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Separated Representations and PGD-Based Model Reduction

Fundamentals and Applications

  • Book
  • © 2014

Overview

Editors:
  1. Francisco Chinesta

    1. Ecole Centrale de Nantes, Nantes, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Pierre Ladevèze

    1. Ecole Normale Supérieure de Cachan, Cachan, France

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    You can also search for this editor in PubMed   Google Scholar

  • First book on this topic addressing a large audience (from undergraduate students to experienced researchers)
  • New ways of problem solving

Part of the book series: CISM International Centre for Mechanical Sciences (CISM, volume 554)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-vii
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  2. Model Order Reduction based on Proper Orthogonal Decomposition

    • Elías Cueto, Francisco Chinesta, Antonio Huerta
    Pages 1-26

  3. PGD for solving multidimensional and parametric models

    • Francisco Chinesta, Elías Cueto, Antonio Huerta
    Pages 27-89

  4. PGD in linear and nonlinear Computational Solid Mechanics

    • Pierre Ladevèze
    Pages 91-152

  5. Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications

    • Gianluigi Rozza
    Pages 153-227
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About this book

The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,…), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.

Editors and Affiliations

  • Ecole Centrale de Nantes, Nantes, France

    Francisco Chinesta

  • Ecole Normale Supérieure de Cachan, Cachan, France

    Pierre Ladevèze

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