IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs: Cetraro, Italy 2012 (Lecture Notes in Mathematics Book 2161)

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow. The contributions were written by Carla Manni and Hendrik Speelers , Vibeke Skytt and Tor Dokken, Lourenco Beirao da Veiga, Annalisa Buffa, Giancarlo Sangalli and Rafael Vazquez, and finally by John Evans and Thomas J.R. Hughes. Providing An Introduction To Isogeometric Methods With A Focus On Their Mathematical Foundations, This Book Is Composed Of Four Chapters, Each Devoted To A Topic Of Special Interests For Isogeometric Methods And Their Theoretical Understanding. It Contains A Tutorial On Splines And Generalizations That Are Used In Cad Parametrizations, And Gives An Overview Of Geometric Modeling Techniques That Can Be Used Within The Isogeometric Approach, With A Focus On Non-tensor Product Splines. Finally, It Presents The Mathematical Properties Of Isogeometric Spaces And Spline Spaces For Vector Field Approximations, And Treats In Detail An Application Of Fundamental Importance: The Isogeometric Simulation Of A Viscous Incompressible Flow. Preface -- Standard And Non‐standard Cagd Tool For Isogeometric Analysis: A Tutorial -- Models For Isogeometric Analysis From Cad -- An Introduction To The Numerical Analysis Of Isogeometric Methods -- Isogeometric Compatible Discretizations For Viscous Incompressible Flow. Edited By Annalisa Buffa, Giancarlo Sangalli. Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow. The contributions were written by Carla Manni and Hendrik Speelers__,__ Vibeke Skytt and Tor Dokken, Lourenco Beirao da Veiga, Annalisa Buffa, Giancarlo Sangalli and Rafael Vazquez, and finally byJohn Evans and Thomas J.R. Hughes. Le site internet de l'éditeur indique : "Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric methods and their theoretical understanding. It contains a tutorial on splines and generalizations that are used in CAD parametrizations, and gives an overview of geometric modeling techniques that can be used within the isogeometric approach, with a focus on non-tensor product splines. Finally, it presents the mathematical properties of isogeometric spaces and spline spaces for vector field approximations, and treats in detail an application of fundamental importance: the isogeometric simulation of a viscous incompressible flow." Front Matter....Pages i-ix Standard and Non-standard CAGD Tools for Isogeometric Analysis: A Tutorial....Pages 1-69 Models for Isogeometric Analysis from CAD....Pages 71-86 An Introduction to the Numerical Analysis of Isogeometric Methods....Pages 87-154 Isogeometric Compatible Discretizations for Viscous Incompressible Flow....Pages 155-193 Back Matter....Pages 195-196