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Definition of columns

name
Code Name of code
# of Cores Number of used CPU cores
# of Processes Number of MPI processes
# of Threads Number of threads for each process
$N_{c}$ Truncation lavel for Chebyshev polynomials
$l_{max}$ Truncation lavel for spherical harmonnics
$(N_{r},N_{\theta},N_{\phi})$ Number of grids in spherical coordinate
Elapsed Elapsed (wall clock time) for one time step
Nonlinear Elapsed (wall clock time) for evaluation of nonlinear terms
Solver Elapsed (wall clock time) for linear solver (including communications)
Efficiency Parallel efficiency
SUs Service unit for $10^{4}$ time steps (Core hours)

Single processors Result

Spherical harmonics expansion with Chebyshev expansion

Code $N_{c}$ $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
H2000 48 47 ( 72,72,144) 1.38531
MagIC 48 47 ( 72,72,144) 0.35723
GFD-Dennou 48 42 (48,64,128) 0.445464 0.233546 0.183094
Simitev-Busse-drs 47 42 (48,64,128) 0.460322 0.378743 0.0565741 0.005765

Spherical harmonics expansion with FDM

Code $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
Calypso V.1.1 47 (73,72,144) 1.604797 1.56274 0.04205857 0.508469
Calypso (Latest) 47 (73,72,144) 0.839953 0.797941 0.0399720 0.04934
Parody 47 ( 73,72,144) 0.269091 0.257912 0.00424973 Use 4 MPI threads
ETH 47 (72,72,144) 1.049 0.880913 0.168083 0.360225
LSD 48 ( 73,72,144) 0.774053 0.647997 0.647997 Nonlinear terms are evaluated twice
xshells 47 ( 73,72,144) 0.26967

Spherical harmonics expansion with Compact FDM

Code $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
TITECH 47 (73,72,144) 0.678760 0.488277 0.190479 0.029903 Nonlinear terms are evaluated twice


Elapsed (wall clock) time with single core.

256 Processes results

Spherical harmonics expansion with Chebyshev expansion

Code $N_{c}$ $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
UCSC 255 170 (257,256,512) 1.33908 1.06534 0.273739 0.080553 used 257 Cores
UCSC_latest 255 511 (257,768,1536) 8.6780 used 257 Cores
MagIC5 255 170 (257,256,512) 0.213723 0.120045 0.062081 0.0240802 4 SMP threads
MagIC5 511 256 (513,384,763) 2.22868 0.850126 0.442441 0.129714 8 SMP threads
GFD-Dennou 64 170 (64,256,512) 8.5006 3.08209 5.17536

Spherical harmonics expansion with FDM

Code $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
Calypso V.1.1 255 (513,384,768) 6.74711 6.69947 0.0476359 0.72289 4 SMP threads
Calypso (Latest) 255 (513,384,768) 2.30595 2.25802 0.0409069 0.632535 4 SMP threads
Parody 255 (512,384,768) 0.951109 0.779863 0.122069 8 SMP threads
ETH 255 (512,384,768) 5.49180 5.33942 0.152376 2.2764
LSD 256 (512,384,768) 4.08026 3.85867 0.0918966 Nonlinear terms are evaluated twice
xshells 256 (512,384,768) 0.30811 0.2502 0.02765 0.0302

Spherical harmonics expansion with Compact FDM

Code $l_{max}$ $(N_{r},N_{\theta},N_{\phi})$ Elapsed Nonlinear Solver Communication Note
TITECH 255 (256,384,768) 1.86101 1.7352 0.125808 0.475738 Nonlinear terms are evaluated twice

FEM

Code $N_{r}$ $N_{sph}$ Elapsed time Solver time Comm. time Note
GeoFEM 65 31106 12.0594 11.5573 1.29915 4 SMP threads


Elapsed (wall clock) time with 256 cores.

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