Proper Generalized Decompositions - Cueto, Elías

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Auteur(s) : Cueto, Elías - Alfaro, Icíar - González, David

Editeur : Springer International Publishing Ag

Langue : Anglais

Parution : 01/03/2016

Format : Moyen, de 350g à 1kg

Nombre de pages : 108

Expédition : 178

Dimensions : 23.5 x 15.5 x 0.7

ISBN : 331929993X

Résumé :
This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, non-linear model order reduction and real-time simulation, among others.

Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of Proper Orthogonal Decomposition or Principal Component Analysis to an arbitrary number of dimensions, PGD is able to provide the analyst with very accurate solutions for problems defined in high dimensional spaces, parametric problems and even real-time simulation.

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Biographie:
El?as Cueto is professor of continuum and structural mechanics at the university of Zaragoza since 2010. His research has been devoted to the development of advanced numerical strategies for the simulation of complex phenomena. In particular, in the last years he has worked in model order reduction techniques and real-time simulation for computational surgery and augmented reality applications. His work has been recognized with the J. C. Simo award of the Spanish Society of Numerical Methods in Engineering, the European Scientific Association of Material Forming (ESAFORM) Scientific Prize, and the O.C. Zienkiewicz prize of the European Community on Computational Methods in Applied Sciences, ECCOMAS, among others. He has published more than one hundred papers in the field and is from 2016 president of the Spanish Society of Numerical Methods in Engineering (SEMNI).

Sommaire:
Introduction.- 2 To begin with: PGD for Poisson problems.- 2.1 Introduction.- 2.2 The Poisson problem.- 2.3 Matrix structure of the problem.- 2.4 Matlab code for the Poisson problem.- 3 Parametric problems.- 3.1 A particularly challenging problem: a moving load as a parameter.- 3.2 The problem under the PGD formalism.- 3.2.1 Computation of S(s) assuming R(x) is known.- 3.2.2 Computation of R(x) assuming S(s) is known.- 3.3 Matrix structure of the problem.- 3.4 Matlab code for the influence line problem.- 4 PGD for non-linear problems.- 4.1 Hyperelasticity.- 4.2 Matrix structure of the problem.- 4.2.1 Matrix form of the term T2.- 4.2.2 Matrix form of the term T4.- 4.2.3 Matrix form of the term T6.- 4.2.4 Matrix form for the term T8.- 4.2.5 Matrix form of the term T9.- 4.2.6 Matrix form of the term T10.- 4.2.7 Final comments.- 4.3 Matlab code.- 5 PGD for dynamical problems.- 5.1 Taking initial conditions as parameters.- 5.2 Developing the weak form of the problem.- 5.3 Matrix form of the problem.- 5.3.1 Time integration of the equations of motion.- 5.3.2 Computing a reduced-order basis for the field of initial conditions.- 5.3.3 Projection of the equations onto a reduced, parametric basis.- 5.4 Matlab code.- References.- Index. ...