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.
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
CollocationMethods.- 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.
