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
Author Details
Meng Wu Email
Bernard Mourrain Email
André Galligo Email
Boniface Nkonga Email
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