Mesh smoothing is an essential technique for the improvement of mesh quality in finite element analysis, due to the fact that mesh quality has a large impact on the convergence of the computational scheme and the accuracy of the numerical results. A novel mesh smoothing method based on regular-position-guided operations is presented in this paper. The method introduced here contains two main stages: The first stage computes the regular position of each vertex based on the shape of the element and conducts regular-position-oriented-based element transformations independently; the second stage determines the finial position of each vertex according to its surrounding elements with an assembly strategy. This method is not limited to planar triangular mesh, but applicable to surface polygonal mesh. Numerical experiments on various mesh models demonstrate the effectiveness and potential of this method.

网格平滑是提高有限元分析中网格质量的一项必不可少的技术，因为网格质量对计算方案的收敛性和数值结果的准确性影响很大。提出了一种新的基于规则位置引导的网格平滑方法。这里介绍的方法包括两个主要阶段：第一阶段根据元素的形状计算每个顶点的规则位置，并独立进行基于规则位置的元素转换。第二阶段根据组装策略，根据每个顶点的周围元素确定其最终位置。该方法不限于平面三角形网格，而是适用于表面多边形网格。