Sparse Grids and Applications - Munich 2012

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Jochen Garcke, Dirk Pflüger
Springer Science & Business Media, Apr 11, 2014 - Mathematics - 344 pages

Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, 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, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.

 

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Contents

Efficient Pseudorecursive Evaluation Schemes for Nonadaptive Sparse Grids
1
The Lognormal Case
29
On the Convergence of the Combination Technique
54
Fast Discrete Fourier Transform on Generalized Sparse Grids
75
DimensionAdaptive Sparse Grid Quadrature for Integrals with Boundary Singularities
109
An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Equations with Random Input Data
137
Robust Solutions to PDEs with Multiple Grids
171
Efficient Regular Sparse Grid Hierarchization by a Dynamic Memory Layout
194
Alternating Direction Method of Multipliers for Hierarchical Basis Approximators
221
An Opticom Method for Computing Eigenpairs
239
Classification with Probability Density Estimation on Sparse Grids
254
Adjoint Error Estimation for Stochastic Collocation Methods
271
PODGalerkin Modeling and SparseGrid Collocation for a Natural Convection Problem with Stochastic BoundaryConditions
295
Opticom and the Iterative Combination Technique for Convex Minimisation
316
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