Huerta, A.; Nadal, E.; Chinesta Soria, FJ. (2018). Proper Generalized Decomposition solutions within a Domain Decomposition strategy. International Journal for Numerical Methods in Engineering. 113(13):1972-1994. https://doi.org/10.1002/nme.5729
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/146190
Title:
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Proper Generalized Decomposition solutions within a Domain Decomposition strategy
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Author:
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Huerta, Antonio
Nadal, Enrique
Chinesta Soria, Francisco Jose
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UPV Unit:
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Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials
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Issued date:
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Abstract:
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[EN] Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The ...[+]
[EN] Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in-plane-out-of-plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user-defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.
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Subjects:
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Domain decomposition
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Parameterized solutions
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Proper generalized decomposition
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Reduced-order models
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Copyrigths:
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Reserva de todos los derechos
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Source:
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International Journal for Numerical Methods in Engineering. (issn:
0029-5981
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DOI:
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10.1002/nme.5729
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Publisher:
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John Wiley & Sons
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Publisher version:
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https://doi.org/10.1002/nme.5729
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Project ID:
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info:eu-repo/grantAgreement/EC/H2020/675919/EU
MINECO/DPI2017-85139-C2-2-R
GC/2014SGR1471
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Description:
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"This is the peer reviewed version of the following article: Huerta, Antonio, Enrique Nadal, and Francisco Chinesta. 2018. Proper Generalized Decomposition Solutions within a Domain Decomposition Strategy. International Journal for Numerical Methods in Engineering 113 (13). Wiley: 1972 94. doi:10.1002/nme.5729, which has been published in final form at https://doi.org/10.1002/nme.5729. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."
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Thanks:
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European Commission, Grant/Award Number: MSCA ITN-ETN 675919; ESI group, Grant/Award Number: ENSAM ESI Chair; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: DPI2017-85139-C2-2-R; Generalitat de ...[+]
European Commission, Grant/Award Number: MSCA ITN-ETN 675919; ESI group, Grant/Award Number: ENSAM ESI Chair; Spanish Ministry of Economy and Competitiveness, Grant/Award Number: DPI2017-85139-C2-2-R; Generalitat de Catalunya, Grant/Award Number: 2014SGR1471
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Type:
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Artículo
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