摘要
介绍传统Bowyer-Watson三角网逐点插入法的原理与实现步骤,并将固定边界限制、Laplacian光顺、边压缩、边分裂、点插入等拓扑变换技术应用于网格剖分的优化;为了使数值解的误差在全域内接近于均匀分布,通过间隔函数法实现点源、线源等网格渐变控制,结合局部粗化或细化技术,建立高质量Delaunay三角形网格,实现自适应网格剖分。通过1个起伏地表与断层模型网格剖分实例验证非结构化网格对于物性参数分布复杂或几何特征不规则的地电模型的适应性。根据GPR有限元波动方程,应用三角形剖分、线性插值的Galerkin有限单元法进行求解。建立1个复杂GPR地电模型,利用Delaunay三角形对该GPR地电模型进行自适应网格剖分。研究结果表明:非结构化网格对于物性参数分布复杂或几何特征不规则的地电模型都具有良好的适应性;非结构化三角形网格剖分质量好,单元密度易控制,易于实现自适应有限元,能提高复杂模型正演精度。
The theories and steps of traditional Bowyer-Watson triangulation incremental insertion method were introduced, and the fixed boundary limitation and topological transformation technology such as Laplacian smoothing,edge contraction, edge division and point insertion were applied to mesh generation optimization. In order to make the numerical solution error approach to the uniform distribution in the whole domain, mesh gradation controls such as point source and line source were realized by interval function method combined with local coarsening or local refinement technology, and high quality Delaunay triangle mesh was built to realize self-adaption mesh generation. A complex GPR geoelectric model was built, and the self-adaption mesh generation was made about this model by Delaunay triangle. The results show that the unstructured mesh has good adaption to the geoelectric model whose physical parameter distribution is complex or whose geometric features are irregular. Unstructured triangle mesh generation has high quality and easy controlling mesh density to realize self-adaption finite element algorithm, which can improve the complex model forward precision.
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2015年第4期1326-1334,共9页
Journal of Central South University:Science and Technology
基金
国家自然科学基金资助项目(41074085)
教育部新世纪优秀人才支持计划项目(NCET-12-0551)
湖湘青年创新创业平台培养对象基金资助项目(2013)
中南大学升华育英计划项目(2012年)~~
