Splines and PDEs: From Approximation Theory to Numerical Linear Algebra - Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Cetraro, Italy 2017
Buch | Softcover
IX, 318 Seiten
2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-94910-9 (ISBN)
74,89 inkl. MwSt
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.

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.

Erscheinungsdatum
Reihe/Serie C.I.M.E. Foundation Subseries
Lecture Notes in Mathematics
Zusatzinfo IX, 318 p. 62 illus., 51 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 504 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Adaptive Multiscale Methods • isogeometric analysis • Numerical Treatment of PDEs • Partial differential equations • Spectral Analysis • Spline Approximation
ISBN-10 3-319-94910-1 / 3319949101
ISBN-13 978-3-319-94910-9 / 9783319949109
Zustand Neuware
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