中文摘要：

最优Delaunay三角剖分（ODT）是生成区域网格剖分的一种优化方法.从数值优化的角度来看,现有的ODT优化方法属于局部方法,对于任意给定初值容易陷入较差的局部极小值点,从而不能产生高质量网格.为此提出一种简单的拓扑优化方法,使得ODT方法能有效地从局部极小值点中跳出,进一步提高网格的质量.该方法只涉及到局部的边翻转操作,实现简单;而且具有显式的目标函数,能在理论上保证算法的收敛性.实验结果表明,文中算法运行速度快,不论是在拓扑连接关系还是在三角形的形状上都显著地提高了ODT方法生成的网格质量.

英文摘要：

Optimal Delaunay triangulation（ODT） is an optimization method for mesh generation.From the point of view of numerical optimization,existing ODT methods are local optimization methods,which can be easily fallen into a local minimum corresponding to a mesh with low quality.In this paper,a topology improvement method is introduced into the ODT optimization procedure,which effectively enables the ODT method to jump out from a poor local minimum and therefore improves the qualities of generated meshes.The proposed topology improvement method consists of only local operations of edge flipping,which is easy to implement.Moreover,our topology improvement method has an explicit objective function,and its convergence is guaranteed theoretically.Experimental results show that our algorithm is fast and can greatly improves the qualities of meshes generated from ODT,with respect to the regularities of the mesh and the aspect ratios of the triangles.