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El. knyga: Sparse Grids and Applications - Munich 2018

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Sparse grids are a popular tool 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 flavors, are frequently the method of choice.









This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.
On Expansions and Nodes for Sparse Grid Collocation of Lognormal
Elliptic PDEs.- Sparse Grids Approximation of Goldstone Diagrams in
Electronic Structure Calculations.- Generalized Sparse Grid Interpolation
Based on the Fast Discrete Fourier Transform.- Fast Sparse Grid Operations
using the Unidirectional Principle: A Generalized and Unified
Framework.- Propagation of Uncertainties in Density-Driven Flow.- A
Posteriori Error Estimation for the Stochastic Collocation Finite Element
Approximation of the Heat Equation with Random Coefficients.- A Spatially
Adaptive Sparse Grid Combination Technique for Numerical
Quadrature.- Hierarchical Extended B-splines for Approximations on Sparse
Grids.- Analysis of Sparse Grid Multilevel Estimators for Multi-dimensional
Zakai Equations.- Efficiently Transforming from Values of a Function on a
Sparse Grid to Basis Coefficients.- A Sparse-Grid Probabilistic Scheme
for Approximation of the Runaway Probability of Electrons in Fusion Tokamak
Simulation.