SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A980-A1000, January 2021.
Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the finite element method analysis and often requires human assistance, especially in complex three-dimensional geometries. When using alternative mesh-free approaches, the problem of mesh generation is simplified to the problem of positioning nodes, a much simpler task, though still not trivial. In this paper we present an algorithm for generation of nodes on arbitrary $d$-dimensional surfaces. This algorithm complements a recently published algorithm for generation of nodes in domain interiors and represents another step toward a fully automated dimension-independent solution procedure for solving partial differential equations. The proposed algorithm generates nodes with variable density on surfaces parameterized over arbitrary parametric domains in a dimension-independent way in $O(N\log N)$ time. It is also compared with existing algorithms for generation of surface nodes for mesh-free methods in terms of quality and execution time.

中文翻译：

---

参数曲面上快速可变密度节点的生成及其在无网格方法中的应用

SIAM科学计算杂志，第43卷，第2期，第A980-A1000页，2021年1月。
域离散化被认为是求解偏微分方程的求解程序的主要部分。网格生成是有限元方法分析中最麻烦的部分，并且通常需要人工协助，尤其是在复杂的三维几何体中，这一点已被广泛接受。当使用替代的无网格方法时，网格生成的问题被简化为定位节点的问题，这是一个简单得多的任务，尽管仍然不容易。在本文中，我们提出了一种在任意$ d $维表面上生成节点的算法。该算法是对最近发布的用于在域内部生成节点的算法的补充，代表了朝着完全自动的与尺寸无关的求解过程求解偏微分方程的步骤。所提出的算法以与尺寸无关的方式在$ O（N \ log N）$的时间内生成在参数化任意参数域上的表面上具有可变密度的节点。在质量和执行时间方面，它也与现有的生成无网格方法的表面节点的算法进行了比较。