Keyword

sparse grids

Description: A numerical approximation technique that reduces the cost of computations on high-dimensional domains by using a structured subset of grid points.

Primary topic: Mathematical Approximation and Integration (24%)

Wikidata ID: wiki/Q7573793

OpenAlex ID: keywords/sparse-grids

High-Order Collocation Methods for Differential Equations with Random Inputs

2005 · Dongbin Xiu, Jan S. Hesthaven · SIAM Journal on Scientific Computing · 1,522

Sparse grids

2004 · Hans-Joachim Bungartz, Michael Griebel · Acta Numerica · 1,063

Numerical integration using sparse grids

1998 · Thomas Gerstner, Michael Griebel · Numerical Algorithms · 922

High dimensional polynomial interpolation on sparse grids

2000 · Volker Barthelmann, Erich Novak, et al. · Advances in Computational Mathematics · 632

Likelihood approximation by numerical integration on sparse grids

2008 · Florian Heiss, Viktor Winschel · Journal of Econometrics · 375

Sparse grids

2004 · Hans-Joachim Bungartz, Michael Griebel · Cambridge University Press eBooks · 368

Taichi

2019 · Yuanming Hu, Tzu-Mao Li, et al. · ACM Transactions on Graphics · 258

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Algorithm 847

2005 · Andreas Klimke, Barbara Wohlmuth · ACM Transactions on Mathematical Software · 197

Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields

2015 · P. Perdikaris, D. Venturi, et al. · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 173

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On the Optimal Polynomial Approximation of Stochastic Pdes by Galerkin and Collocation Methods

2012 · JOAKIM BECK, RAUL TEMPONE, et al. · Mathematical Models and Methods in Applied Sciences · 136

Topology optimization considering material and geometric uncertainties using stochastic collocation methods

2012 · Boyan S. Lazarov, Mattias Schevenels, et al. · Structural and Multidisciplinary Optimization · 133

Spatially Adaptive Sparse Grids for High-Dimensional Problems.

2010 · Dirk Pflüger · 133

Sparse Grids and Applications

2012 · Jochen Garcke, Michael Griebel · Lecture notes in computational science and engineering · 127

A new sparse grid based method for uncertainty propagation

2009 · Fenfen Xiong, Steven Greene, et al. · Structural and Multidisciplinary Optimization · 127

Numerical solution of parabolic equations in high dimensions

2004 · Tobias von Petersdorff, Christoph Schwab · ESAIM Mathematical Modelling and Numerical Analysis · 127

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Probabilistic Hosting Capacity for Active Distribution Networks

2017 · Hassan Al-Saadi, Rastko Zivanovic, et al. · IEEE Transactions on Industrial Informatics · 122

An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media

2008 · G. Lin, A.M. Tartakovsky · Advances in Water Resources · 116

Data Mining with Sparse Grids

2001 · J. Garcke, M. Griebel, et al. · Computing · 115

New Error Bounds for Deep ReLU Networks Using Sparse Grids

2019 · Hadrien Montanelli, Qiang Du · SIAM Journal on Mathematics of Data Science · 113

Spatially adaptive sparse grids for high-dimensional data-driven problems

2010 · Dirk Pflüger, Benjamin Peherstorfer, et al. · Journal of Complexity · 105

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Sparse Polynomial Space Approach to Dissipative Quantum Systems: Application to the Sub-Ohmic Spin-Boson Model

2009 · A. Alvermann, H. Fehske · Physical Review Letters · 105

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An automatic three-dimensional finite element mesh generation system for the Poisson-Boltzmann equation

1997 · Christian M. Cortis, Richard A. Friesner · Journal of Computational Chemistry · 102

FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps

2012 · Charbel Farhat, Jean-Frédéric Gerbeau, et al. · Journal of Computational Physics · 94

Sparse grids for the Schrödinger equation

2007 · Michael Griebel, Jan Hamaekers · ESAIM Mathematical Modelling and Numerical Analysis · 94

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Gradient-Based Aerodynamic Optimization with the elsA Software

2014 · Gerald Carrier, D. Destarac, et al. · AIAA Aerospace Sciences Meeting · 92

Works count: 1,219

Citation count: 15,920