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== Description ==
The proper generalized decomposition is characterized by a [[variational formulation]] of the problem, a discretization of the ___domain in the style of the [[finite element method]] and a numerical solution algorithm based on a [[greedy algorithm]] that assumes the solution as a separated representation.
PGD assumes that the solution '''u''' of a multidimensional problem can be approximated as a separated representation '''u'''<sup>''N''</sup> of the form
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