The LATIN multiscale computational method and the Proper Generalized Decomposition

By Pierre Ladevèze, Jean-Charles Passieux, David Néron. 2010

329 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5d60818e4060e98cedd6e1ce881cf12f2ff7caf5

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “or the model reduction of parameterdependent or stochastic equations (see Section 7.5 and references [63, 64, 68, 20, 79]), and also for the model reduction of time-dependent evolution equations (see [55, 56, 66]). Optimal construction with nested minimal subspaces. Thesequence of rank-rapproximatio”
A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “…micromechanics-based methods [47,48], the transformation field analysis (TFA) [49], the nonuniform transformation field analysis (NTFA) [50], the principal component analysis [51–53] also known as proper orthogonal decomposition (POD) [54,55], and the proper generalized decomposition (PGD) [56,57].”
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem (2015, unknown): “…DD and MOR techniques for the reduction via projection of linear and nonlinear models was proposed in [24] for linear aerodynamics flow field, in [25] for simulation of a rather large scale heterogeneous structure with multicracks, in [26] for elastic–viscoplastic static analysis and in [27,28]…”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, methodology): “In the literature , two variants of PGD have been proposed for the progressive construction of (1), respectively based on a Galerkin formulation [21] [12] [22] [9] or a Minimal Residual formulation [31] [23] of the evolution problem.”
Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces (2011, unknown): “Another family of methods, called Proper Generalized Decomposition (PGD) methods [9,16, 27,33,34], have been introduced for the direct construction of representations of type (1).”
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems (2013, methodology): “In the examples presented in the next section, following [37], the number of iterations was arbitrarily set to a small value (‘max 1⁄4 2).”
PGD-Based Computational Vademecum for Efficient Design, Optimization and Control (2013, background): “The interested reader can refer to the numerous Ladeveze’s works [44–49, 59, 68].”
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].”
Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation (2015, unknown): “This method has been studied and successfully applied to various problems in computational mechanics, see [16, 17, 31, 4, 37].”
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.”
Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials (2016, methodology): “Analytical micromechanical methods20 [14, 15, 16, 17], the Voronoi cell finite element method [18], fast Fourier transforms [19], spectral methods21 [20], the generalized method of cells [21], the transformation field analysis (TFA) [22], the nonuniform trans-22 formation field analysis (NTFA) [23, ”
Nonlinear reduced order homogenization of materials including cohesive interfaces (2015, unknown): “, [27–29]).”