Sparse Grids and Applications - Stuttgart 2014

1. Front Matter

   Pages i-viii

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2. Adaptive Sparse Grid Model Order Reduction for Fast Bayesian Estimation and Inversion

   • Peng Chen, Christoph Schwab

   Pages 1-27

3. From Data to Uncertainty: An Efficient Integrated Data-Driven Sparse Grid Approach to Propagate Uncertainty

   • Fabian Franzelin, Dirk Pflüger

   Pages 29-49

4. Combination Technique Based Second Moment Analysis for Elliptic PDEs on Random Domains

   • Helmut Harbrecht, Michael Peters

   Pages 51-77

5. Adaptive Sparse Grids and Extrapolation Techniques

   • Brendan Harding

   Pages 79-102

6. A Cache-Optimal Alternative to the Unidirectional Hierarchization Algorithm

   • Philipp Hupp, Riko Jacob

   Pages 103-132

7. Spatially-Dimension-Adaptive Sparse Grids for Online Learning

   • Valeriy Khakhutskyy, Markus Hegland

   Pages 133-162

8. Sparse Grids for the Vlasov–Poisson Equation

   • Katharina Kormann, Eric Sonnendrücker

   Pages 163-190

9. An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient

   • Fabio Nobile, Lorenzo Tamellini, Francesco Tesei, Raúl Tempone

   Pages 191-220

10. A New Subspace-Based Algorithm for Efficient Spatially Adaptive Sparse Grid Regression, Classification and Multi-evaluation

    • David Pfander, Alexander Heinecke, Dirk Pflüger

    Pages 221-246

11. High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

    • Sharif Rahman, Xuchun Ren, Vaibhav Yadav

    Pages 247-264

12. Efficient Spectral-Element Methods for the Electronic Schrödinger Equation

    • Jie Shen, Yingwei Wang, Haijun Yu

    Pages 265-289

13. A Sparse Grid Method for Bayesian Uncertainty Quantification with Application to Large Eddy Simulation Turbulence Models

    • Hoang Tran, Clayton G. Webster, Guannan Zhang

    Pages 291-313

14. Hierarchical Gradient-Based Optimization with B-Splines on Sparse Grids

    • Julian Valentin, Dirk Pflüger

    Pages 315-336

15. Back Matter

    Pages 337-344

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This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.

• high-dimensional approximation
• sparse grids
• efficient data structures and algorithms
• combination technique
• uncertainty quantification
• algorithm analysis and problem complexity

• Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

  Jochen Garcke

• Institute for Parallel and Distributed S, Universität Stuttgart, Stuttgart, Germany

  Dirk Pflüger

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