Mesh size functions for implicit geometries and PDE-based gradient limiting
Mesh size functions for implicit geometries and PDE-based gradient limiting
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DOI：
10.1007/s00366-006-0014-1
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发表时间：
2006-09-01
影响因子：
8.7
通讯作者：
Persson, Per-Olof
中科院分区：
文献类型：
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作者：
Persson, Per-Olof
网格生成和网格增强算法通常需要一个网格大小函数来指定所需的单元大小。我们提出的算法自动生成的尺寸函数，离散化的背景网格，通过使用距离函数和数值PDE求解器。考虑到局部特征尺寸和边界曲率，尺寸函数适应于几何形状。它还遵守限制相邻图元的大小比例的放坡约束。我们制定的中轴变换的特征尺寸，并展示了如何计算它准确地从距离函数。我们提出了一个新的梯度限制方程的网格分级的要求，我们展示了如何解决它的数值与Hamilton-Jacobi求解器。我们展示了在2D和3D中使用笛卡尔和非结构化背景网格的技术的例子，以及图像的数值适应和网格生成的应用程序。
Mesh generation and mesh enhancement algorithms often require a mesh size function to specify the desired size of the elements. We present algorithms for automatic generation of a size function, discretized on a background grid, by using distance functions and numerical PDE solvers. The size function is adapted to the geometry, taking into account the local feature size and the boundary curvature. It also obeys a grading constraint that limits the size ratio of neighboring elements. We formulate the feature size in terms of the medial axis transform, and show how to compute it accurately from a distance function. We propose a new Gradient Limiting Equation for the mesh grading requirement, and we show how to solve it numerically with Hamilton-Jacobi solvers. We show examples of the techniques using Cartesian and unstructured background grids in 2D and 3D, and applications with numerical adaptation and mesh generation for images.