最大准则优化技术在贴体网格中的应用

贴体网格在地质数值模拟中具有广阔的应用前景，为解决贴体网格生成时边界离散问题，提出了最大长度准则和最大面积准则，把曲线逼近和曲面网格优化问题转化为数学优化问题，为求解该问题，提出了改进的单粒子优化算法.试验表明，最大长度准则和最大面积准则的优化效果好于常规方法；以改进的单粒子优化算法求解该问题时，计算效率是智能单粒子优化算法的30倍左右（节点量为200），从而实现最大长度准则和最大面积准则在贴体网格生成中的应用.针对最大面积准则优化曲面网格不能控制网格步长的情况，提出了限定步长的网格优化算法，使网格步长合理化，并通过实例验证了该算法的有效性.研究成果提供了生成贴体网格时边界优化准则和求解方法，对今后复杂边界的贴体网格生成具有重要意义.

The application of the maximum criteria optimizing technique in generation of body-fitted grids

Body-fitted grids have a wide application prospect in numerical simulation of geology. In order to solve the boundary discrete problem in generation of body-fitted grids, we put forward the maximum length criteria and the maximum area criteria which transform the curve approximation and the surface grid optimization problems into a mathematical optimization problem. We further propose a single particle optimization algorithm for solving this problem. Tests show that the maximum length criteria and the maximum area criteria have better optimization effects than the conventional methods. The calculation efficiency of the improved single particle optimizer is thirty times of the intelligent single particle optimizer (200 nodes) when solving this problem, and it achieves the application goal of the maximum length criteria and the maximum area criteria in generating body-fitted grids. Because the maximum area criteria cannot control the grid step length, we propose a limited step length grid optimizer which makes the step length more reasonable. We have tested and verified the effectiveness of this algorithm. The research results provide boundary optimal criteria and the solutions, which have important significance in generating body-fitted grids with complex boundaries in the future.