Württemberg according to the “State Postgraduate Scholarships Act“ (Landesgraduiertenförderungsgesetz)

10/2003 to 10/2009

Studies of Mathematics at Ulm University, Minor in Computer Science
Thesis: Speech Signal Noise Reduction with Wavelets 
Degree: Diplom Mathematiker

08/2007 to 05/2008

Studies in Applied Mathematics at Florida Institute of Technology in Melbourne, FL, United States of America 
Scholarship: Fulbright Travel Grant
Degree: MSc in Applied Mathematics

     

TEACHING

Sommersemester 2013: Numerik II, Übungen

Sommersemester 2013, 12, 11, 10: Mathematische Modellierung und Simulation in der Mechanik II: Dynamische Probleme, Übungen und Computerpraktikum

Wintersemester 2012/13, 11/12, 10/11: Mathematische Modellierung und Simulation in der Mechanik I: Statische Probleme, Übungen und Computerpraktikum

Sommersemester 2012: Modellierung und Simulation II für CSE, Übungen und Computerpraktikum