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== Description ==
The proper generalized decomposition is a method characterized by (1) a [[variational formulation]] of the problem, (2) a discretization of the [[Domain of a function|___domain]] in the style of the [[finite element method]] and (3) a numerical [[greedy algorithm]] that assumes the solution as a separated representation.<ref>{{Cite journal|last=Amine Ammar, Béchir Mokdad, Francisco Chinesta, Roland Keunings|first=|date=2006|title=A New Family of Solvers for Some Classes of Multidimensional Partial Differential Equations Encountered in Kinetic Theory Modeling of Complex Fluids|url=https://hal.archives-ouvertes.fr/hal-01004909/document|journal=Journal of Non-Newtonian Fluid Mechanics|volume=|pages=|via=}}</ref><ref>{{Cite journal|last=Amine Ammar, Béchir Mokdad, Francisco Chinesta, Roland Keunings|first=|date=2007|title=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 separated representations|url=https://hal.archives-ouvertes.fr/hal-01004910/document|journal=Journal of Non-Newtonian Fluid Mechanics|volume=|pages=|via=}}</ref>
The most implemented variational formulation in PGD is the [[Bubnov-Galerkin method]],<ref name=":0">{{Cite thesis|title=Proper generalised decompositions: theory and applications|url=http://orca.cf.ac.uk/73515/|publisher=Cardiff University|date=2015-04-09|degree=phd|language=en|first=Thomas Lloyd David|last=Croft}}</ref><ref>{{Cite book|last=Chinesta|first=Francisco|url=https://www.springer.com/gp/book/9783319028644|title=The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer|last2=Keunings|first2=Roland|last3=Leygue|first3=Adrien|date=2014|publisher=Springer International Publishing|isbn=978-3-319-02864-4|series=SpringerBriefs in Applied Sciences and Technology|language=en}}</ref> although other implementations exist.<ref>{{Cite web|url=https://hal.archives-ouvertes.fr/tel-01926078/document|title=Advanced strategies for the separated formulation of problems in the Proper Generalized Decomposition framework|last=Aguado|first=José Vicente|date=18 Nov 2018|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref><ref name=":0" />
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