SIAM Journal on Scientific Computing, Volume 43, Issue 1, Page A242-A257, January 2021.
Mesh-free solvers for partial differential equations perform best on scattered quasi-uniform nodes. Computational efficiency can be improved by using nodes with greater spacing in regions of less activity. However, there is no ideal way to generate nodes for these solvers. We present an advancing front type method to generate variable density nodes in two dimensions (2-D) and three dimensions (3-D) with clear generalization to higher dimensions. The exhibited cost of generating a node set of size $N$ in 2-D and 3-D with the present method is $O(N)$.

中文翻译：

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快速可变密度3-D节点生成

SIAM科学计算杂志，第43卷，第1期，第A242-A257页，2021年1月。无
网格的偏微分方程求解器在分散的拟均匀节点上表现最佳。通过在活动较少的区域中使用具有较大间距的节点，可以提高计算效率。但是，没有为这些求解器生成节点的理想方法。我们提出了一种先进的前沿类型方法，可以在二维（2-D）和三维（3-D）中生成可变密度节点，并且可以将其推广到更高的维度。用本方法生成2-D和3-D尺寸为$ N $的节点集的展示成本为$ O（N）$。