Survey of multifidelity methods in uncertainty propagation, inference, and optimization

B Peherstorfer, K Willcox, M Gunzburger - Siam Review, 2018 - SIAM
In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

A literature survey of low‐rank tensor approximation techniques

L Grasedyck, D Kressner, C Tobler - GAMM‐Mitteilungen, 2013 - Wiley Online Library
During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

A short review on model order reduction based on proper generalized decomposition

F Chinesta, P Ladeveze, E Cueto - Archives of Computational Methods in …, 2011 - Springer
This paper revisits a new model reduction methodology based on the use of separated
representations, the so called Proper Generalized Decomposition—PGD. Space and time …

Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's bound

S Saeb, P Steinmann, A Javili - Applied …, 2016 - asmedigitalcollection.asme.org
The objective of this contribution is to present a unifying review on strain-driven
computational homogenization at finite strains, thereby elaborating on computational …

Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models

F Chinesta, A Ammar, E Cueto - Archives of Computational methods in …, 2010 - Springer
This paper revisits a powerful discretization technique, the Proper Generalized
Decomposition—PGD, illustrating its ability for solving highly multidimensional models. This …

A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations

A Nouy - Computer Methods in Applied Mechanics and …, 2010 - Elsevier
Over the past years, model reduction techniques have become a necessary path for the
reduction of computational requirements in the numerical simulation of complex models. A …

The latin multiscale computational method and the proper generalized decomposition

P Ladevèze, JC Passieux, D Néron - Computer Methods in Applied …, 2010 - Elsevier
The LATIN multiscale computational method and the Proper Generalized Decomposition -
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Recent developments in spectral stochastic methods for the numerical solution of stochastic partial differential equations

A Nouy - Archives of Computational Methods in Engineering, 2009 - Springer
Uncertainty quantification appears today as a crucial point in numerous branches of science
and engineering. In the last two decades, a growing interest has been devoted to a new …

On the verification of model reduction methods based on the proper generalized decomposition

P Ladeveze, L Chamoin - Computer Methods in Applied Mechanics and …, 2011 - Elsevier
In this work, we introduce a consistent error estimator for numerical simulations performed
by means of the proper generalized decomposition (PGD) approximation. This estimator …

On the deterministic solution of multidimensional parametric models using the proper generalized decomposition

E Pruliere, F Chinesta, A Ammar - Mathematics and Computers in …, 2010 - Elsevier
This paper focuses on the efficient solution of models defined in high dimensional spaces.
Those models involve numerous numerical challenges because of their associated curse of …