Laplacian与局部优化方法相结合的网格光滑技术

One Mesh Smoothing Algorithm Combining Laplacian and Local Optimization-Based Mesh Smoothing Techniques

在优化方法中构造了一种新的、可以方便应用到不同维数问题的目标函数.在网格光滑数值模拟中,当Laplacian方法使网格品质下降或者产生无效网格,数次缩短移动距离仍不能使网格品质提高时,改用局部优化方法.将Laplacian方法与局部优化方法相结合,保证了所有网格品质都得到提高,同时只在少数网格内使用优化方法,可以降低计算量.数值结果表明,新的目标函数在混合网格中也能取得较好的结果.

A new objective function is defined for two and three dimensions. In numerical simulation, if the mesh quality cannot be improved by constrained Laplacian smoothing, local optimization-based smoothing algorithm is used. Thus none mesh gets worse while optimization- based smoothing applied only to limited number of meshes and efficiency of optimization is highly improved. Numerical result indicated that however applied in mixed grids the new objective function is effective.