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Higher-order meshing of implicit geometries, Part II: Approximations on manifolds

机译:隐式几何的高阶网格划分,第二部分:流形上的逼近

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A new concept for the higher-order accurate approximation of partial differential equations on manifolds is proposed where a surface mesh composed by higher-order elements is automatically generated based on level-set data. Thereby, it enables a completely automatic workflow from the geometric description to the numerical analysis without any user-intervention. A master level-set function defines the shape of the manifold through its zero-isosurface which is then restricted to a finite domain by additional level-set functions. It is ensured that the surface elements are sufficiently continuous and shape regular which is achieved by manipulating the background mesh. The numerical results show that optimal convergence rates are obtained with a moderate increase in the condition number compared to handcrafted surface meshes. (C) 2017 Elsevier B.V. All rights reserved.
机译:提出了关于流形上偏微分方程的高阶精确逼近的新概念,其中基于水平集数据自动生成由高阶元素组成的曲面网格。因此,它可以实现从几何描述到数值分析的全自动工作流程,而无需用户干预。主水平集函数通过其零等值面定义歧管的形状,然后通过其他水平集函数将其限制为有限域。确保表面元素足够连续且形状规则,这是通过操纵背景网格实现的。数值结果表明,与手工制作的表面网格相比,在条件数适度增加的情况下可获得最佳收敛速度。 (C)2017 Elsevier B.V.保留所有权利。

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