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Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

  • Angela Kunoth
  • Tom Lyche
  • Giancarlo Sangalli
  • Stefano Serra-Capizzano
  • Tom Lyche
  • Carla Manni
  • Hendrik Speleers

Part of the Lecture Notes in Mathematics book series (LNM, volume 2219)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2219)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Thomas J. R. Hughes, Giancarlo Sangalli, Mattia Tani
    Pages 237-315
  3. Back Matter
    Pages 317-318

About this book

Introduction

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.

Keywords

Adaptive Multiscale Methods Isogeometric Analysis Numerical Treatment of PDEs Spectral Analysis Spline Approximation

Authors and affiliations

  • Angela Kunoth
    • 1
  • Tom Lyche
    • 2
  • Giancarlo Sangalli
    • 3
  • Stefano Serra-Capizzano
    • 4
  1. 1.Mathematical InstituteUniversity of CologneCologneGermany
  2. 2.Department of MathematicsUniversity of OsloOsloNorway
  3. 3.Department of MathematicsUniversity of PaviaPaviaItaly
  4. 4.Department of Science and High TechnologyUniversity of InsubriaComoItaly

Editors and affiliations

  • Tom Lyche
    • 1
  • Carla Manni
    • 2
  • Hendrik Speleers
    • 3
  1. 1.Department of MathematicsUniversity of OsloOsloNorway
  2. 2.Department of MathematicsTor Vergata UniversityRomaItaly
  3. 3.Department of MathematicsUniv degli Studi di Roma Tor VergataRomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-94911-6
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-94910-9
  • Online ISBN 978-3-319-94911-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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