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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DOI：
10.4208/cicp.oa-2016-0030
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发表时间：
2017-02
影响因子：
3.7
通讯作者：
Meng Wu;B. Mourrain;A. Galligo;B. Nkonga
中科院分区：
文献类型：
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作者：
Meng Wu;B. Mourrain;A. Galligo;B. Nkonga
受托卡马克磁流体动力学（MHD）模拟等几何分析的启发，本文提出了一种新的定义在任意拓扑矩形网格上的样条函数，它是二次（d，d）的分段多项式函数，且C^r参数连续。特别地，我们计算了它们的维数，并给出了双三次样条空间的Hermite基函数。我们研究他们的潜在应用解决偏微分方程（PDE）在一个复杂的物理域的框架中的等几何分析。特别地，我们分析了这些样条空间的L2-范数逼近的性质。尽管事实上，基函数是奇异的非常顶点，我们表明，最佳逼近阶和数值收敛速度达到通过设置一个适当的参数化。
Motivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present a new type of splines defined over a rectangular mesh with arbitrary topology, which are piecewise polynomial functions of bidegree (d,d) and C^r parameter continuity. In particular, 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 complex physical domain in the framework of Isogeometric analysis. In particular, we analyze the property of approximation of these spline spaces for the L2-norm. Despite the fact that the basis functions are singular at extraordinary vertices, we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization.