论文标题
在参数表面上生成快速可变密度节点，并应用于无网格的方法
Fast variable density node generation on parametric surfaces with application to mesh-free methods
论文作者
论文摘要
域离散化被认为是解决部分微分方程的解决方案程序的主要部分。人们普遍认为，网格产生是FEM分析中最麻烦的部分之一，通常需要人类援助，尤其是在复杂的3D几何形状中。当使用替代网格的方法时，将网格生成问题简化为定位节点的问题，这是一个更简单的任务，尽管仍然并不小。在本文中，我们提出了一种用于在任意$ d $维表面上产生节点的算法。该算法补充了最近发表的算法，用于生成域内部的节点，并代表了朝着完全自动化的尺寸无关的解决方案过程迈出的又一步，以求解部分微分方程。所提出的算法在表面上以$ o（n \ log n）$时间的方式以尺寸无关的方式在表面上以可变密度的形式生成节点。还将其与现有的算法在质量和执行时间上生成无网格方法的表面节点。
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 FEM analysis and often requires human assistance, especially in complex 3D 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 towards 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.
