Alleviating mesh constraints : Model reduction, parallel time integration and high resolution homogenization

By Francisco Chinesta, Amine Ammar, F. Lemarchand, P. Beauchêne, F. Boust. 2008

86 citations recorded by the source corpus.

Industrial processes involving composite materials need for efficient numerical simulations in order to optimize the process parameters. Even if the thermo-mechanical models are nowadays well established, efficient simulations need for further developments. In this work we are addressing some of these issues, in particular the one related to fast solutions combining model reduction and parallel time integration. A separated representation will be also proposed in the context of material homogenization allowing to alleviate the usual mesh constraints.

Subfields: Mechanics of Materials, Statistical and Nonlinear Physics, Numerical Methods & Scientific Computing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…[46,160,172,184,192,193]; • computational tasks in micromagnetics [80,81]; • rational approximation problems [242]; • computational homogenization [42,96,176]; • computational ﬁnance [134,137]; • the approximation of stationary states of stochastic automata networks [38]; • multivariate…”
The LATIN multiscale computational method and the Proper Generalized Decomposition (2010, methodology): “This technique has already been used in the context of stochastic problems [19] and multidimensional problems [1, 2, 6].”
Tensor-based methods for numerical homogenization from high-resolution images (2013, methodology): “Note that a basic PGD algorithm has been used in [11] for the numerical solution of PDEs with heterogeneous materials whose geometry is easily represented in a tensor format.”
Routes for Efficient Computational Homogenization of Nonlinear Materials Using the Proper Generalized Decompositions (2010, background): “In [11] the use of separated representations for computing the homogenized behavior of linear thermal models was already addressed.”
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.”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, unknown): “[68,70,93,3] for spacetime separation, [27] for space-space separation, [2] for multi-dimensional separation).”
An error estimator for separated representations of highly multidimensional models (2010, background): “In this case the use of separated representations could be an appealing choice [9].”