Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

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Cetraro, Italy 2017
Author(s): Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano, Tom Lyche, Carla Manni, Hendrik Speleers
Format: Paperback
Publisher: Springer International Publishing AG, Switzerland
Imprint: Springer International Publishing AG
ISBN-13: 9783319949109, 978-3319949109

Synopsis

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 [url] 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.