Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017
 
 
Springer (Verlag)
  • erschienen am 21. September 2018
 
  • Buch
  • |
  • Softcover
  • |
  • IX, 318 Seiten
978-3-319-94910-9 (ISBN)
 
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.
Book
1st ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 51 farbige Abbildungen, 11 s/w Abbildungen
  • |
  • Bibliographie
  • Höhe: 233 mm
  • |
  • Breite: 154 mm
  • |
  • Dicke: 25 mm
  • 527 gr
978-3-319-94910-9 (9783319949109)
10.1007/978-3-319-94911-6
weitere Ausgaben werden ermittelt
To be Provided.

Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement.- Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs.- Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations.- Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications.

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