A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations

Kookjin Lee, Howard C. Elman

Type: Article

Publication Date: 2017-01-01

Citations: 24

DOI: https://doi.org/10.1137/16m1075582

View Publication

Locations

SIAM Journal on Scientific Computing - View
arXiv (Cornell University) - View - PDF
OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) - View

Similar Works

Action	Title	Year	Authors
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2016	Kookjin Lee Howard C. Elman
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2016	Kookjin Lee Howard C. Elman
+ PDF Chat	An alternating low-rank projection approach for partial differential equations with random inputs	2024	Guanjie Wang Qifeng Liao
+ PDF Chat	A Low-Rank Inexact Newton–Krylov Method for Stochastic Eigenvalue Problems	2018	Peter Benner Akwum Onwunta Martin Stoll
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2018	Howard C. Elman Tengfei Su
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2019	Howard C. Elman Tengfei Su
+ PDF Chat	A low-rank solver for the stochastic unsteady Navier–Stokes problem	2020	Howard C. Elman Tengfei Su
+ PDF Chat	Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs	2020	Kejun Tang Qifeng Liao
+	Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs	2018	Kejun Tang Qifeng Liao
+	Oblique projection for scalable rank-adaptive reduced-order modeling of nonlinear stochastic PDEs with time-dependent bases	2023	Michael Donello G. Palkar M. H. Naderi D. C. Del Rey Fernández Hessam Babaee
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2016	Howard C. Elman Tengfei Su
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2018	Howard C. Elman Tengfei Su
+	Deterministic matrix sketches for low-rank compression of high-dimensional simulation data	2021	Alec M. Dunton Alireza Doostan
+	Low rank approximation method for perturbed linear systems with applications to elliptic type stochastic PDEs	2023	Yujun Zhu Ming Ju Jie Zhu Zhongming Wang
+ PDF Chat	Low Rank Approximation Method for Perturbed Linear Systems with Applications to Elliptic Type Stochastic Pdes	2023	Yujun Zhu Ming Ju Jie Zhu Zhong-Ming Wang
+	Krylov Methods for Low-Rank Regularization	2019	Silvia Gazzola Chang Meng J.I. Nagy
+	Krylov Methods for Low-Rank Regularization	2019	Silvia Gazzola Chang Meng James G. Nagy
+ PDF Chat	Truncation Preconditioners for Stochastic Galerkin Finite Element Discretizations	2021	Alex Bespalov Daniel Loghin Rawin Youngnoi
+	Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method	2016	Kevin Carlberg Virginia Forstall Ray Tuminaro
+	An Efficient Solver for Sparse Linear Systems Based on Rank-Structured Cholesky Factorization	2015	Jeffrey N. Chadwick David Bindel

Works That Cite This (18)

Action	Title	Year	Authors
+ PDF Chat	Multilevel tensor approximation of PDEs with random data	2017	Jonas Ballani Daniel Kreßner Michael Peters
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2019	Howard C. Elman Tengfei Su
+ PDF Chat	A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity	2019	Kookjin Lee Howard C. Elman Bedřich Sousedík
+	Krylov Methods for Low-Rank Regularization	2019	Silvia Gazzola Chang Meng James G. Nagy
+ PDF Chat	Krylov Methods for Low-Rank Regularization	2020	Silvia Gazzola Chang Meng James G. Nagy
+	Proximal linearization methods for Schatten p-quasi-norm minimization	2022	Chao Zeng
+	Multilevel tensor approximation of PDEs with random data	2016	Jonas Ballani Daniel Kreßner Michael Peters
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2018	Howard C. Elman Tengfei Su
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2016	Howard C. Elman Tengfei Su
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2018	Howard C. Elman Tengfei Su

Works Cited by This (11)

Action	Title	Year	Authors
+ PDF Chat	A projection method to solve linear systems in tensor format	2012	Jonas Ballani Lars Grasedyck
+ PDF Chat	Krylov Subspace Methods for Linear Systems with Tensor Product Structure	2010	Daniel Kreßner Christine Tobler
+	Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition	1970	J. Douglas Carroll Jih-Jie Chang
+ PDF Chat	Existence and Computation of Low Kronecker-Rank Approximations for Large Linear Systems of Tensor Product Structure	2004	Lars Grasedyck
+ PDF Chat	Algorithms for Numerical Analysis in High Dimensions	2005	Gregory Beylkin Martin J. Mohlenkamp
+ PDF Chat	Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems	2011	Daniel Kreßner Christine Tobler
+ PDF Chat	GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems	1986	Yousef Saad Martin H. Schultz
+	On solving elliptic stochastic partial differential equations	2002	Ivo Babuška Panagiotis Chatzipantelidis
+ PDF Chat	Parametric PDEs: sparse or low-rank approximations?	2017	Markus Bachmayr Albert Cohen Wolfgang Dahmen
+	Kolmogorov widths and low-rank approximations of parametric elliptic PDEs	2016	Markus Bachmayr Albert Cohen