Titlebook: Sparse Grids and Applications - Munich 2012; Jochen Garcke,Dirk Pflüger Conference proceedings 2014 Springer International Publishing Swit

改变立场

Dimension-Adaptive Sparse Grid Quadrature for Integrals with Boundary Singularities,uniformly bounded. The aim of this paper is to construct generalized Gaussian quadrature rules based on non-polynomial basis functions, which yield exponential convergence even for integrands with (integrable) boundary singularities whose exact type is not a-priori known. Moreover, we use sparse ten

HAIL

An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Partial Differential Eom input data is proposed. The uncertainty in the input data is assumed to depend on a finite number of random variables. In case the dimension of this stochastic domain becomes moderately large, we show that utilizing a hierarchical sparse-grid AWSCM (sg-AWSCM) not only combats the curse of dimensi

GOAD

Robust Solutions to PDEs with Multiple Grids, combine the solution from multiple grids using ideas related to the sparse grid combination technique and multivariate extrapolation. By utilising the redundancy between the solutions on different grids we will demonstrate how this approach can be adapted for fault-tolerance. Much of this will be a

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Efficient Regular Sparse Grid Hierarchization by a Dynamic Memory Layout,ent algorithms. It is based on a cache-friendly layout of a compact data storage, and the idea of rearranging the data for the different phases of the algorithm. The core steps of the algorithm can be phrased as multiplying the input vector with two sparse matrices. A generalized counting makes it p

Constitution

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Outspoken

Classification with Probability Density Estimation on Sparse Grids,o an Offline phase (pre-processing) and a very rapid Online phase. For each class of the training data the underlying probability density function is estimated on a sparse grid. The class of a new data point is determined by the values of the density functions at this point. Our classification metho

inquisitive

Adjoint Error Estimation for Stochastic Collocation Methods,ion on sparse grids. For higher efficiency and a better understanding of the method, we derive adjoint error estimates for nonlinear stochastic solution functionals. The resulting adjoint problem also involves random parameters and can be treated by stochastic collocation as well. Only a few adjoint

Mystic

POD-Galerkin Modeling and Sparse-Grid Collocation for a Natural Convection Problem with Stochastic llocation points. We propose a way to reduce the total computation time by replacing the deterministic model with its Galerkin projection on the space spanned by a small number of basis functions. The proper orthogonal decomposition (POD) is used to compute the basis functions from the solutions of

把手

Opticom and the Iterative Combination Technique for Convex Minimisation,fully employed to approximate sparse grid solutions of multi-dimensional problems. In this paper we study the technique for a minimisation problem coming from statistics. Our methods can be applied to other convex minimisation problems. We improve the combination technique by adapting the “Opticom”