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Smooth Bezier surfaces over unstruct...

Bercovier, Michel.

Smooth Bezier surfaces over unstructured quadrilateral meshes

Record Type:	Electronic resources : Monograph/item
Title/Author:	Smooth Bezier surfaces over unstructured quadrilateral meshesby Michel Bercovier, Tanya Matskewich.
Author:	Bercovier, Michel.
other author:	Matskewich, Tanya.
Published:	Cham :Springer International Publishing :2017.
Description:	xx, 192 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Finite element method.
Online resource:	http://dx.doi.org/10.1007/978-3-319-63841-6
ISBN:	9783319638416$q(electronic bk.)

Smooth Bezier surfaces over unstructured quadrilateral meshes
Bercovier, Michel.

Smooth Bezier surfaces over unstructured quadrilateral meshes[electronic resource] /by Michel Bercovier, Tanya Matskewich. - Cham :Springer International Publishing :2017. - xx, 192 p. :ill., digital ;24 cm. - Lecture notes of the Unione Matematica Italiana,221862-9113 ;. - Lecture notes of the Unione Matematica Italiana ;15..

Introduction -- G1-smooth Surfaces -- C1 smooth surfaces -- MDSs: quadrilateral meshes -- Global MDSs -- MDSs for a smooth boundary -- Computational examples -- Conclusions -- Two-patch geometry and the G1 construction -- Illustrations for the thin plate problem -- Mixed MDSs of degrees 4 and 5 -- Technical lemmas -- Minimisation problems -- G1 is equivalent to C1 -- Bibliography -- References.

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 Bezier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bezier 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.

ISBN: 9783319638416$q(electronic bk.)

Standard No.: 10.1007/978-3-319-63841-6doiSubjects--Topical Terms:

184533
Finite element method.

LC Class. No.: TA347.F5

Dewey Class. No.: 518.25

Smooth Bezier surfaces over unstructured quadrilateral meshes
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505 0 $a Introduction -- G1-smooth Surfaces -- C1 smooth surfaces -- MDSs: quadrilateral meshes -- Global MDSs -- MDSs for a smooth boundary -- Computational examples -- Conclusions -- Two-patch geometry and the G1 construction -- Illustrations for the thin plate problem -- Mixed MDSs of degrees 4 and 5 -- Technical lemmas -- Minimisation problems -- G1 is equivalent to C1 -- Bibliography -- References.
520 $a 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 Bezier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bezier 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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