Effective approaches and solution techniques for conditioning, robust design and control in the subsurface

• Applicants: Professor Dr. Hermann Georg Matthies; Professor Dr.-Ing. Wolfgang Nowak
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management
• Term: from 2011 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 195436228

• Final Report Year: 2016

Final Report Abstract

In this project not all the envisioned goals could be reached. Namely, the uncertainty quantification of the CO2 storage could not be performed, due to the aforementioned problems with the simulator software. Furthermore, the modelling and quantification of extreme events proved not to be feasible with spectral methods as planned, and probably needs more fundamental research. However, great progress could be achieved in the application of low-rank formats for the representation of the stochastic inputs as well as for the computational core, the output quantities, and the also the final post-processing of those quantities. Substantial progress could also be shown in the field of parameter estimation using Bayesian methodologies, especially due to the direct, sampling-free updating of the spectral representations, which could be applied in several fields of application. For the future we see here great potential, especially when those methods are combined with reliable error estimation, adaptive schemes and low-rank representation of all of the involved quantities and computational paths.

Publications

• “Efficient Analysis of High Dimensional Data in Tensor Formats”. In: Sparse Grids and Applications. Ed. by J. Garcke and M. Griebel. Vol. 88. Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2013, pp. 31–56. ISBN: 978-3-642-31702-6
  M. Espig, W. Hackbusch, A. Litvinenko, H. G. Matthies, and E. Zander
  
• “Efficient lowrank approximation of the stochastic Galerkin matrix in tensor formats”. In: Computers and Mathematics with Applications 67 (2014), pp. 818–829
  M. Espig, W. Hackbusch, A. Litvinenko, H. G. Matthies, and P. Wähnert
  
• “To be or not to be intrusive? The ”plain vanilla” Galerkin case”. In: SIAM Journal of Scientific Computing 36 (2014), A2720–A2744. ISSN: 0377-0427
  L. Giraldi, A. Litvinenko, D. Liu, H. G. Matthies, and A. Nouy
  
• “A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes”. In: ESAIM: Mathematical Modelling and Numerical Analysis 49.5 (2015), pp. 1367–1398
  M. Eigel, C. J. Gittelson, C. Schwab, and E. Zander
  
• “Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format”. In: SIAM/ASA Journal on Uncertainty Quantification 3.1 (2015), pp. 1109–1135
  S. Dolgov, B. N. Khoromskij, A. Litvinenko, and H. G. Matthies