多网格谱元法及其在高性能计算中的应用*

针对传统谱元法在每个单元内只能存在单一均匀介质,应用在复杂非均匀介质的波传播模拟中可能造成极大计算规模的问题,发展了多网格谱元法。该方法在谱元法单元内引入独立的辅助网格,用于精细描述单元内的介质和外力分布变化,在较稀疏的主网格上进行波场的求解。基于声波和弹性波方程推导了多网格谱元法公式,并对几种典型模型进行了波场的数值模拟。与传统谱元法的对比结果表明,此算法在复杂非均匀介质的弹性波传播模拟中可以利用较少的网格点数达到不低于传统算法的精度。此外,实现了并行化的多网格谱元法,获得了较好的并行效率。

The poly-grid spectral element method and its implementation in high performance computing

When traditional spectral element method is used to numerically simulating wave propagation in complex media, it may result in solving a huge computational problem. To alleviate this issue, a poly-grid spectral element method is developed, in which independent auxiliary grids are introduced to represent property changes and force distribution inside the elements, while the wave equation is solved on a set of primary grids at macroscopic level. In this paper, the mathematical formulations of poly-grid spectral element method are derived for both acoustic and elastic wave modellings. Numerical examples are carried out on specific models and the results are compared with traditional spectral element method. The results show that the poly-grid method maintains high accuracy using much fewer computation grids in wave modeling in complex media. Moreover, the method is parallelized and a good parallel efficiency is achieved.