Dr. Bettina Schieche

Technische Universität Darmstadt
Fachbereich Mathematik
AG Numerik und Wiss. Rechnen / Graduate School CE
Dolivostr. 15
64293 Darmstadt

E-Mail: schiechemathematik.tu-darmstadt.de
Tel: +49 (0)6151 16-2488
Fax: +49 (0)6151 16-2747

 

Unsteady Adaptive Stochastic Collocation Methods on Sparse Grids

Numerical simulations become more reliable if random effects are taken into account. To this end, the describing parameters can be expressed by correlated random fields, which leads to partial differential equations (PDEs) with random parameters. Common numerical methods to solve such problems are spectral methods of Galerkin type and stochastic collocation on sparse grids. We focus on stochastic collocation, because it decouples the random PDE into a set of deterministic equations that can be solved in parallel. By mean of interpolation, the procedure provides a functional dependency between random input parameters and response of the system.

The aim of this work is to derive error estimates for adaptive strategies in order to gain efficiency for the more and more complex problems arising in Computational Engineering. We want to combine stochastic collocation with an adjoint approach in order to estimate and control the error of some stochastic quantity, such as the mean or variance of a solution functional.

 

Publications

  • B. Schieche and J. Lang, Uncertainty Quantification for Thermo-Convective Poiseuille Flow Using Stochastic Collocation, to appear in Int. J. of Computational Science and Engineering
  • B. Schieche, Unsteady Adaptive Stochastic Collocation Methods on Sparse Grids, Dissertation, TU Darmstadt (2012), ISBN 978-3-8439-0762-0 (Verlag Dr. Hut)
  • B. Schieche, Adaptive Stochastic Collocation on Sparse Grids, GAMM Proceedings 2012, 653-654
  • B. Schieche and J. Lang, Stochastic Analysis of Nusselt Numbers for Natural Convection with Uncertain Boundary Conditions, 2010, Preprint FB4, TUD, 2608
  • B. Schieche, Stochastische Finite Elemente, Diplomarbeit, TU Darmstadt (2009)

Talks

  • B. Schieche, Analysis and Application of PDEs with Random Parameters, 2012, 2nd Workshop on Sparse Grids and Applications (SGA), München
  • B. Schieche, Analysis and Application of PDEs with Random Parameters, 2012, European Seminar on Computing (ESCO), Pilsen, Czech Republic
  • B. Schieche, Adjoint Error Estimation for Stochastic Collocation Methods, 2012, SIAM Conference on Uncertainty Quantification (UQ), Raleigh, North Carolina, USA
  • B. Schieche, Adaptive Stochastic Collocation on Sparse Grids, 2012, Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Darmstadt
  • B. Schieche, Adjoint Error Estimation for Stochastic Collocation Methods, 2011, 2nd International Conference on Computational Engineering (ICCE), Darmstadt
  • B. Schieche, Unsteady Adaptive Stochastic Collocation Methods on Sparse Grids, 2011, annual retreat of DFG Graduate School of Computational Engineering, Heppenheim
  • B. Schieche, Unsteady Adaptive Stochastic Collocation Methods on Sparse Grids, 2010, annual retreat of DFG Graduate School of Computational Engineering, Heppenheim

Poster Presentations

  • B. Schieche, Adaptive Stochastic Collocation on Sparse Grids, 2011, Workshop on Numerical Analysis of Multiscale Problems & Stochastic Modelling, Linz, Austria
  • B. Schieche, Uncertainty Quantification for Poiseuille Flow Using Stochastic Collocation, 2010, International Workshop on Multi-Scale Methods in Computational Engineering, Darmstadt

 

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