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A unified approach to the deformation of simplicial and non-simplicial meshes in two and three dimensions with guaranteed validity

机译：保证有效性的统一方法，用于在两个和三个维度上简化单纯形和非单纯形网格

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摘要

In this paper we present a unified formulation that embraces the problem of deformation of simplicial and non-simplicial, structured and unstructured, two and three dimensional meshes. The method is formulated so as to avoid, by construction, the generation of invalid elements. At first, we show that in all cases above, invalid elements are generated by the same collapse mechanism. Specifically, an invalid element is formed when a mesh vertex leaves its ball, i.e. the polyhedral cavity formed by all triangular faces (in three dimensions) or edges (in two dimensions) that are edge-connected to the vertex. Next, we show that, in all cases above, collapse of elements is avoided by connecting with a spring each vertex in the grid with its normal projection on the ball boundaries. The proposed method is demonstrated on a number of difficult example problems denoted by severe grid deformations, and with the help of a variety of grid types.
机译：在本文中，我们提出了一个统一的公式，其中包含了简单网格和非简单网格，结构化网格和非结构化二维和三维网格的变形问题。制定该方法以便通过构造避免生成无效元素。首先，我们表明在以上所有情况下，无效元素都是由相同的折叠机制生成的。具体地，当网格顶点离开其球时，即由边缘连接到该顶点的所有三角形面（在三个维度上）或边缘（在两个维度上）形成的多面体腔，会形成无效元素。接下来，我们表明，在上述所有情况下，通过使用弹簧连接网格中每个顶点（其法线投影在球边界上）来避免元素崩溃。在许多严重的网格变形所代表的困难示例问题上，并借助各种网格类型，对所提出的方法进行了演示。

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