Benchmark and comparison of Julia, Matlab, Octave, and Fortran for a 2D Poisson problem solved on a unit square. The problem is discretized with Q1 bilinear Lagrange finite elements.
The Octave and Matlab code is derived from the production FEATool Multiphysics code. The Fortran 77 code is using the Feat2D FEM library found in the FEM CFD Solver FeatFlow from which the Julia code is a direct port. The problem setup is identical and the codes really are equivalent and not dummied down to perform better in the benchmark, as they still feature all relevant code paths to allow different finite element shape functions, variable coefficients, unstructured grids, etc. Thus the results are relevant and comparable. The main difference is that Octave, Matlab, and Julia use the default sparse linear solver (currently the Umfpack direct solver) which the FeatFem Fortran code uses a more efficient geometric multigrid iterative solver.
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Download and unzip or clone the repository.
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Set up and install Matlab, Octave, Julia, and a Fortran compiler (tested with gfortran and the Intel Fortran compiler).
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Edit the testrun_param.txt file, which contains three parameters
N0 - the grid resolution of the coarsest test grid (grid level) (the number of cells in x and y-directions) NLEV - The number of grid levels to run tests for NRUNS - Number of test runs for each grid level, the timings are averaged for all runs -
On Windows edit the OCTAVE, MATLAB, and JULIA paths in the run_tests.bat script and execute the script to automatically run the benchmarks and generate the output files. (Note that to run the Fortran code under Windows the Ubuntu Bash on Windows is required)
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On other systems the run_matlab.m, run_julia.jl, and run_fortran.sh shell scripts can be run manually.
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The Octave/Matlab postprocessing script src_matlab/process_results.m file can be run manually to generate the results and output files.
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The NNWORK parameter in the main Fortran source file src_fortran/src/featfem.f controls the static memory allocation and might have to be increased and recompiled to run > 4 GB runs.
After running the tests the output directory will contain results files, table.txt with tabulated times, and results.html which shows Plotly comparison graphs. Sample output is shown here below
The complete results for the current testruns can be viewed here with the tabulated data below
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Octave | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_solve | t_tot |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 2.60e-003 | 2.60e-003 | 1.65e-002 | 1.30e-002 | 2.61e-003 | 0.00e+000 | 4.34e-003 | 4.17e-002 |
| 64 | 8.67e-004 | 8.70e-004 | 1.91e-002 | 1.22e-002 | 5.21e-003 | 3.47e-003 | 2.20e-002 | 6.37e-002 |
| 128 | 7.82e-003 | 5.21e-003 | 3.82e-002 | 2.60e-002 | 1.22e-002 | 6.08e-003 | 9.33e-002 | 1.89e-001 |
| 256 | 1.65e-002 | 2.43e-002 | 1.35e-001 | 9.64e-002 | 3.99e-002 | 3.21e-002 | 5.14e-001 | 8.57e-001 |
| 512 | 7.64e-002 | 8.94e-002 | 4.92e-001 | 7.28e-001 | 1.58e-001 | 1.38e-001 | 2.74e+000 | 4.42e+000 |
| 1024 | 2.96e-001 | 3.43e-001 | 1.93e+000 | 7.33e+000 | 6.70e-001 | 5.39e-001 | 1.82e+001 | 2.93e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Matlab | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_solve | t_tot |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 1.88e-003 | 1.87e-003 | 2.81e-003 | 3.26e-003 | 2.66e-003 | 2.12e-003 | 4.19e-003 | 1.88e-002 |
| 64 | 7.05e-004 | 1.09e-003 | 6.61e-003 | 4.15e-003 | 5.95e-003 | 9.56e-003 | 2.17e-002 | 4.97e-002 |
| 128 | 1.44e-003 | 6.26e-003 | 1.62e-002 | 1.24e-002 | 2.28e-002 | 4.07e-002 | 9.02e-002 | 1.90e-001 |
| 256 | 5.21e-003 | 2.53e-002 | 5.54e-002 | 5.06e-002 | 8.99e-002 | 1.47e-001 | 4.46e-001 | 8.20e-001 |
| 512 | 3.05e-002 | 9.79e-002 | 2.03e-001 | 3.39e-001 | 3.67e-001 | 6.10e-001 | 2.53e+000 | 4.18e+000 |
| 1024 | 1.24e-001 | 3.95e-001 | 8.15e-001 | 3.30e+000 | 1.51e+000 | 2.52e+000 | 1.49e+001 | 2.36e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Julia | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_solve | t_tot |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 1.67e-004 | 5.81e-004 | 8.92e-004 | 4.27e-004 | 4.90e-005 | 2.95e-004 | 7.65e-003 | 1.01e-002 |
| 64 | 5.45e-004 | 2.16e-003 | 3.56e-003 | 1.86e-003 | 7.68e-005 | 1.48e-003 | 3.03e-002 | 4.00e-002 |
| 128 | 1.80e-003 | 7.35e-003 | 1.43e-002 | 6.77e-003 | 1.29e-004 | 1.09e-002 | 1.23e-001 | 1.64e-001 |
| 256 | 9.42e-003 | 9.52e-002 | 6.13e-002 | 2.69e-002 | 2.45e-004 | 2.55e-002 | 5.23e-001 | 7.41e-001 |
| 512 | 1.60e-001 | 1.32e-001 | 3.00e-001 | 1.14e-001 | 4.58e-004 | 1.85e-001 | 2.66e+000 | 3.55e+000 |
| 1024 | 4.82e-001 | 7.00e-001 | 9.57e-001 | 5.18e-001 | 9.76e-004 | 5.70e-001 | 1.37e+001 | 1.69e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Fortran | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_solve | t_tot |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 0.00e+000 | 0.00e+000 | 1.74e-003 | 0.00e+000 | 0.00e+000 | 0.00e+000 | 8.68e-004 | 2.60e-003 |
| 64 | 0.00e+000 | 0.00e+000 | 6.08e-003 | 8.68e-004 | 0.00e+000 | 0.00e+000 | 0.00e+000 | 6.94e-003 |
| 128 | 3.47e-003 | 0.00e+000 | 2.26e-002 | 0.00e+000 | 8.68e-004 | 0.00e+000 | 1.39e-002 | 4.08e-002 |
| 256 | 6.94e-003 | 1.91e-002 | 6.42e-002 | 8.68e-003 | 1.74e-003 | 0.00e+000 | 4.51e-002 | 1.46e-001 |
| 512 | 3.04e-002 | 9.90e-002 | 2.20e-001 | 4.25e-002 | 0.00e+000 | 0.00e+000 | 1.80e-001 | 5.72e-001 |
| 1024 | 1.40e-001 | 3.85e-001 | 8.98e-001 | 1.62e-001 | 0.00e+000 | 0.00e+000 | 7.71e-001 | 2.36e+000 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
Copyright (C) 2013-2016 J.S. Hysing.
Author: J.S. Hysing, [email protected]
Keywords: Finite Element, FEM, Julia, Matlab, Octave, Fortran, Benchmark
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.
FeatFlow and the Feat library is Copyright (C) of S. Turek et al. and may fall under a different license agreement.