论文详情
基于窄带技术的旅行时快速推进算法在迭代计算过程中需要频繁更新窄带点,通过优化窄带点排序方案,可有效提升该算法的计算精度和效率。传统快速推进算法在选取排序方法时仅考虑方法的排序能力强弱,认为排序能力强的堆排序方法能更好地处理窄带点的排序任务,忽略了作为排序目标的旅行时场所具有的有序性。分析程函方程的因果关系条件可知,旅行时场隐含了由小到大的分布规律。基于这一规律,采用简单的插入排序方法即可很好地完成窄带点的排序任务。插入排序方法属于稳定类排序方法,较堆排序方法具有更低的实现成本和更高的稳定性,更加符合程函方程因果关系条件的要求。通过引入插入排序方法,设计了一种适合快速推进算法的排序流程,用于替换常规算法所采用的堆排序方法,后经不断改进,提出了基于插入排序方法的快速推进算法。通过数值模拟,测试和比较了插入排序快速推进算法、三叉树堆排序快速推进算法和快速扫描算法,数值模拟结果表明,对于压制了源点奇异性问题的快速推进算法,插入排序快速推进算法的精度和计算效率均优于传统的三叉树堆排序快速推进算法。
The method for calculating the traveltime based on wavefront extension,which uses the narrowband technique,requires the frequent updating of the narrow-band points.Optimizing the method for sorting the narrow-band points can effectively improve the computational accuracy and efficiency of the fast-marching method.The conventional fast-marching method uses the heapsort method to sort the narrow-band points.This method has a strong sorting ability,yet ignores the ordering of the traveling place as the sorting target.An implicit order in the traveltime field was demonstrated by analyzing the causality conditions of the eikonal equation.As a consequence,a simple sorting method should be able,in principle,to sort the narrow-band points completely.On this basis,an insertion sorting method suitable for the fast-marching method was proposed to replace the conventional heapsort method.The proposed method is stable and has higher compliance with the requirement of causality condition.The numerical simulation results showed that the insertion-sorting was more accurate than the ternary tree fast marching and the conventional fast sweeping method.In cases in which the source singularity is suppressed,the insertion-sorting fast-marching method is superior to the traditional method both in terms of accuracy and efficiency.
国家自然科学基金(41504095,41764006,41804116)、江西省教育厅基金(GJJ160570)和国家留学基金委项目(201708360042)共同资助。