On the Existence of a Progressive Variational Vademecum based on the Proper Generalized Decomposition for a Class of Elliptic Parameterized Problems
Visualitza/
Impacte
Scholar |
Altres documents de l'autoria: Falco, Antonio; Montes Sánchez, Nicolás; Chinesta, F.; Hilario Pérez, Lucia; Mora, Marta Covadonga
Metadades
Mostra el registre complet de l'elementcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7035
comunitat-uji-handle3:10234/8617
comunitat-uji-handle4:
INVESTIGACIONMetadades
Títol
On the Existence of a Progressive Variational Vademecum based on the Proper Generalized Decomposition for a Class of Elliptic Parameterized ProblemsAutoria
Data de publicació
2018-03Editor
ElsevierCita bibliogràfica
FALCÓ, A., et al. On the Existence of a Progressive Variational Vademecum based on the Proper Generalized Decomposition for a Class of Elliptic Parameterized Problems. Journal of Computational and Applied Mathematics, 2018, vol. 330, p. 1093-1107.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://www.sciencedirect.com/science/article/pii/S0377042717303965#d1e512Versió
info:eu-repo/semantics/publishedVersionParaules clau / Matèries
Resum
In this study, we present the mathematical analysis needed to explain the convergence of a progressive variational vademecum based on the proper generalized decomposition (PGD). The PGD is a novel technique that was ... [+]
In this study, we present the mathematical analysis needed to explain the convergence of a progressive variational vademecum based on the proper generalized decomposition (PGD). The PGD is a novel technique that was developed recently for solving problems with high dimensions, and it also provides new approaches for obtaining the solutions of elliptic and parabolic problems via the abstract separation of variables method. This new scenario requires a mathematical framework in order to justify its application to the solution of numerical problems and the PGD can help in the change to this paradigm. The main aim of this study is to provide a mathematical environment for defining the notion of progressive variational vademecum. We prove the convergence of this iterative procedure and we also provide the first order optimality conditions in order to construct the numerical approximations of the parameterized solutions. In particular, we illustrate this methodology based on a robot path planning problem. This is one of the common tasks when designing the trajectory or path of a mobile robot. The construction of a progressive variational vademecum provides a novel methodology for computing all the possible paths from any start and goal positions derived from a harmonic potential field in a predefined map. [-]
Drets d'accés
© 2017 Elsevier B.V. All rights reserved.
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
Apareix a les col.leccions
- EMC_Articles [832]