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.)
Free Preview- 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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- About this book
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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. - About the authors
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To be Provided.
- Table of contents (4 chapters)
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Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement
Pages 1-76
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Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs
Pages 77-159
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Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations
Pages 161-236
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Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications
Pages 237-315
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Table of contents (4 chapters)
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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
-
- Angela Kunoth
- Tom Lyche
- Giancarlo Sangalli
- Stefano Serra-Capizzano
- 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
