Proper generalized decomposition solutions within a domain decomposition strategy

descriptionPublicationkeyboard_double_arrow_right Article 19 Jan 2018 France, Spain, Spain English Publisher:WileyJournal:International Journal for Numerical Methods in Engineering, volume 113, pages 1,972-1,994 (issn: 0029-5981, eissn: 1097-0207,

Copyright policy )Funded by:EC | AdMoRe

Authors: Huerta, Antonio; Nadal, Enrique; Chinesta, Francisco;

doi: 10.1002/nme.5729

handle: 2117/116428 , 10985/13823

Proper generalized decomposition solutions within a domain decomposition strategy

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Abstract

SummaryDomain 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.

Countries

France, Spain, Spain

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
Universitat Politècnica de València
Spain
Arts et Métiers Institute of Technology
France
Université de Nantes
France
ESI (France)
France

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Keywords

Reduced-order models, Multigrid methods; domain decomposition for boundary value problems involving PDEs, INGENIERIA MECANICA, :Matemàtiques i estadística::Geometria::Geometria algebraica [Àrees temàtiques de la UPC], parameterized solutions, Corbes, 510, [SPI]Engineering Sciences [physics], Equacions diferencials el·líptiques, :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, proper generalized decomposition, Domain Decomposition, Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type, Proper Generalized Decomposition, Classificació AMS::14 Algebraic geometry::14H Curves, Reduced Order Models; Proper Generalized Decomposition; Domain Decomposition; Parameterized solutions, Engineering, Mechanical, Geometria algèbrica--Aritmètica, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials, domain decomposition, Differential equations, Engineering, Civil, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria, Differential equations, Elliptic, [SPI] Engineering Sciences [physics], Proper generalized decomposition, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC], Engineering, Multidisciplinary, Geometry, Sciences de l'ingénieur, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), :35 Partial differential equations::35J Partial differential equations of elliptic type [Classificació AMS], :14 Algebraic geometry::14H Curves [Classificació AMS], Reduced Order Models, Engineering, Ocean, Domain decomposition, Engineering, Aerospace, Engineering, Biomedical, Curves, Elliptic, reduced-order models, Geometria, :51 Geometry::51M Real and complex geometry [Classificació AMS], Computer Science, Software Engineering, Engineering, Marine, Engineering, Manufacturing, Classificació AMS::51 Geometry::51M Real and complex geometry, FISICA APLICADA, Engineering, Industrial, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], Arithmetical algebraic geometry, :Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC], Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, Parameterized solutions

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