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Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

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  • © 2018

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Overview

Authors:
  1. Angela Kunoth

    1. Mathematical Institute, University of Cologne, Cologne, Germany

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  2. Tom Lyche

    1. Department of Mathematics, University of Oslo, Oslo, Norway

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  3. Giancarlo Sangalli

    1. Department of Mathematics, University of Pavia, Pavia, Italy

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  4. Stefano Serra-Capizzano

    1. Department of Science and High Technology, University of Insubria, Como, Italy

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Editors:
  1. Tom Lyche

    1. Department of Mathematics, University of Oslo, Oslo, Norway

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  2. Carla Manni

    1. Department of Mathematics, University of Rome Tor Vergata, ROMA, Italy

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  3. Hendrik Speleers

    1. Department of Mathematics, University of Rome Tor Vergata, ROMA, Italy

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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

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

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

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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)

  1. Front Matter

    Pages i-ix
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  2. Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement

    • Tom Lyche, Carla Manni, Hendrik Speleers
    Pages 1-76
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  3. Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs

    • Angela Kunoth
    Pages 77-159
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  4. Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations

    • Carlo Garoni, Stefano Serra-Capizzano
    Pages 161-236
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  5. Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications

    • Thomas J. R. Hughes, Giancarlo Sangalli, Mattia Tani
    Pages 237-315
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  6. Back Matter

    Pages 317-318
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Authors, Editors and Affiliations

  • Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche, Tom Lyche

  • Department of Mathematics, University of Rome Tor Vergata, ROMA, Italy

    Carla Manni, Hendrik Speleers

  • Mathematical Institute, University of Cologne, Cologne, Germany

    Angela Kunoth

  • Department of Mathematics, University of Pavia, Pavia, Italy

    Giancarlo Sangalli

  • Department of Science and High Technology, University of Insubria, Como, Italy

    Stefano Serra-Capizzano

About the editors

To be Provided.

Bibliographic Information

  • Book Title: Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

  • Book Subtitle: Cetraro, Italy 2017

  • Authors: Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano

  • Editors: Tom Lyche, Carla Manni, Hendrik Speleers

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-94911-6

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Softcover ISBN: 978-3-319-94910-9Published: 21 September 2018

  • eBook ISBN: 978-3-319-94911-6Published: 20 September 2018

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 318

  • Number of Illustrations: 11 b/w illustrations, 51 illustrations in colour

  • Topics: Numerical Analysis, Approximations and Expansions, Partial Differential Equations

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