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快速泡泡布点方法
引用本文:齐楠,聂玉峰,张伟伟.快速泡泡布点方法[J].计算物理,2012,29(3):333-339.
作者姓名:齐楠  聂玉峰  张伟伟
作者单位:西北工业大学理学院应用数学系, 陕西 西安, 710129
基金项目:国家自然科学基金(11071196,90916027);西北工业大学本科毕业设计重点扶持项目,西北工业大学博士论文创新基金资助项目
摘    要:泡泡布点算法能够在复杂区域上不经过人工干预生成高质量的节点集,为提高其计算效率,本文对泡泡布点法做三方面修正:①让泡泡运动的粘性系数c随时间的推移逐渐增大以加速收敛,每轮模拟结束后需增删泡泡时再给c赋一个较小的值以确保泡泡分布的质量;②求解控制泡泡运动的常微分方程组时选用时间复杂度较小的数值算法.算例表明数值方法精度在一定程度上的降低对节点质量的影响不大,能有效的节约计算时间;③取消对泡泡交叠率的排序,通过设置阈值控制泡泡的增删.算例表明以上方案节约运行时间40%以上,所布置节点对应的Delaunay三角单元网格平均质量高于0.9.该快速算法高效且能够生成高质量的节点集.

关 键 词:泡泡布点方法  粘性系数  计算效率  网格生成  
收稿时间:2011-08-08
修稿时间:2011-12-09

A Fast Node Placement Method with Bubble Simulation
QI Nan , NIE Yufeng , ZHANG Weiwei.A Fast Node Placement Method with Bubble Simulation[J].Chinese Journal of Computational Physics,2012,29(3):333-339.
Authors:QI Nan  NIE Yufeng  ZHANG Weiwei
Institution:Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China
Abstract:Node placement method with bubble simulation can generate high-qualify node sets in complex domains.However,its efficiency needs to be increased.Several modifications were done to reduce the cost of simulation.Firstly,let viscosity coefficient c gradually increases instead of being taken as a constant.It speeds up convergency.Moreover,at the end of each round simulation,in which bubbles additions or deletions are operated,c is assigned to a small value in order to ensure quality of bubble distribution.Secondly,as solving ordinary differential equations that control movement of bubbles,a low order numerical algorithm is chosen.Finally,sort process of overlapping rate of bubbles is removed.It is replaced by setting only threshold for bubbles additions and deletions.Numerial examples show that computing cost decreases by approximately 40% and average quality of Delaunay triangulation corresponding to node set is over 0.9.It shows that the algorithms are efficient and generate node sets with high-quality.
Keywords:node placement method with bubbles simulation  viscosity coefficient  algorithm efficiency  mesh generation
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