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, [[partial differential equation]]s constrained by a set of boundary conditions, such as the [[Poisson's equation]] or the [[Laplace's equation]].

The PGD algorithm computes an approximation of the solution of the BVP by successive enrichment. This means that, in each iteration, a new component (or ''mode'') is computed and added to the approximation. In principle, the more modes obtained, the closer the approximation is to its theoretical solution. However, due to the [[greedy algorithm|greedy]] nature of the PGD algorithm, some modes may actually worsen the approach. The stopping criterion of the algorithm then plays a very important role in obtaining the best approximation.

By selecting only the most relevant PGD modes, a [[reduced order model]] of the solution is obtained. Because of this, PGD is considered a [[dimensionality reduction]] algorithm.