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Proper Generalized Decompositions

An Introduction to Computer Implementation with Matlab

  • Book
  • © 2016

Overview

Authors:
  1. Elías Cueto

    1. Aragon Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

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  2. David González

    1. Aragon Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

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    You can also search for this author in PubMed   Google Scholar

  3. Icíar Alfaro

    1. Aragon Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

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    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Elías Cueto, David González, Icíar Alfaro
    Pages 1-5

  3. To Begin With: PGD for Poisson Problems

    • Elías Cueto, David González, Icíar Alfaro
    Pages 7-19

  4. Parametric Problems

    • Elías Cueto, David González, Icíar Alfaro
    Pages 21-38

  5. PGD for Non-linear Problems

    • Elías Cueto, David González, Icíar Alfaro
    Pages 39-63

  6. PGD for Dynamical Problems

    • Elías Cueto, David González, Icíar Alfaro
    Pages 65-89

  7. Back Matter

    Pages 91-96
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Keywords

About this book

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.

  


Reviews

“This book provides a brief introduction to Proper Generalized Decompositions (PGD), with strong emphasis on computational aspects. The book discusses the implementation of PGD for the Poisson problem, parameter-dependent problems, linear-elasticity, and dynamical problems. For every problem, matrix assembly is developed and Matlab routines are presented.” (Dante Kalise, Mathematical Reviews, July, 2017)

Authors and Affiliations

  • Aragon Institute of Engineering Research, University of Zaragoza, Zaragoza, Spain

    Elías Cueto, David González, Icíar Alfaro

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