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===== compile options =====

F90OPTFLAGS = -O3 -warn all -g -xhost   -openmp

===== Definition of columns =====

^  name  ^    ^
|  # 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 polynomial  |
|  $l_{max}$  |  Truncation lavel for spherical harmonincs  |
|  $(N_{r},N_{\theta},N_{\phi})$  |  Nuber of grids in spherical coordinate  |
|  Elapsed time  |  Elapsed (wall clock time) for one time step  |
|  Efficiency  |  Parallel efficiency  |
|  SUs  |  Service unit for $10^{4}$ time steps (Core hours)  |


===== Single Processor Result =====

^  $N_{c}$  ^  $l_{max}$  ^  $(N_{r},N_{\theta},N_{\phi})$  ^  Elapsed time  ^
|  47  |  48  |  (72,72,144)  |  0.35723  |

===== Strong Scaling Results =====
In the present test, spatial resolution is fixed, and change the parallelization. 
Elapsed time is inverse proportion to the number of Cores in ideal scaling.

^  $N_{c}$  ^  $l_{max}$  ^  $(N_{r},N_{\theta},N_{\phi})$  ^
|  47  |  48  |  (72,72,144)  |

^  # of Cores  ^  # of Processes  ^  # of Threads  ^  Elapsed time  ^  Efficiency  ^  SUs  ^
|  1  |  1  |  1  |  0.35723  |  1.0  |  15.8769  |
|  2  |  1  |  2  |  0.18729  |  0.953681  |  8.32400  |
|  4  |  1  |  4  |  0.10288  |  0.868074  |  4.57244  |
|  8  |  1  |  8  |  0.05784  |  0.772022  |  2.57067  |

^  $N_{c}$  ^  $l_{max}$  ^  $(N_{r},N_{\theta},N_{\phi})$  ^
|  97  |  170  |  (145,256,512)  |

^  # of Cores  ^  # of Processes  ^  # of Threads  ^  Elapsed time  ^  Efficiency  ^  SUs  ^
|  1  |  1  |  1  |  18.3200  |  1.0   |  814.222  |
|  2  |  1  |  2  |  8.69336  |  1.05368   |  386.372  |
|  4  |  1  |  4  |  4.51397  |  1.01463   |  200.621  |
|  8  |  1  |  8  |  2.53104  |  0.904766   |  112.491  |
|  16  |  1  |  16  |  2.16658  |  0.528483  |  96.2924  |

{{wg:dynamo:Performance_results:magic:MagIC_scaling.png?480}}\\
Elapsed (wall clock) time for the strong scaling for $(N_{c},l_{max}) = (97,170)$ case. Number of OpenMP threads are shown by the numbers. Ideal scaling is plotted by dotted line.

{{wg:dynamo:Performance_results:magic:MagIC_efficiency.png?480}}\\
Parallel Efficiency for the strong scaling for $(N_{c},l_{max}) = (97,170)$ case. Number of OpenMP threads are shown by the numbers.

===== Weak Scaling Results =====

=== Weak Scaling in horizontal direction ===
In the present benchmark, radial resolution is fixed, and horizontal resolution is increased with parallelization.

^  # of Cores  ^  # of Processes  ^  # of Threads  ^  $N_{c}$  ^  $l_{max}$  ^  $(N_{r},N_{\theta},N_{\phi})$  ^  Elapsed time  ^  SUs  ^
|  1  |  1  |  1  |  97  |  42  |  (145,64,128)  |  0.61665  |  27.4067  |
|  4  |  1  |  4  |  97  |  84  |  (145,128,256)  |  0.623898  |  27.564  |
|  16  |  1  |  16  |  97  |  170  |  (145,256,512)  |  2.16658  |  96.2924  |

{{wg:dynamo:Performance_results:magic:MagIC_weak_sph.png?480}}\\
Elapsed (wall clock) time for the weak scaling in the horizontal resolutions. Number of OpenMP threads are shown by the numbers. 

=== Weak Scaling in radial direction ===
In the present benchmark, horizontal resolution is fixed, and radial resolution is increased with parallelization.

^  # of Cores  ^  # of Processes  ^  # of Threads  ^  $N_{c}$  ^  $l_{max}$  ^  $(N_{r},N_{\theta},N_{\phi})$  ^  Elapsed time  ^  SUs  ^
|  1  |  1  |  1  |  9  |  170  |  (8,256,512)  |  0.65988  |  29.328  |
|  2  |  1  |  2  |  17  |  170  |  (16,256,512)  |  0.74609  |  33.1596  |
|  4  |  1  |  4  |  33  |  170  |  (32,256,512)  |  0.79330  |  35.2578  |
|  8  |  1  |  8  |  63  |   170  |  (64,256,512)  |  1.01657   |  45.1809  |
|  16  |  1  |  16  |  129  |  170  |  (128,256,512)  |  1.85728  |  82.5458  |

{{wg:dynamo:Performance_results:magic:MagIC_weak_r.png?480}} \\
Elapsed time for the weak scaling in the radial resolution. Number of OpenMP threads are shown by the numbers.

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