We propose an algorithm based on Hilbert space-filling curves to reorder mesh elements in memory for use with the Spectral Element Method, aiming to attain fewer cache misses, better locality of data reference and faster execution. We present a technique to numerically simulate acoustic wave propagation in 2D domains using the Spectral Element Method, and discuss computational performance aspects of this procedure. We reorder mesh-related data via Hilbert curves to achieve sizable reductions in execution time under several mesh configurations in shared-memory systems. Our experiments show that the Hilbert curve approach works well with meshes of several granularities and also with small and large variations in element sizes, achieving reductions between 9% and 25% in execution time when compared to three other ordering schemes.

中文翻译：

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用希尔伯特空间填充曲线提高谱元方法的内存访问局部性

我们提出了一种基于希尔伯特空间填充曲线的算法，以对光谱元素方法中的网格元素进行重新排序，以实现更少的缓存未命中，更好的数据引用局部性和更快的执行速度。我们提出了一种使用频谱元素方法对二维域中声波传播进行数值模拟的技术，并讨论了此过程的计算性能方面。我们通过Hilbert曲线对与网格相关的数据进行重新排序，以在共享内存系统中的几种网格配置下大幅减少执行时间。我们的实验表明，希尔伯特曲线方法适用于多种粒度的网格，并且元素大小的大小差异也很大，与其他三种排序方案相比，执行时间减少了9％到25％。