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Réduction de modèles par des méthodes de décomposition orthogonale propre by Henri, Thibault

Réduction de modèles par des méthodes de décomposition orthogonale propre

by Thibault Henri
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Book cover type: Paperback
  • ISBN13: 9798873861477
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 140
  • Original Price: USD 41.04
  • Language: French
  • Edition: N/A
  • Item Weight: 254 grams
  • BISAC Subject(s): Schools / Levels / Higher

La décomposition orthogonale propre (proper orthogonal decomposition - POD) est connue sous d'autres noms: la décomposition de Karhunen-Loeve et l'analyse en composantes principales (principal component analysis) renvoient à des méthodes statistiques. Le terme de décomposition orthogonale propre est introduit dans le cadre de l'étude de la turbulence, l'idée consiste à étudier la turbulence en extrayant des modes propres de l'écoulement - appelés structures cohérentes - qui maximisent l'énergie. La décomposition orthogonale propre apparaît également comme une méthode de Galerkin en analyse numérique et on utilise alors le terme de méthode de POD-Galerkin. Qu'il s'agisse de l'étude des systèmes entrée/sortie ou de la résolution numérique d'équations aux dérivées partielles, l'intérêt de ces méthodes est de permettre une réduction des modèles, l'obtention de modèles réduits présente un intérêt particulier dans le cadre des problèmes de contrôle des équations aux dérivées partielles.

Cet ouvrage propose un essai de présentation unifiée de ces méthodes de décomposition orthogonale propre, avant d'aborder le point de vue de la résolution numérique des équations aux dérivées partielles, notamment dans le cadre d'un exemple de problème de contrôle optimal.

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