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),. thatThat is, [[partial differential equation]]s constrained by a set of boundary conditions, such as [[Poisson's equation]] or [[Laplace's equation]], among others.

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. The more modes obtained, the closer the approximation is to its theoretical solution. 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. In addition, it is considered as a generalized form of the [[proper orthogonal decomposition]].