Sparse grid

About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.

Combining Sparse Grids, Multilevel MC and QMC for Elliptic PDEs with Random Coefficients

Abstract: Building on previous research which generalized multilevel Monte Carlo methods using either sparse grids or Quasi-Monte Carlo methods, this paper considers the combination of all these ideas applied to elliptic PDEs with finite-dimensional uncertainty in the coefficients. It shows the potential for the computational cost to achieve an \(O(\varepsilon )\) r.m.s. accuracy to be \(O(\varepsilon ^{-r})\) with \(r\!<\!2\), independently of the spatial dimension of the PDE.

An Optimized; Grid Independent; Narrow Band Data Structure for High Resolution Level Sets

Abstract: Level sets have recently proven successful in many areas of computer graphics including water simulations[Enright et al. 2002] and geometric modeling[Museth et al. 2002]. However, current implementations of these level set methods are limited by factors such as computational efficiency, storage requirements and the restriction to a domain enforced by the convex boundaries of an underlying cartesian computational grid. Here we present a novel very memory efficient narrow band data structure, dubbed the Sparse Grid, that enables the representation of grid independent high resolution level sets. The key features our new data structure are

Sparse Grid Approximation Spaces for Space-Time Boundary Integral Formulations of the Heat Equation

Abstract: The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary integral formulations depends mainly on the choice of discretisation space. We develop a-priori error analysis utilising a proof technique that involves norm equivalences in hierarchical wavelet subspace decompositions. We apply this to a full tensor product discretisation, showing improvements over existing results, particularly for discretisation spaces having low polynomial degrees. We then use the norm equivalences to show that an anisotropic sparse grid discretisation yields even higher convergence rates. Finally, a simple adaptive scheme is proposed to suggest an optimal shape for the sparse grid index sets.

Eddy-current NDE inverse problem with sparse grid algorithm

Abstract: In model-based inverse problems, the unknown parameters (such as length, width, depth) need to be estimated. When the unknown parameters are few, the conventional mathematical methods are suitable. But the increasing number of unknown parameters will make the computation become heavy. To reduce the burden of computation, the sparse grid algorithm was used in our work. As a result, we obtain a powerful interpolation method that requires significantly fewer support nodes than conventional interpolation on a full grid.

Local grid and photon encryption method in radiation energy propagation Monte-Carlo algorithm

Abstract: The invention provides a local grid and photon encryption method in a radiation energy propagation Monte-Carlo algorithm. The method includes firstly, selecting grids different in size for different components in propagation media according to optical characteristics and shape structures of the corresponding components; secondly, selecting a total photon number required by optical propagation computation in the propagation media according to the size of the sparsest grid, wherein the total photon number is bound to meet the statistics requirement of the photon energy distribution in the grid when computation is performed according to the size of the sparsest grid, and when entering a small-sized dense grid from a large-sized sparse grid, photons split. The local grid and photon encryption method is put forward according to the optical characteristics and the shape structures of the propagation media on the basis of 'a voxel-based Monte-Carlo method', so that computation efficiency of the Monte-Carlo method is improved greatly.