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ZEUS-MP vs. ZEUS-3D Scaling Studies

by streeter — last modified 2007-03-30 04:37

CODES:ZEUS-MP version 1.2 vs. ZEUS-3D version 3.4.2
MACHINES (Jump to performance data):
PROBLEM: Blast -- the expansion of a hot sphere of plasma into an initially uniform medium (Sedov-Taylor Blast Wave).
GEOMETRY: Cartesian XYZ
GRIDS: For ZEUS-MP, the full grid is uniform and evenly partitioned into 3-D "tiles", with each process is assigned to 1 tile. For ZEUS-3D, the full grid is also uniform, but the partitioning is done automatically by the compiler.
ALGORITHMS: ZEUS-MP uses MPI to pass messages; ZEUS-3D uses shared memory.
COMMUNICATION: The ZEUS codes evolve the equations of ideal hydrodynamics via a multistep, time-explicit method. After each of the six substeps is performed, some updated values of the field variables must be exchanged between processes. The messages consist of the values of one field variable for each zone in one plane. For a 32-cubed tile size, the message length is actually 37 * 37 * 8 B = 10952 B, because there are 5 extra layers of zones for storing boundary data (ghost zones). At the end of each timestep, a global reduction operation is performed to determine the size of the next timestep. The messages passed are just two (double) words. For pure hydro or even MHD, the computations performed to evolve the field variables in each substep consist entirely of algebraic expressions (i.e., no linear systems to solve). Thus, the computational work to be done is relatively small and scales linearly with the total number of mesh zones.
PRECISION: Single precision on Crays (64-bits), DOUBLE PRECISION on others.
DATA: In the tables below, "tused" is the CPU seconds used by the master process in computing the evolution (some system and ZEUS overhead is excluded). The Zone-Cycles/sec is the total number of mesh zones times the number of time steps divided by tused.
TESTS: Two types of scaling studies are presented here. In the first type, the size of the full mesh is scaled with the number of processors, so that the amount of work (and memory) per processor is constant. In the second type, the size of the full mesh is held constant while the number of processors is increased. In this case, each processor gets less and less work to do as the number of processes increases.

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ZEUS-MP vs. ZEUS-3D Scaling Studies