Overview
- With a foreword by T.J.R. Hughes
- Represents a step forward in Isogeometric Analysis and its applications
- Provides a bridge between Finite Element Methods and Isogeometric Analysis
Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 22)
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Table of contents (7 chapters)
Keywords
About this book
Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.
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Bibliographic Information
Book Title: Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes
Authors: Michel Bercovier, Tanya Matskewich
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-319-63841-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-63840-9Published: 11 October 2017
eBook ISBN: 978-3-319-63841-6Published: 03 October 2017
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: XX, 192
Number of Illustrations: 5 b/w illustrations, 59 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Geometry