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Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  07 February 2017

Meng Wu ,
Bernard Mourrain ,
André Galligo  and
Boniface Nkonga
Meng Wu*
Affiliation:
Galaad2, Inria, Sophia Antipolis, France School of Mathematics, Hefei University of Technology, Hefei, Anhui 230000, P.R. China
Bernard Mourrain*
Affiliation:
Galaad2, Inria, Sophia Antipolis, France
André Galligo*
Affiliation:
Laboratoire J. A. Dieudonné, University of Nice, Nice, France
Boniface Nkonga*
Affiliation:
Laboratoire J. A. Dieudonné, University of Nice, Nice, France
*
*Corresponding author. Email addresses: meng.wu@hfut.edu.cn, wumeng@mail.ustc.edu.cn (M. Wu), Bernard.Mourrain@inria.fr (B. Mourrain), Andre.Galligo@unice.fr (A. Galligo), boniface.nkonga@unice.fr (B. Nkonga)
*Corresponding author. Email addresses: meng.wu@hfut.edu.cn, wumeng@mail.ustc.edu.cn (M. Wu), Bernard.Mourrain@inria.fr (B. Mourrain), Andre.Galligo@unice.fr (A. Galligo), boniface.nkonga@unice.fr (B. Nkonga)
*Corresponding author. Email addresses: meng.wu@hfut.edu.cn, wumeng@mail.ustc.edu.cn (M. Wu), Bernard.Mourrain@inria.fr (B. Mourrain), Andre.Galligo@unice.fr (A. Galligo), boniface.nkonga@unice.fr (B. Nkonga)
*Corresponding author. Email addresses: meng.wu@hfut.edu.cn, wumeng@mail.ustc.edu.cn (M. Wu), Bernard.Mourrain@inria.fr (B. Mourrain), Andre.Galligo@unice.fr (A. Galligo), boniface.nkonga@unice.fr (B. Nkonga)
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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 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.

Keywords

Splinemeshes with complex topological structuresextraordinary verticesdimension and basisisogeometric analysisMHD simulation

MSC classification

Secondary: 65D05: Interpolation
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 835 - 866
Copyright
Copyright © Global-Science Press 2017 

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