A New Method for Adaptive Grid Generation

当函数求值的点选择得很好时，找到数值解是最有效的；这通常意味着使用自适应计划，其中每个选择都可以根据之前的选择和已经进行的计算进行修改。本课题的目标是开发一种有效的自适应生成点选择序列的新方法。发展一种直接控制网格大小的自适应策略可以提高数值解的准确性，同时减少计算机时间和存储空间。该项目将开发这样一个自适应网格程序，也确保网格无纠缠。

Finding numerical solutions is most efficient when the points where the function is to be evaluated are well-chosen; often this means using an adaptive plan where each choice may be modified based on the previous choices and calculations already made. The object of this project is to develop an efficient new methodology for generating the sequence of choices of points adaptively. The development of an adaptive strategy involving direct control over grid size should improve the accuracy of numerical solutions while reducing computer time and storage. This project will develop such an adaptive grid procedure which also ensures entanglement-free grids.