Volume 21, Issue 3
Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures

Meng Wu ,  Bernard Mourrain ,  Andre Galligo and Boniface Nkonga


Commun. Comput. Phys., 21 (2017), pp. 835-866.

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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 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.

  • History

Published online: 2018-04

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