03655nam a2200505 i 4500991003636149707536m o d cr cnu|||unuuu190408s2018 sz a o 100 0 eng d331994911X(electronic bk.)9783319949116(electronic bk.)9783319949109(print)10.1007/978-3-319-94911-6doib14363884-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.353AMS 65-06C.I.M.E. Summer School "Splines and PDEs"<2017 ;Cetraro, Italy>785950Splines and PDEs: from approximation theory to numerical linear algebra[e-book] :Cetraro, Italy 2017 /by Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano ; edited by Tom Lyche, Carla Manni, Hendrik SpeleersCham :Springer,20181 online resource (ix, 318 pages) :illustrations (some color)texttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture Notes in Mathematics,0075-8434 ;2219C.I.M.E. Foundation Subseries ;2219Foundations 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 ApplicationsThis 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.Numerical analysisDifferential equations, partialKunoth, Angelaauthorhttp://id.loc.gov/vocabulary/relators/aut785951Lyche, Tomauthorhttp://id.loc.gov/vocabulary/relators/aut60177Sangalli, GiancarloSerra-Capizzano, StefanoManni, CarlaSpeleers, HendrikPrinted edition:9783319949109Printed edition:9783319949123Lecture notes in mathematics (Springer-Verlag).CIME Foundation subseriesAn electronic book accessible through the World Wide Webhttp://link.springer.com/10.1007/978-3-319-94911-6.b1436388403-03-2208-04-19991003636149707536Splines and PDEs: from approximation theory to numerical linear algebra1749889UNISALENTOle01308-04-19m@ -engsz 00