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Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision

机译：基于扩展Catmull-Clark细分的最小曲面的等几何分析

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We study the application of Isogeometric Analysis based on extended Catmull-Clark subdivision approach for the minimal surface models on planar domains. Subdivision approaches are compatible with NURBS as the standard of CAD systems which are capable of the refinability of B-spline techniques. The exactness of the physical domain of interest is fixed patchwise by the coarsest quadrilateral mesh and maintained through refinement. By performing extended Catmull-Clark subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of bicubic splines while maintaining its original exactness. The finite element space is spanned by the limit form of extended Catmull-Clark subdivision, which possesses C-1 smoothness and the flexibility of mesh topology. In this work we establish the approximation properties and inverse inequalities for this space which are similar to the ones of classical finite elements. The approximation estimates for the minimal surface models are developed with the aid of the H-1-norm convergence property of its linearization model. The performance of numerical tests is consistent with the theoretical results. We also compare these numerical calculations with classical linear finite element methods. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们研究了基于扩展Catmull-Clark细分方法的等几何分析在平面域上最小曲面模型中的应用。细分方法与作为CAD系统标准的NURBS兼容，能够完善B样条技术。感兴趣的物理域的准确性由最粗的四边形网格逐块固定，并通过精化来保持。通过执行扩展的Catmull-Clark细分，可以重复完善控制网格，并将几何形状描述为无限的双三次样条集，同时保持其原始精度。有限元空间由扩展的Catmull-Clark细分的极限形式扩展，该细分形式具有C-1平滑度和网格拓扑的灵活性。在这项工作中，我们建立了与经典有限元相似的近似性质和逆不等式。借助其线性化模型的H-1-范数收敛性，可以开发出最小曲面模型的近似估计。数值测试的性能与理论结果一致。我们还将这些数值计算与经典线性有限元方法进行比较。 （C）2018 Elsevier B.V.保留所有权利。

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