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Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures

Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures
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Year:    2017

Author:    Meng Wu, Bernard Mourrain, André Galligo, Boniface Nkonga

Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 835–866

Abstract

Motivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present splines defined over a rectangular mesh with a complex topological structure, i.e., with extraordinary vertices. These splines are piecewise polynomial functions of bi-degree (d,d) and $C^r$ parameter continuity. And we compute their dimension and exhibit basis functions called Hermite bases for bicubic spline spaces. We investigate their potential applications for solving partial differential equations (PDEs) over a physical domain in the framework of Isogeometric analysis. For instance, we analyze the property of approximation of these spline spaces for the $L^2$-norm; we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization, although the fact that the basis functions are singular at extraordinary vertices.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0030

Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 835–866

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:   

Author Details

Meng Wu

Bernard Mourrain

André Galligo

Boniface Nkonga

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