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  • © 2016

IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs

Cetraro, Italy 2012

  • Contains a clear exposition of the mathematical structure of isogeometric analysis

  • Contains a very illustrative application to the Navier Stokes equation

  • The format of courses is well-balanced with an excellent presentation

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2161)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
  2. Models for Isogeometric Analysis from CAD

    • Vibeke Skytt, Tor Dokken
    Pages 71-86
  3. An Introduction to the Numerical Analysis of Isogeometric Methods

    • L. Beirão da Veiga, A. Buffa, G. Sangalli, R. Vázquez
    Pages 87-154
  4. Isogeometric Compatible Discretizations for Viscous Incompressible Flow

    • John A. Evans, Thomas J. R. Hughes
    Pages 155-193
  5. Back Matter

    Pages 195-196

About this book

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance:  the isogeometric simulation of a viscous incompressible flow. 

The contributions were written by Carla Manni and Hendrik SpeelersVibeke Skytt and Tor Dokken, Lourenco Beirao da Veiga, Annalisa Buffa, Giancarlo Sangalli and Rafael Vazquez, and finally by John Evans and Thomas J.R. Hughes. 




Keywords

  • Isogeometric analysis
  • Splines
  • Finite element method
  • Computer aided geometric design
  • Approximation of partial differential equations

Reviews

“All chapters are illustrated with many high-quality figures, most of them in color. This greatly helps the reader understand the underlying concepts. … I fully recommend it as good material for traditionally educated finite element experts who want to extend their knowledge to this new area, and also for finite element novices who want to get into the field.” (Kai Diethelm, Computing Reviews, February, 2017)

Editors and Affiliations

  • IMATI - CNR , Pavia, Italy

    Annalisa Buffa

  • Dipartimento di Matematica, Università di Pavia, Pavia, Italy

    Giancarlo Sangalli

Bibliographic Information

  • Book Title: IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs

  • Book Subtitle: Cetraro, Italy 2012

  • Editors: Annalisa Buffa, Giancarlo Sangalli

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-42309-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Softcover ISBN: 978-3-319-42308-1Published: 06 October 2016

  • eBook ISBN: 978-3-319-42309-8Published: 05 October 2016

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 193

  • Number of Illustrations: 11 b/w illustrations, 70 illustrations in colour

  • Topics: Numerical Analysis, Computational Science and Engineering, Computer Graphics

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions