Sparse Grids and Applications - Stuttgart 2014

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Jochen Garcke, Dirk Pflüger
Springer, Mar 16, 2016 - Computers - 336 pages
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.
 

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Contents

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