DHP_PE_RA_FDM

DHP_PE_RA_FDM - Dirichlet-Problem-Poisson's-Equation-Rectangular-Area-Finite-Difference-Method

This algorithm solves the Dirichlet problem for Poisson's equation in rectangular area using "steep descent iterations" for first several iterations and "conjugate gragient iterations" afterwards.

Method keypoints:

• five-point difference equation for Laplace operator approximation
• grid fragmentation are regular
• MPI technology for counting under supercomputers
• OpenMP technology for parallelization between processor cores
• scalar product: (a, b) = \sum_{i=1}^{i=n-1} ( \sum_{j=1}^{j=m-1} ( h'i * h'j * a(i, j) * b(i, j) ))

Algorithm parameters:

• boundary conditions: function 'fi'
• right side of Laplace operator: function 'F'
• stopping criteria: function 'stopCriteria'

Usage:

• you have to inherit from class DHP_PE_RA_FDM and write realization for algorithm parameters (virtual functions).

C++ exceptions:

• exception class DHP_PE_RA_FDM_Exception is successor of std::exception
• exception can be thrown by any process
• exist some warranties that errors concering algorithm (not MPI errors) will result in throwing exception by each involved into computations process (processes with rank [0, x_proc_num * y_proc_num])

C++ version:

• -std=gnu++98

Considered supercomputers:

• Lomonosov
• Blue Gene/P (g++ -std=gnu++98)

Example:

• example, realized in main benchmark is 2-nd variant in task description in algorithm.pdf on page 6
• for mentioned example etalon graph and computed graph were generated

Repository structure

• Makefile - contains a lot of instructions for mounting, uploading, compiling, etc. under supercomputers and local machine

• ./main.cpp - C++ file containing benchmark for algorithm

• ./DHP_PE_RA_FDM.h and ./DHP_PE_RA_FDM.cpp - C++ DHP_PE_RA_FDM realization

• ./generate_gnuplot.py - generates ./*.dat files for their plotting

• ./gnuplot.plt - gnuplot script which generates plots

• ./algorithm/ - problem formulation (russian only) (contains calculating formules) and scheme of numerical method

• ./joutput/ and ./loutput/ - directories contain some results of running benchmark under BlueGene/P and Lomonosov supercomputers

supercomputer commands

Blue Gene

mpisubmit.bg -n 1 -m smp -w 02:00:00 -t PREFER_TORUS ./superPrac2 1000 0.0001 output/bgp-out-1-1000 # 50:15 sec
mpisubmit.bg -n 1 -m smp -w 02:00:00 -t PREFER_TORUS ./superPrac2 2000 0.0001 output/bgp-out-1-2000 # --:--
mpisubmit.bg -n 1 -m smp -env OMP_NUM_THREADS=3 -w 02:00:00 -t PREFER_TORUS ./superPrac2-omp 1000 0.0001 output/bgp-out-1-1000-omp # 04:22
mpisubmit.bg -n 1 -m smp -env OMP_NUM_THREADS=3 -w 02:00:00 -t PREFER_TORUS ./superPrac2-omp 2000 0.0001 output/bgp-out-1-2000-omp # 35:37

mpisubmit.bg -n 2 -m smp -w 01:00:00 -t PREFER_TORUS ./superPrac2 1000 0.0001 output/bgp-out-2-1000 # 21:37 sec
mpisubmit.bg -n 2 -m smp -w 02:00:00 -t PREFER_TORUS ./superPrac2 2000 0.0001 output/bgp-out-2-2000 # --:--
mpisubmit.bg -n 2 -m smp -env OMP_NUM_THREADS=3 -w 01:00:00 -t PREFER_TORUS ./superPrac2-omp 1000 0.0001 output/bgp-out-2-1000-omp # 02:12
mpisubmit.bg -n 2 -m smp -env OMP_NUM_THREADS=3 -w 01:00:00 -t PREFER_TORUS ./superPrac2-omp 2000 0.0001 output/bgp-out-2-2000-omp # 17:50

mpisubmit.bg -n 128 -m smp -w 00:02:00 -t PREFER_TORUS ./superPrac2 1000 0.0001 output/bgp-out-128-1000 # 0:24 sec
mpisubmit.bg -n 128 -m smp -w 00:05:00 -t PREFER_TORUS ./superPrac2 2000 0.0001 output/bgp-out-128-2000 # 3:10 sec
mpisubmit.bg -n 128 -m smp -env OMP_NUM_THREADS=3 -w 00:01:00 -t PREFER_TORUS ./superPrac2-omp 1000 0.0001 output/bgp-out-128-1000-omp # 0:04 sec
mpisubmit.bg -n 128 -m smp -env OMP_NUM_THREADS=3 -w 00:01:00 -t PREFER_TORUS ./superPrac2-omp 2000 0.0001 output/bgp-out-128-2000-omp # 0:31 sec

