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Lyche / Manni / Speleers

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

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eBook. PDF

eBook

2018

318 S. IX, 318 p. 62 illus., 51 illus. in color..

In englischer Sprache

Springer International Publishing. ISBN 978-3-319-94911-6

Das Werk ist Teil der Reihe: C.I.M.E. Foundation Subseries Lecture Notes in Mathematics

Produktbeschreibung

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.