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Parametric PDEs: sparse or low-rank approximations?

Published:2017-09-16 Issue:4 Volume:38 Page:1661-1708
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Bachmayr Markus¹,Cohen Albert²,Dahmen Wolfgang³

Affiliation:

1. Hausdorff Center for Mathematics & Institute for Numerical Simulation, University of Bonn, Bonn, Germany

2. Sorbonne Universités, UPMC Univ Paris, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, Jussieu, Paris, France

3. Department of Mathematics, University of South Carolina, Columbia, SC, USA

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

http://academic.oup.com/imajna/article-pdf/38/4/1661/25956676/drx052.pdf

Reference49 articles.

1. A stochastic collocation method for elliptic partial differential equations with random input data.;Babuška;SIAM Rev,2010

2. Kolmogorov widths and low-rank approximations of parametric elliptic PDEs.;Bachmayr;Math. Comp.,2017

3. Fully discrete approximation of parametric and stochastic elliptic PDEs.;Bachmayr;SIAM J. Numer. Anal.,2017

4. Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients.;Bachmayr;J. Fourier Anal. Appl.,2017

5. Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients.;Bachmayr;ESAIM Math. Model. Numer. Anal.,2017

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2. A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations;IMA Journal of Numerical Analysis;2024-05-04

3. A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations;Journal of Scientific Computing;2024-03-21

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