局部到整体的六面体网格质量优化算法

网格质量是影响有限元分析结果准确性和可靠性的关键因素之一。为了提高六面体网格的质量，提出一种局部到整体的六面体网格质量优化算法。针对每个六面体单元采用双八面体几何变换进行局部规则化操作，得到高质量的规则六面体网格。在此基础上，通过迭代优化一个二次能量函数，对规则化后的网格进行整体拼接和优化，该能量函数由节点内力和表面几何约束组成，节点内力保证了规则化后六面体单元的连接性，表面几何约束保持了原始模型的几何形状。应用实例表明，该方法稳定可靠，显著提高了六面体网格的质量。

Local to Global Optimization Algorithm for Hexahedral Mesh Quality

The quality of finite element meshes is one of the key factors that affects the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, a local to global hexahedral mesh optimization algorithm is presented. A double octahedron based geometric transformation is used to regularize a hexahedron locally, and regular hexahedral elements are obtained for all meshes. On the basis of local operations, these regular hexahedral meshes can be further stitched and optimized by iteratively minimizing a quadric energy function, which composed of two main terms. One part is the node internal force which ensures the connectivity of regular hexahedral meshes and another is the geometric constraint which keeps the shape of original model. Applications show that the proposed algorithm is stable, and the hexahedral mesh quality is highly improved.