Proper generalized decomposition: Difference between revisions

Revision as of 20:16, 13 April 2020

Revision as of 20:20, 13 April 2020

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::<math> \mathbf{u} \approx \mathbf{u}^N(x_1, x_2, \ldots, x_d) = \sum_{i=1}^N \mathbf{X_1}_i(x_1) \cdot \mathbf{X_2}_i(x_2) \cdots \mathbf{X_d}_i(x_d), </math>

where the number of termsaddends ''N'' and the functional products '''X₁'''(''x''₁), '''X₂'''(''x''₂), ..., '''X_d'''(''x''_d), each depending on a variable (or variables), are unknown beforehand.

The solution is sought by applying a [[greedy algorithm]], usually the [[fixed point algorithm]], to the [[weak formulation]] of the problem.