Topic
Sparse grid
About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: It will be demonstrated that the resulting approxIMations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that the authors may lose is independent of the space dimension n.
Abstract: Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly.
70 citations
••
TL;DR: A robust finite volume method for the solution of high-speed compressible flows in multi-material domains involving arbitrary equations of state and large density jumps is presented.
70 citations
••
TL;DR: This work solves the stationary monochromatic radiative transfer equation with a multi-level Galerkin FEM in physical space and a spectral discretization with harmonics in solid angle and shows that the benefits of the concept of sparse tensor products, known from the context of sparse grids, can also be leveraged in combination with a spectralDiscretization.
68 citations
••
TL;DR: A comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids to overcome the curse of dimensionality for approximations and provides all algorithms in the open source software JBendge for the solution and estimation of a general class of models.
Abstract: We present a comprehensive framework for Bayesian estima- tion of structural nonlinear dynamic economic models on sparse grids. The Smolyak operator underlying the sparse grids approach frees global approx- imation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from ratio- nal expectations and in three new nonlinear state space fllters. The fllters substantially decrease the computational burden compared to the sequential importance resampling particle fllter. The posterior of the structural pa- rameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifles the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge 4 for the solution and estimation of a
66 citations
••
TL;DR: The combination technique is introduced for the numerical solution of d -dimensional eigenproblems on sparse grids and is applied to solve the three-dimensional Schrodinger equation for hydrogen (one-electron problem) and the six-dimensionalSchrodinger equations for helium (two-electrons problem) in strong magnetic and electric fields.
66 citations