一种快速求解程函方程的间断伽辽金方法

A discontinuous Galerkin method to solve eikonal equation fast

作为一种在勘探地震学里近期发展起来的有限元类数值求解程函方程的算法,间断伽辽金方法通过拓展基函数空间提高数值精度,但存在计算效率低的问题。为了解决该问题,提出一种并行快速扫描间断伽辽金方法。算法在快速扫描过程中对节点的计算顺序进行Cuthill-McKee变换,将能够并行计算的节点分为不同任务集合,进而实现不同任务集的并行计算。数值结果的分析表明:并行快速扫描间断伽辽金方法在保证计算精度的前提下,能稳定地提升计算效率,并且还能适应各种复杂速度模型。

As a recently developed finite element numerical algorithm for solving eikonal equations in exploration seismology,discontinuous Galerkin method can be used to improve numerical accuracy by extending basis function space,but there exists a problem of low computational efficiency.To solve this problem,for discontinuous Galerkin method obtained by combining fast sweeping method,Cuthill-McKee transformation of calculating order is performed in fast sweeping process and nodes which can be calculated at the same time are divided into different task sets,so as to realize the parallel calculation of task sets.The numerical analysis and examples show that the algorithm improved calculating efficiency while taking account of accuracy,and adapted in conditions with complex velocity models.