Partitioning with Space-Filling Curves on the Cubed-Sphere

John Dennis

Computational Science Section
National Center for Atmospheric Research

April 11, 2003 – 10:30 am – Suite 150, Mesa Laboratory

Abstract:

Solving partial differential equations arising in geophysical fluid dynamics on distributed memory computers requires partitioning of the computational domain.

The choice of partitioning algorithm can have a significant impact on the sustained floating-point execution rate of a prototype atmospheric model.  The NCAR spectral element model employs a gnomonic projection of a cube onto the surface of the sphere.  The six cube faces are subdivided into an array of quadrilateral spectral element. When the cubed-sphere is partitioned using METIS, both load imbalance and communication requirements leads to sub-optimal performance.  Hilbert and Peano space-filling curves are investigated as alternative partitioning algorithms.  The resulting partitions allow a maximum 22\% increase in the sustained floating point execution rate versus METIS on768 processors of the IBM P690 cluster.