A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations

By Anthony Nouy. 2010

351 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/917add87c721c24bd4213eb1a506faf8b5130b3a

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In Biomedical Engineering

In Statistical and Nonlinear Physics

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Citations in the corpus

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, neutral): “Promising recent eﬀorts towards this goal use tensor techniques [182, 186].”
Proper Generalized Decomposition and layer-wise approach for the modeling of composite plate structures (2013, background): “Usually, only a maximum of three iterations is required to reach the convergence as in Nouy (2010).”
Model order reduction based on proper generalized decomposition for the propagation of uncertainties in structural dynamics (2012, neutral): “PGD methods have been recently introduced for the a priori construction of separated representations of the solution of variational problems deﬁned in tensor product spaces [14, 3, 4, 29, 8, 24].”
Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces (2011, neutral): “For many applications, these updating strategies allow recovering good convergence properties of separated representations [31,33,34].”
Composite beam finite element based on the Proper Generalized Decomposition (2012, background): “For a review about the PGD and its fields of applications, the reader can refer to [39,40].”
Greedy algorithms for high-dimensional non-symmetric linear problems (2012, methodology): “1 MiniMax algorithm A first algorithm based on a dual formulation of problem (16) is the MiniMax algorithm proposed by Nouy [16].”
Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation (2015, neutral): “For this reason this algorithm was originally developed for non-symmetric convective-dominated problems with space-time decompositions, see [21].”
A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart–Young approach (2011, methodology): “[20, 23, 5]) and have proved their efficiency in practical applications.”
Parametric solutions involving geometry: A step towards efficient shape optimization (2014, methodology): “The PGD approach assumes, see [23], that the solution of (2) can be approximated by a rank-n separable approximation of the solution, u(x,μ),”
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems (2013, methodology): “This technique, introduced in [28] under the name ‘‘radial loading approximation’’, was originally limited to the separation of time and space variables (see [29]).”
Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems (2010, methodology): “Some variants of this methodology have been proposed for the a priori construction of such separated representations of functions in tensor product spaces [27,28,41,5,1,21,29, 39].”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, methodology): “This allows us to establish a connection between the AMEn method and the greedy approximations, in particular, the Minimax Proper Generalized Decomposition [22].”
Tensor-based methods for numerical homogenization from high-resolution images (2013, methodology): “Note that the proposed adaptive strategy could also be used in other context for goal-oriented approximation of PDEs in tensor formats.”