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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

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 Cr 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 L2-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 Email

Bernard Mourrain Email

André Galligo Email

Boniface Nkonga Email

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