C.I.M.E. Foundation Subseries

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

Authors: Kunoth, A., Lyche, T., Sangalli, G., Serra-Capizzano, S.

Editors: Lyche, Tom, Manni, Carla, Speleers, Hendrik (Eds.)

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  • Contains a multi-perspective exposition of the use of splines in the numerical treatment of PDEs
  • Covers mathematical foundations, numerical paradigms, and implementational issues
  • Collects contributions from internationally renowned experts in the field
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eBook $59.99
price for USA in USD
  • ISBN 978-3-319-94911-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-94910-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. 
A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. 
The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.

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Table of contents (4 chapters)

Table of contents (4 chapters)
  • Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement

    Pages 1-76

    Lyche, Tom (et al.)

  • Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs

    Pages 77-159

    Kunoth, Angela

  • Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations

    Pages 161-236

    Garoni, Carlo (et al.)

  • Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications

    Pages 237-315

    Hughes, Thomas J. R. (et al.)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-319-94911-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-94910-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Splines and PDEs: From Approximation Theory to Numerical Linear Algebra
Book Subtitle
Cetraro, Italy 2017
Authors
Editors
  • Tom Lyche
  • Carla Manni
  • Hendrik Speleers
Series Title
C.I.M.E. Foundation Subseries
Series Volume
2219
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-94911-6
DOI
10.1007/978-3-319-94911-6
Softcover ISBN
978-3-319-94910-9
Edition Number
1
Number of Pages
IX, 318
Number of Illustrations
11 b/w illustrations, 51 illustrations in colour
Topics