Comparison of Clenshaw–Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

Fabio Nobile, Lorenzo Tamellini, Raúl Tempone

Type: Book-Chapter

Publication Date: 2015-01-01

Citations: 16

DOI: https://doi.org/10.1007/978-3-319-19800-2_44

View Publication

Locations

Lecture notes in computational science and engineering - View

Similar Works

Action	Title	Year	Authors
+	Quasi-Monte Carlo methods for elliptic PDEs with random coefficients	2016	Dirk Nuyens Ivan G. Graham Frances Y. Kuo Robert Scheichl Ian H. Sloan
+ PDF Chat	Application of Quasi-Monte Carlo Methods to PDEs with Random Coefficients – An Overview and Tutorial	2018	Frances Y. Kuo Dirk Nuyens
+	A practical multilevel quasi-Monte Carlo method for PDEs with random coefficients	2016	Pieterjan Robbe Dirk Nuyens Stefan Vandewalle
+	A practical multi-index quasi-Monte Carlo method for simulating elliptic PDEs with random coefficients	2015	Pieterjan Robbe Dirk Nuyens Stefan Vandewalle
+	Multi-level Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic PDEs with Random Coefficients	2015	Frances Y. Kuo Christoph Schwab Ian H. Sloan
+	Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs	2015	Fabio Nobile Lorenzo Tamellini Raúl Tempone
+	Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients	2011	K. A. Cliffe Michael B. Giles Robert Scheichl Aretha L. Teckentrup
+	Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial	2017	Frances Y. Kuo Dirk Nuyens
+	Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial	2017	Frances Y. Kuo Dirk Nuyens
+	Dimension-Adaptive Multi-Index Quasi-Monte Carlo for PDEs with Random Coefficients	2017	Pieterjan Robbe Dirk Nuyens Stefan Vandewalle
+ PDF Chat	Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation	2014	Akil Narayan John Jakeman
+	Quasi-Monte Carlo methods using circulant embedding techniques for elliptic PDEs with random coefficients	2016	Dirk Nuyens Ivan G. Graham Frances Y. Kuo Robert Scheichl Ian H. Sloan
+	Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients	2014	Ivan G. Graham Frances Y. Kuo James Nichols Robert Scheichl Ch. Schwab Ian H. Sloan
+	Quasi-Monte Carlo finite element methods for elliptic PDEs with log-normal random coefficient	2013	Ivan G. Graham Frances Y. Kuo James Nichols Robert Scheichl Christoph Schwab Ian H. Sloan
+ PDF Chat	Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation	2016	Frances Y. Kuo Dirk Nuyens
+	Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation	2016	Frances Y. Kuo Dirk Nuyens
+	Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation	2016	Frances Y. Kuo Dirk Nuyens
+ PDF Chat	Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling	2021	Matteo Croci Michael B. Giles Patrick E. Farrell
+	An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient	2016	Fabio Nobile Lorenzo Tamellini Francesco Tesei Raúl Tempone
+	A Full Multigrid-Multilevel Quasi-Monte Carlo Approach for Elliptic PDE with Random Coefficients	2019	Yang Liu

Works That Cite This (13)

Action	Title	Year	Authors
+ PDF Chat	Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity	2016	Abdul-Lateef Haji-Ali Fabio Nobile Lorenzo Tamellini Raúl Tempone
+	An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient	2016	Fabio Nobile Lorenzo Tamellini Francesco Tesei Raúl Tempone
+ PDF Chat	ASSESSING THE PERFORMANCE OF LEJA AND CLENSHAW-CURTIS COLLOCATION FOR COMPUTATIONAL ELECTROMAGNETICS WITH RANDOM INPUT DATA	2018	Dimitrios Loukrezis Ulrich Römer Herbert De Gersem
+	Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity	2015	Abdul-Lateef Haji-Ali Fabio Nobile Lorenzo Tamellini Raúl Tempone
+	Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs	2015	Fabio Nobile Lorenzo Tamellini Raúl Tempone
+	A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty	2015	Gabriela Malenova Mohammad Motamed Olof Runborg Raúl Tempone
+ PDF Chat	Multi-Index Stochastic Collocation for random PDEs	2016	Abdul-Lateef Haji-Ali Fabio Nobile Lorenzo Tamellini Raúl Tempone
+ PDF Chat	IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains	2019	Joakim Beck Lorenzo Tamellini Raúl Tempone
+ PDF Chat	An <i>hp</i>‐adaptive multi‐element stochastic collocation method for surrogate modeling with information re‐use	2023	Armin Galetzka Dimitrios Loukrezis Niklas Georg Herbert De Gersem Ulrich Römer
+ PDF Chat	On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion	2022	Martin Eigel Oliver G. Ernst Björn Sprungk Lorenzo Tamellini

Works Cited by This (11)

Action	Title	Year	Authors
+	Dimension?Adaptive Tensor?Product Quadrature	2003	Thomas Gerstner Michael Griebel
+	Sparse, adaptive Smolyak quadratures for Bayesian inverse problems	2013	Claudia Schillings Christoph Schwab
+	Optimized general sparse grid approximation spaces for operator equations	2009	Michael Griebel S. Knapek
+	ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS	2012	Joakim Beck Raúl Tempone Fabio Nobile Lorenzo Tamellini
+ PDF Chat	A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data	2010	Ivo Babuška Fabio Nobile Raúl Tempone
+	On the Lebesgue constant of Leja sequences for the complex unit disk and of their real projection	2012	Abdellah Chkifa
+	A Quasi-optimal Sparse Grids Procedure for Groundwater Flows	2013	Joakim Beck Fabio Nobile Lorenzo Tamellini Raúl Tempone
+	High-Order Collocation Methods for Differential Equations with Random Inputs	2005	Dongbin Xiu Jan S. Hesthaven
+ PDF Chat	Adaptive Leja Sparse Grid Constructions for Stochastic Collocation and High-Dimensional Approximation	2014	Akil Narayan John Jakeman
+ PDF Chat	ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S	2011	Albert Cohen Ronald DeVore Christoph Schwab