Bajaj Chandrajit
Center for Computational Visualization, Department of Computer Sciences, & Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, http://www.cs.utexas.edu/users/bajaj.
Jpn J Ind Appl Math. 2005 Jun 1;22(2):167-177. doi: 10.1007/BF03167436.
We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initial quadrilateral or an initial hexahedral scaffold conforming to individual particles. The scaffolds are subsequently refined via applications of recursive subdivision (splitting and averaging rules). Our choice of averaging rules yield a particle conforming quadrilateral/hexahedral mesh, of good quality, along with being smooth and differentiable in the limit. Extensions of the basic scheme to dynamic re-meshing in the case of addition, deletion, and moving particles are also discussed. Motivating applications of the use of these static and dynamic meshes for particle systems include the mechanics of epoxy/glass composite materials, bio-molecular force field calculations, and gas hydrodynamics simulations in cosmology.
我们分别提出了基于拉盖尔-沃罗诺伊的细分算法，用于二维和三维有界区域内粒子系统的四边形和六面体网格划分。粒子是圆形或球形域上的光滑函数。该算法首先将包含粒子的有界区域分解为沃罗诺伊单元，然后将这些单元进一步分解为符合单个粒子的初始四边形或初始六面体支架。随后通过应用递归细分（分裂和平均规则）对支架进行细化。我们选择的平均规则产生了一个与粒子相符的高质量四边形/六面体网格，并且在极限情况下是光滑且可微的。还讨论了在添加、删除和移动粒子的情况下将基本方案扩展到动态重新网格化的问题。将这些静态和动态网格用于粒子系统的激励应用包括环氧/玻璃复合材料的力学、生物分子力场计算以及宇宙学中的气体流体动力学模拟。
