In this paper, we introduce an innovative approach to generate a high-quality mesh with a density function in a given domain. Our method involves solving a variational problem that optimizes the energy function of the optimal Delaunay triangulation (ODT). To achieve this, we have developed a modified whale optimization algorithm (MWOA) based population that is combined with the quasi-Newton method (L-BFGS) to optimize ODT energy on a global level. Our experiments have demonstrated the impressive efficiency of this optimization algorithm in searching for better minima and producing high-quality meshes. Remarkably, the algorithm’s powerful global optimization capability makes it insensitive to initialization, which eliminates the need for any special initialization procedures. Furthermore, our proposed algorithm can easily handle complex domains and non-uniform density functions, making it a versatile tool for mesh generation. Overall, our method offers a promising solution for generating practicable meshes with a density function.

在本文中，我们介绍了一种创新方法，可以在给定域中生成具有密度函数的高质量网格。我们的方法涉及解决一个变分问题，该问题优化最优 Delaunay 三角剖分 (ODT) 的能量函数。为了实现这一目标，我们开发了一种基于种群的改进鲸鱼优化算法（MWOA），该算法与拟牛顿法（L-BFGS）相结合，在全球范围内优化 ODT 能量。我们的实验证明了这种优化算法在搜索更好的最小值和生成高质量网格方面具有令人印象深刻的效率。值得注意的是，该算法强大的全局优化能力使其对初始化不敏感，从而无需任何特殊的初始化过程。此外，我们提出的算法可以轻松处理复杂域和非均匀密度函数，使其成为网格生成的通用工具。总的来说，我们的方法为生成具有密度函数的实用网格提供了一种有前景的解决方案。