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Quadratic splines on quad-tri meshes: Construction and an application to simulations on watertight reconstructions of trimmed surfaces
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-10-15 , DOI: 10.1016/j.cma.2021.114174
Deepesh Toshniwal 1
Affiliation  

Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar and non-planar meshes of arbitrary topology), we present the construction of quadratic splines of mixed smoothness — C1 smooth away from the unstructured regions of T and C0 smooth otherwise. The splines have several useful B-spline-like properties – partition of unity, non-negativity, local support and linear independence – and allow for straightforward imposition of boundary conditions. We propose a non-nested refinement process for the splines with multiple advantages — a simple computer implementation, reduction in the footprint of C0 smoothness, boundary preservation, and excellent approximation behaviour in simulations. Furthermore, the refinement process leaves the splines invariant on the mesh boundary. Numerical tests indicate that the spline spaces demonstrate optimal approximation behaviour in the L2 and H1 norms under mesh refinement, and provide a viable approach to simulations on watertight reconstructions of trimmed surfaces.



中文翻译:

四边形网格上的二次样条:构造及其在修剪表面水密重建模拟中的应用

给定一个由四边形和三角形组成的非结构化网格(我们允许任意拓扑的平面和非平面网格),我们提出了混合光滑度的二次样条的构造—— C1 平滑远离非结构化区域 C0否则平滑。样条具有几个有用的类似 B 样条的属性——统一性、非负性、局部支持和线性独立性的划分——并允许直接施加边界条件。我们为具有多种优势的样条提出了一个非嵌套的细化过程——一个简单的计算机实现,减少了C0模拟中的平滑度、边界保持和出色的近似行为。此外,细化过程使网格边界上的样条保持不变。数值测试表明,样条空间在2H1 网格细化下的规范,并提供一种可行的方法来模拟修剪表面的水密重建。

更新日期:2021-10-15
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