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

1. Front Matter

   Pages i-ix

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2. Standard and Non-standard CAGD Tools for Isogeometric Analysis: A Tutorial

   • Carla Manni, Hendrik Speleers

   Pages 1-69

3. Models for Isogeometric Analysis from CAD

   • Vibeke Skytt, Tor Dokken

   Pages 71-86

4. An Introduction to the Numerical Analysis of Isogeometric Methods

   • L. Beirão da Veiga, A. Buffa, G. Sangalli, R. Vázquez

   Pages 87-154

5. Isogeometric Compatible Discretizations for Viscous Incompressible Flow

   • John A. Evans, Thomas J. R. Hughes

   Pages 155-193

6. Back Matter

   Pages 195-196

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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 Speelers, Vibeke 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. 

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

“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)

• IMATI - CNR , Pavia, Italy

  Annalisa Buffa

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

  Giancarlo Sangalli

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