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.
Spis treści
Gerrit Buse, Dirk Pfl¨uger, and Riko Jacob: Efficient Pseudorecursive Evaluation Schemes for Non-Adaptive Sparse Grids.- Oliver G. Ernst and Bj¨orn Sprungk: Stochastic Collocation for Elliptic PDEs with Random Data – The Lognormal Case.- Michael Griebel and Helmut Harbrecht: On the Convergence of the Combination Technique.- Michael Griebel and Jan Hamaekers: Fast Discrete Fourier Transform on Generalized Sparse Grids.- Michael Griebel and Jens Oettershagen: Dimension-adaptive Sparse Grid Quadrature for Integrals with Boundary Singularities.- Max Gunzburger, Clayton G. Webster, and Guannan Zhang: An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Equations with Random Input Data.- Brendan Harding and Markus Hegland: Robust Solutions to PDEs with Multiple Grids.- Riko Jacob: Efficient Regular Sparse Grid Hierarchization by a Dynamic Memory Layout.- Valeriy Khakhutskyy and Dirk Pflüger: Alternating Direction Method of Multipliers for Hierarchical Basis Approximators.- Christoph Kowitz and Markus Hegland: An Opticom Method for Computing Eigenpairs.- Benjamin Peherstorfer, Fabian Franzelin, Dirk Pfl¨uger, and Hans-Joachim Bungartz: Classification with Probability Density Estimation on Sparse Grids.- Bettina Schieche and Jens Lang: Adjoint Error Estimation for Stochastic Collocation Methods.- Sebastian Ullmann and Jens Lang: POD-Galerkin Modeling and Sparse-Grid Collocation for a Natural Convection Problem with Stochastic Boundary Conditions.- Matthias Wong and Markus Hegland: Opticom and the Iterative Combination Technique for Convex Minimisation.
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