mpisubmit.bg -n 256 -m smp -w 00:01:00 -t PREFER_TORUS ./superPrac2 1000 0.0001 output/bgp-out-256-1000 # 0:12 sec
mpisubmit.bg -n 256 -m smp -w 00:03:00 -t PREFER_TORUS ./superPrac2 2000 0.0001 output/bgp-out-256-2000 # 1:35 sec
mpisubmit.bg -n 256 -m smp -env OMP_NUM_THREADS=3 -w 00:00:30 -t PREFER_TORUS ./superPrac2-omp 1000 0.0001 output/bgp-out-256-1000-omp # 0:03 sec
mpisubmit.bg -n 256 -m smp -env OMP_NUM_THREADS=3 -w 00:01:00 -t PREFER_TORUS ./superPrac2-omp 2000 0.0001 output/bgp-out-256-2000-omp # 0:16 sec

mpisubmit.bg -n 512 -m smp -w 00:00:30 -t PREFER_TORUS ./superPrac2 1000 0.0001 output/bgp-out-512-1000 # 0:06 sec
mpisubmit.bg -n 512 -m smp -w 00:03:00 -t PREFER_TORUS ./superPrac2 2000 0.0001 output/bgp-out-512-2000 # 1:48 sec
mpisubmit.bg -n 512 -m smp -env OMP_NUM_THREADS=3 -w 00:00:30 -t PREFER_TORUS ./superPrac2-omp 1000 0.0001 output/bgp-out-512-1000-omp # 0:2 sec
mpisubmit.bg -n 512 -m smp -env OMP_NUM_THREADS=3 -w 00:01:00 -t PREFER_TORUS ./superPrac2-omp 2000 0.0001 output/bgp-out-512-2000-omp # 0:9 sec


mpisubmit.bg -n 1 -m smp -w 02:00:00 -t PREFER_TORUS
mpisubmit.bg -n 16 -m smp -w 02:00:00 -t PREFER_TORUS
mpisubmit.bg -n 64 -m smp -w 02:00:00 -t PREFER_TORUS
mpisubmit.bg -n 128 -m smp -w 00:15:00 -t PREFER_TORUS
mpisubmit.bg -n 256 -m smp -w 00:10:00 -t PREFER_TORUS
mpisubmit.bg -n 512 -m smp -w 00:05:00 -t PREFER_TORUS
mpisubmit.bg -n 1024 -m smp -w 00:02:00 -t PREFER_TORUS

Lomonosov

Lomonosov execute tasks in context of ~/_scratch directory.

sbatch -p test -n 1 --time=0-00:07:00 impi ./superPrac2 1000 0.0001 output/lom-out-1-1000 # 5:09 sec
sbatch -p regular4 -n 1 --time=0-00:59:30 impi ./superPrac2 2000 0.0001 output/lom-out-1-2000 # 41:10 sec

sbatch -p test -n 8 --time=0-00:01:00 impi ./superPrac2 1000 0.0001 output/lom-out-8-1000 # 0:39 sec
sbatch -p test -n 8 --time=0-00:07:00 impi ./superPrac2 2000 0.0001 output/lom-out-8-2000 # 5:11 sec
sbatch -p test -n 16 --time=0-00:01:00 impi ./superPrac2 1000 0.0001 output/lom-out-16-1000 # 0:19 sec
sbatch -p test -n 16 --time=0-00:03:50 impi ./superPrac2 2000 0.0001 output/lom-out-16-2000 # 2:36 sec
sbatch -p test -n 32 --time=0-00:00:30 impi ./superPrac2 1000 0.0001 output/lom-out-32-1000 # 0:9 sec
sbatch -p test -n 32 --time=0-00:02:00 impi ./superPrac2 2000 0.0001 output/lom-out-32-2000 # 1:18 sec
sbatch -p test -n 64 --time=0-00:00:10 impi ./superPrac2 1000 0.0001 output/lom-out-64-1000 # 0:5 sec
sbatch -p test -n 64 --time=0-00:02:00 impi ./superPrac2 2000 0.0001 output/lom-out-64-2000 # 0:39 sec
sbatch -p test -n 128 --time=0-00:00:10 impi ./superPrac2 1000 0.0001 output/lom-out-128-1000 # 0:2 sec
sbatch -p test -n 128 --time=0-00:01:00 impi ./superPrac2 2000 0.0001 output/lom-out-128-2000 # 0:19 sec