基于不可微问题优化的四面体网格光顺算法

提出一种基于不可微问题优化的四面体网格光顺算法。针对四面体网格光顺的最小最大约束优化问题，应用一类不可微优化问题的有效解法，提出与不可微目标函数等价的可微目标函数，进一步转化为无约束极小优化问题，进而调用现有的优化程序库进行网格优化。该算法实现了多点并发优化技术，能够有效地实现四面体网格的质量优化，特别是能够有效地解决非孤立劣质单元优化问题。算例表明，该算法计算效率高，且易于实现，能够优化得到较高质量的四面体网格。

TETRAHEDRAL MESH SMOOTHING BASED ON NON-SMOOTH OPTIMIZATION PROBLEM

A tetrahedral mesh smoothing algorithm based on non-smooth problem optimization is presented. Firstly the tetrahedral mesh smoothing problem is formulated as a min-max constrained optimization problem. And then an efficient solution algorithm based on entropy theory for non-smooth optimization problem is employed. The algorithm provides an equivalent smooth function of the non-smooth objective function and transforms the constrained optimization problem into a minimum unconstraint optimization problem, and then it is solved with the common optimization toolkit. In the process of mesh smoothing, a multi-point concurrent optimization technique is proposed, which can solve the optimization of tetrahedral mesh efficiently, and especially will be suitable for the optimization problem of non-insular bad element. The numerical examples show that the algorithm is efficient, easy to be implemented and can get quality elements.