A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids - Part II: Transient simulation using space-time…

By Amine Ammar, B. Mokdad, Francisco Chinesta, Roland Keunings. 2007

375 citations recorded by the source corpus.

Kinetic theory models described within the Fokker-Planck formalism involve high-dimensional spaces (including physical and conformation spaces and time). One appealing strategy for treating this kind of problems lies in the use of separated representations and tensor product approximations basis. This technique that was introduced in a former work [A. Ammar, B. Mokdad, E Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, J. Non-Newtonian Fluid Mech. 139 (2006) 153-176] for treating steady state kinetic theory models is extended here for treating transient models. (c) 2007 Elsevier B.V. All rights reserved.

Subfields: Computational Mechanics, Fluid Flow and Transfer Processes, Statistics and Probability

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “An alternative, which allows to control the error global-in-time, is to apply iterative solvers to a space-time formulation [5,8,62,65,95].”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “[3, 66, 68, 92] for space-time separation, [26] for space-space separation, [2] for multi-dimensional separation).”
An error estimator for separated representations of highly multidimensional models (2010, background): “We proposed in some of our former works [2,3] a separated representation strategy able to circumvent the curse of dimensionality that those models involve.”
Non incremental strategies based on separated representations: applications in computational rheology (2010, background): “The present work will focus on the second kind of models described at the beginning of this section.”
A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart–Young approach (2011, background): “It has been also introduced for the separation of coordinate in multidimensional PDEs [1, 2], with many applications in kinetic theory of complex fluids, financial mathematics, computational chemistry.”
A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations (2010, positive): “…separation of physical variables and parameters (or random variables) in the context of parametrized (or stochastic ) PDEs [27] [28] [32] [29] 3 , with a possible additional separation of parameters [11] [30] 4 , separation of coordinate variables in multi-dimensional PDEs [6] [1] [2] [8] 5 .”