Splines and PDEs: From Approximation Theory to Numerical Linear Algebra - pr_35420

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017

By Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano

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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.

Product code: 9783319949109

ISBN 9783319949109
Dimensions (HxWxD in mm) H235xW155
Edition 1st ed. 2018
No. Of Pages 318
Series Lecture Notes in Mathematics
Publisher Springer International Publishing AG
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.