A parallel fast multipole method for a space-time boundary element method for the heat equation - A guide to reproducing the numerical experiments
This is a short guide that helps to reproduce the numerical experiments from the paper:
Raphael Watschinger, Michal Merta, Günther Of, Jan Zapletal, A parallel fast multipole method for a space-time boundary element method for the heat equation, SIAM J. Sci. Comput. Vol. 44, Iss. 4 (2022), pp. C320-C345, https://doi.org/10.1137/21M1430157
To run the experiments, please build the BESTHEA library as explained in README.md with the option
-DBUILD_EXAMPLES=ON
In the following we will denote the build directory by BUILD and the root directory of the besthea library by BESTHEA. All experiments are based on the same executable distributed_tensor_dirichlet.
After calling make install this executable is located in
BUILD/bin
The input mesh files are copied into the same directory during the installation.
In the following we list the parameters to use to reproduce all the numerical examples. For details about the individual parameters please execute distributed_tensor_dirichlet --help. For details regarding the used hardware we refer to the paper.
The results in Table 5.1 and Figure 5.1 were generated using the following parameters:
--mesh cube_24_half_scale.txt--space_init_refine 2--endtime 0.25--timeslices 16--refine 1--dist_tree_levels 5--n_min_elems_refine 80--st_coupling_coeff 0.9--trunc_space 5--temp_order 6--spat_order 6--gmres_prec 1e-8
The number of OpenMP threads was set using the OMP_NUM_THREADS environmental variable.
The level of the vectorization (used in Figure 5.1) must be set when generating the Cmake configuration (see README.md) passing in appropriate compiler flags. In the case of the Intel Compiler, we used the -no-vec -no-simd -qno-openmp-simd flags for the non-vectorized version and -xcore-avx512 -qopt-zmm-usage=high for the vectorized version with the length of the vector registers set using the BESTHEA_SIMD_WIDTH variable.
Figures 5.2 and 5.3 were generated using the following parameters:
--mesh cube_24_half_scale.txt--space_init_refine 2--endtime 0.25--timeslices 16--refine 2--dist_tree_levels 5--n_min_elems_refine 800--st_coupling_coeff 0.9--trunc_space 5--temp_order 6--spat_order 6--measure_tasks 1--gmres_prec 1e-8
The measured execution times of process p are written to ./task_timer/process_p.m. To plot the times of process p in a figure in the style of Figure 5.2 use Matlab to run ./task_timer/process_p.m and to call the function plot_tasks provided in
BESTHEA/examples/distributed_tensor_dirichlet/plot_tasks.m
as described in the file's documentation.
The results in Table 5.2 were generated using the following parameters:
--mesh cube_12_half_scale.txt--space_init_refine 4--endtime 0.25--timeslices 256--refine 1--dist_tree_levels 9--n_min_elems_refine 800--st_coupling_coeff 4.1--trunc_space 2--temp_order 4--spat_order 12--gmres_prec 1e-8
The results in Table 5.3 were generated using:
--mesh scaled_crankshaft_11k.txt--space_init_refine 0--endtime 0.25--timeslices 256--refine 1--dist_tree_levels 8--n_min_elems_refine 800--st_coupling_coeff 4.5--trunc_space 2--temp_order 3--spat_order 12--gmres_prec 1e-6
Figure 5.5 can be generated using EnSight, ParaView, or any program capable of processing the EnSight file format. For this purpose one has to provide an additional target directory to the executable distributed_tensor_dirichlet via the additional option
--ensight_dir TARGET_DIRECTORY.
All files needed for the visualization of the approximated Neumann datum (in addition to the projections of the Neumann and Dirichlet data) are stored in this directory.