## Sparse Grids and Applications - Stuttgart 2014This 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. |

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### Contents

1 | |

An Efficient Integrated DataDriven Sparse Grid Approach to Propagate Uncertainty | 29 |

Combination Technique Based Second Moment Analysis for Elliptic PDEs on Random Domains | 50 |

Adaptive Sparse Grids and Extrapolation Techniques | 79 |

A CacheOptimal Alternative to the Unidirectional Hierarchization Algorithm | 103 |

SpatiallyDimensionAdaptive Sparse Grids for Online Learning | 133 |

Sparse Grids for the VlasovPoisson Equation | 163 |

An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient | 191 |

A New SubspaceBased Algorithm for Efficient Spatially Adaptive Sparse Grid Regression Classification and Multievaluation | 221 |

HighDimensional Stochastic Design Optimization by AdaptiveSparse Polynomial Dimensional Decomposition | 247 |

Efficient SpectralElement Methods for the Electronic Schrödinger Equation | 265 |

A Sparse Grid Method for Bayesian Uncertainty Quantification with Application to Large Eddy Simulation Turbulence Models | 290 |

Hierarchical GradientBased Optimization with BSplines on Sparse Grids | 315 |

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### Common terms and phrases

adaptive sparse grids analysis approach B-splines basis functions Bayesian inference boundary Bungartz cache misses coefficients collocation method combination technique component grids Computational Science convergence rate data mining data point data set defined density estimation dimension dimensional domain downset Dref efficient error estimator evaluation full grid Galerkin Garcke grid points Grids and Applications Griebel high-dimensional implementation indices input integration iteration Lecture Notes Lemma likelihood function MCMC Meshfree Methods multi-index nodes Notes in Computational number of grid optimization parameter partial differential equations PDEs performance Pflüger piecewise linear polynomial polynomial chaos PPDF probability density function problem quadrature random variables recursive Runtime samples Science and Engineering Sect SGDE SGxSGv simulation solution solve space sparse grid interpolant sparse grid method Springer stochastic collocation streaming algorithm subgrid subspace surrogate modeling tensor product uncertainty quantification unidirectional univariate vector