Mandelbrot set by MPI/OpenMP/OpenACC.

requirements for python:

• numpy
• scipy
• matplotlib
• f90nml

how to run:

• for OpenMP version

$ export FC=ifort
$ make a.out
$ vi fort.11 # adjust the parameters
$ ./a.out
 maximum iteration:         200
 imax:         301 jmax:         251
 time[s]:  1.210000000000000E-002
./draw.py

• for MPI version

$ export MPIFC=mpiifort
$ make a.out.mpi
$ vi fort.11 # adjust the parameters
$ mpirun -np $NP ./a.out.mpi # where $NP must equal to np_i*np_j in fort.11
 maximum iteration:         200
 imax:         301 jmax:         251
 time[s]:  7.543087005615234E-003
./draw_mpi.py

• for OpenACC version

$ export MPIFC=mpif90
$ make a.out.mpi.acc
$ vi fort.11 # adjust the parameters
$ mpirun -np $NP ./a.out.mpi # where $NP must equal to np_i*np_j in fort.11
 maximum iteration:         200
 imax:         301 jmax:         251
 time[s]:  7.543087005615234E-003
./draw_mpi.py

to view the graph

$ display mandelbrot.png
or
$ display mandelbrot_mpi.png

or

$ gnuplot
gnuplot> set pm3d map
gnuplot> splot "fort.100"

MPI version can not use gnuplot because the output is a binary.

• zoomed calculation

&params
iter_max = 200
dx       = 5.0d-4
dy       = 5.0d-4
x_min    = -1.2d0
x_max    = -1.1d0
y_min    = 0.2d0
y_max    = 0.3d0
tol      = 1.0d2
/

performance comparison

CPU: Intel(R) Xeon(R) CPU E5-2450 0 @ 2.10GHz, 8 cores/socket, 2 sockets, 8 nodes
interconnect: 4xFDR infiniband, fat tree
compiler: intel compiler 2018u0
MPI: intel MPI 2018u0

• input:

&params
iter_max = 200
dx       = 2.0d-4
dy       = 2.0d-4
x_min    = -2.25d0
x_max    = 0.75d0
y_min    = -1.25d0
y_max    = 1.25d0
tol      = 1.0d2
/

• serial(1 core)

$ OMP_NUM_THREADS=1 KMP_AFFINITY=compact srun --mpi=pmi2 -N1 -n1 -c1 --cpu_bind=cores -m block:block ./a.out
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   104.264600000000

• OpenMP(1 node, 16 cores)

$ OMP_NUM_THREADS=16 KMP_AFFINITY=compact srun -n1 -c16 --cpu_bind=cores -m block:block ./a.out
srun: Warning: can't run 1 processes on 8 nodes, setting nnodes to 1
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   15.1660000000000

• flat MPI(1 node, 16 cores, np_i=4, np_j=4, 1 thread/process)

$ I_MPI_EXTRA_FILESYSTEM=1 I_MPI_EXTRA_FILESYSTEM_LIST=lustre OMP_NUM_THREADS=1 KMP_AFFINITY=compact srun --mpi=pmi2 -N1 -n16 -c1 --cpu_bind=cores -m block:block ./a.out.mpi
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   23.8055260181427

• hybrid(1 node, 16 cores, np_i=1, np_j=2, 8 threads/process)

$ I_MPI_EXTRA_FILESYSTEM=1 I_MPI_EXTRA_FILESYSTEM_LIST=lustre OMP_NUM_THREADS=8 KMP_AFFINITY=compact srun --mpi=pmi2 -N1 -n2 -c8 --cpu_bind=cores -m block:block ./a.out.mpi
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   15.0692129135132

• flat MPI(8 nodes, 128 cores, np_i=8, np_j=16, 1 thread/process)

$ I_MPI_EXTRA_FILESYSTEM=1 I_MPI_EXTRA_FILESYSTEM_LIST=lustre OMP_NUM_THREADS=1 KMP_AFFINITY=compact srun --mpi=pmi2 -N8 -n128 -c1 --cpu_bind=cores -m block:block ./a.out.mpi
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   3.35678577423096

• hybrid(8 nodes, 128 cores, np_i=4, np_j=4, 8 threads/process)

$ I_MPI_EXTRA_FILESYSTEM=1 I_MPI_EXTRA_FILESYSTEM_LIST=lustre OMP_NUM_THREADS=8 KMP_AFFINITY=compact srun --mpi=pmi2 -N8 -n16 -c8 --cpu_bind=cores -m block:block ./a.out.mpi
 maximum iteration:         200
 imax:       15001 jmax:       12501
 time[s]:   3.36353015899658

• OpenACC(4 nodes, 16 processes, np_i=4, np_j=4, 1 GPU/process) GPU: Tesla P100 x4/node

$ mpirun -x PATH -x LD_LIBRARY_PATH -np 16 -npernode 4 ./a.out.mpi.acc
 maximum iteration:          200
 imax:        15001 jmax:        12501
 time[s]:   9.6851900219917297E-002