On the computation of intrinsic Proper Generalized Decomposition modes of parametric symmetric elliptic problems on Grassmann manifolds

In this work, we introduce an iterative optimization algorithm to obtain the intrinsic Proper Generalized Decomposition modes of elliptic partial differential equations. The main idea behind this procedure is to adapt the general Gradient Descent algorithm to the algebraic version of the intrinsic P...

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Vydané v:Applied mathematics and computation Ročník 470; s. 128579
Hlavní autori: Bandera, Alejandro, Fernández-García, Soledad, Gómez-Mármol, Macarena
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.06.2024
Predmet:
Gradient descent
Grassmann manifold
Proper Generalized Decomposition
Reduced order modeling
Symmetric elliptic problems
Symmetric elliptic problems
Proper Generalized Decomposition
Gradient descent
Grassmann manifold
Reduced order modeling
ISSN:0096-3003, 1873-5649
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Popis
Shrnutí:In this work, we introduce an iterative optimization algorithm to obtain the intrinsic Proper Generalized Decomposition modes of elliptic partial differential equations. The main idea behind this procedure is to adapt the general Gradient Descent algorithm to the algebraic version of the intrinsic Proper Generalized Decomposition framework, and then to couple a one-dimensional case of the algorithm with a deflation algorithm in order to keep enriching the solution by computing further intrinsic Proper Generalized Decomposition modes. For this novel iterative optimization procedure, we present some numerical tests based on physical parametric problems, in which we obtain very promising results in comparison with the ones already presented in the literature. This supports the use of this procedure in order to obtain the intrinsic PGD modes of parametric symmetric problems. •Computation of Proper Generalized Decomposition modes geometrically.•Adaptation of the Gradient Descent algorithm to the Proper Generalized Decomposition matrix framework.•Application to physical problems with very promising results compared to previous literature.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2024.128579