Splines and PDEs: From Approximation Theory to Numerical Linear Algebra
Cetraro, Italy 2017
Seiten
2018
|
1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-94910-9 (ISBN)
Springer International Publishing (Verlag)
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.
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 | 22.09.2018 |
|---|---|
| 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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