Proper generalized decomposition: Difference between revisions

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The '''proper generalized decomposition''' ('''PGD''') is an [[iterative method|iterative]] [[numerical method]] for solving [[boundary value problem]]s (BVPs), that is to say, [[partial differential equation]]s constrained by a set of boundary conditions. The PGD algorithm computes an approximation of the theoretical solution of the BVP by successive enrichment, i.e. byThis addingmeans that, in each iteration, a new components,component (or ''modesmode'') is computed and added to the approximation, ofthus (insuccessively principle)''enriching'' decreasingthe variancesolution. By selecting only the first PGD modes, a [[reduced order model]] of the solution is obtained. Because of thisTherefore, PGD is considered a [[dimensionality reduction]] algorithm.

== Description ==

The proper generalized decomposition is a method characterized by a [[variational formulation]] of the problem, a discretization of the [[Domain of a function|___domain]] in the style of the [[finite element method]] and a numerical [[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'''^''N'' of the form