  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.
