Proper Generalized Decompositions

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Beschreibung

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.



First PGD book intended as a manual in the basics of the method

Only available reference that includes Matlab code to ease the process

Covers some of the most popular aspects of the technique, particularly real-time simulation

Includes supplementary material: sn.pub/extras



Inhalt

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.

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Produktinformationen

Titel
Proper Generalized Decompositions
Untertitel
An Introduction to Computer Implementation with Matlab
Autor
EAN
9783319299938
ISBN
331929993X
Format
Kartonierter Einband
Herausgeber
Springer International Publishing
Genre
Mathematik
Anzahl Seiten
108
Gewicht
178g
Größe
H235mm x B155mm x T6mm
Jahr
2016
Untertitel
Englisch
Auflage
1st ed. 2016
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