Benchmark and comparison of Fortran, Julia, Octave, and Matlab for a FEA Poisson problem solved on a unit square. The problem is discretized with Q1 bilinear Lagrange finite elements.
The Fortran code is using a reference FEM implementation from which the Julia code is a direct port. The Octave and Matlab code is derived from the FEATool Multiphysics production code. The problem setup is identical and the codes are equivalent and not tuned 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), while the Fortran code uses a more efficient iterative geometric multigrid solver.
The results of this benchmark are presented on the FEATool blog: https://www.featool.com/fortran-julia-and-matlab-fem-benchmark-comparison
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Download and unzip or clone the repository.
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Set up and install Octave, Matlab 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 Windows Subsystem for Linux (WSL) 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 the comparison graphs. Sample output is shown here below
Data for the complete results for all testruns are tabulated below
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Octave | | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_tot | t_spmv | t_solve |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 2.37e-003 | 1.50e-003 | 1.77e-002 | 1.07e-002 | 1.06e-003 | 4.16e-004 | 3.37e-002 | 4.62e-005 | 5.78e-003 |
| 64 | 2.76e-003 | 1.95e-003 | 1.99e-002 | 1.15e-002 | 2.76e-003 | 1.84e-003 | 4.07e-002 | 1.55e-004 | 2.28e-002 |
| 128 | 6.28e-003 | 5.33e-003 | 4.39e-002 | 2.27e-002 | 1.13e-002 | 9.03e-003 | 9.86e-002 | 6.29e-004 | 1.04e-001 |
| 256 | 1.74e-002 | 2.43e-002 | 1.28e-001 | 7.38e-002 | 4.25e-002 | 3.30e-002 | 3.19e-001 | 2.38e-003 | 5.10e-001 |
| 512 | 7.38e-002 | 8.25e-002 | 4.92e-001 | 2.73e-001 | 1.57e-001 | 1.35e-001 | 1.21e+000 | 1.07e-002 | 2.66e+000 |
| 1024 | 2.87e-001 | 3.28e-001 | 1.88e+000 | 1.07e+000 | 6.69e-001 | 5.33e-001 | 4.77e+000 | 4.33e-002 | 1.75e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Matlab | | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_tot | t_spmv | t_solve |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 1.74e-003 | 1.26e-003 | 2.50e-003 | 1.88e-003 | 2.22e-003 | 2.05e-003 | 1.16e-002 | 1.18e-005 | 4.05e-003 |
| 64 | 7.09e-004 | 9.97e-004 | 6.51e-003 | 3.00e-003 | 6.13e-003 | 9.71e-003 | 2.71e-002 | 4.62e-005 | 2.17e-002 |
| 128 | 1.58e-003 | 6.25e-003 | 1.58e-002 | 8.54e-003 | 2.28e-002 | 4.07e-002 | 9.57e-002 | 1.84e-004 | 9.43e-002 |
| 256 | 5.06e-003 | 2.44e-002 | 5.49e-002 | 4.11e-002 | 9.02e-002 | 1.47e-001 | 3.63e-001 | 8.68e-004 | 4.48e-001 |
| 512 | 3.06e-002 | 9.75e-002 | 2.05e-001 | 1.57e-001 | 3.74e-001 | 6.11e-001 | 1.47e+000 | 4.90e-003 | 2.54e+000 |
| 1024 | 1.23e-001 | 3.86e-001 | 8.13e-001 | 6.32e-001 | 1.51e+000 | 2.51e+000 | 5.97e+000 | 1.99e-002 | 1.48e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Julia | | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_tot | t_spmv | t_solve |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 1.11e-004 | 3.77e-004 | 8.97e-004 | 2.61e-004 | 6.76e-005 | 2.30e-004 | 1.94e-003 | 2.15e-005 | 6.00e-003 |
| 64 | 2.22e-004 | 1.67e-003 | 3.58e-003 | 1.00e-003 | 9.88e-005 | 1.20e-003 | 7.78e-003 | 8.86e-005 | 2.80e-002 |
| 128 | 5.66e-004 | 6.76e-003 | 1.45e-002 | 3.92e-003 | 1.41e-004 | 5.96e-003 | 3.19e-002 | 3.65e-004 | 1.20e-001 |
| 256 | 3.20e-003 | 2.71e-002 | 5.79e-002 | 1.58e-002 | 2.48e-004 | 2.39e-002 | 1.28e-001 | 1.55e-003 | 5.12e-001 |
| 512 | 1.30e-002 | 1.10e-001 | 2.35e-001 | 6.66e-002 | 4.11e-004 | 1.77e-001 | 6.02e-001 | 7.77e-003 | 2.58e+000 |
| 1024 | 5.35e-002 | 4.60e-001 | 9.57e-001 | 2.76e-001 | 2.22e-003 | 6.20e-001 | 2.37e+000 | 3.12e-002 | 1.34e+001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| Fortran | | | | | | | | | |
| 1/h | t_grid | t_ptr | t_asm_A | t_asm_f | t_bdr | t_sparse | t_tot | t_spmv | t_solve |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
| 32 | 0.00e+000 | 8.68e-004 | 8.68e-004 | 0.00e+000 | 0.00e+000 | 0.00e+000 | 1.74e-003 | 2.60e-005 | 4.34e-003 |
| 64 | 0.00e+000 | 8.68e-004 | 7.81e-003 | 2.60e-003 | 8.68e-004 | 0.00e+000 | 1.22e-002 | 9.55e-005 | 8.68e-004 |
| 128 | 4.34e-003 | 4.34e-003 | 1.82e-002 | 1.74e-003 | 0.00e+000 | 0.00e+000 | 2.86e-002 | 2.95e-004 | 1.13e-002 |
| 256 | 3.47e-003 | 1.91e-002 | 6.94e-002 | 1.13e-002 | 1.74e-003 | 0.00e+000 | 1.05e-001 | 1.12e-003 | 4.08e-002 |
| 512 | 3.30e-002 | 9.20e-002 | 2.26e-001 | 4.17e-002 | 1.74e-003 | 0.00e+000 | 3.94e-001 | 4.93e-003 | 1.77e-001 |
| 1024 | 1.35e-001 | 3.86e-001 | 9.05e-001 | 1.67e-001 | 8.68e-004 | 0.00e+000 | 1.59e+000 | 2.35e-002 | 7.65e-001 |
|---------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------+-----------|
Copyright (C) 2013-2022 Precise Simulation Ltd.
Keywords: Finite Element, FEA, FEM, Fortran, Julia, Octave, Matlab, Benchmark
This program is free software; you can redistribute it and/or modify it under the terms of version 3 of the GNU Affero General Public License (AGPLv3) as published by the Free Software Foundation.
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