pyParareal

Python Parareal is a simple code that is mostly useful to produce matrix formulations of Parareal for linear initial value problems that can then be used for theoretical analysis. The code is not parallelized, it is a tool for theory, not performance measurements.

Attribution

You can freely use and reuse this code in line with its license. If you use it (or parts of it) for a publication, please cite

@article{Ruprecht2018,
author = {Ruprecht, Daniel},
doi = {10.1007/s00791-018-0296-z},
journal = {Computing and Visualization in Science},
pages = {1--17},
title = {Wave propagation characteristics of Parareal},
url = {https://doi.org/10.1007/s00791-018-0296-z},
volume = {19},
year = {2018}
}

Structure of the code

The main functionality is found in the classes located in the

./src

folder. Scripts to produce various figures can be found in the

./scripts

folder and its subfolders. Tests are located in

./tests

and can be run by typing

pytest ./tests/

while in the base folder of the code.

Dependencies

The file

environment.yml

specifies the used Anaconda environment. If Anaconda is installed, the environment can be created by typing

conda env create -f environment.yml

However, to use all functionality, you will also need a working installation of the Dedalus software.

How can I reproduce Figures from the paper "Wave propagation characteristics of Parareal"?

• Fig. 1 and Fig. 2 --> scripts/plot_svd_vs_dt.py
• Fig. 3 --> scripts/plot_dispersion.py with parameter nu=0.0 and nu=0.1
• Fig. 4 --> example/run.py
• Fig. 5 --> scripts/plot_ieuler_dispersion.py
• Fig. 6 --> scripts/plot_dispersion.py with stencil=2 (also set nu=0.0 and dx=1.0)
• Fig. 7 --> scripts/plot_dispersion.py with artificial_coarse=1 and artifical_coarse=2
• Fig. 8 --> example/run.py with artificial_coarse=2
• Fig. 9 --> scripts/plot_svd_vs_waveno_different_G.py
• Fig. 10 -> scripts/plot_dispersion.py with artifical_fine=1
• Fig. 11 -> example/run.py with artifical_fine=1
• Fig. 12 -> scripts/plot_dispersion.py with ncoarse=2
• Fig. 13 -> scripts/plot_dispersion.py with Tend=64 and Nsamples=120
• Fig. 14 -> scripts/plot_svd_vs_P.py
• Fig. 15 -> scripts/plot_conv_vs_waveno.py
• Fig. 16 -> scripts/plot_svd_vs_waveno.py

Pseudo-spectrum of the Parareal iteration matrix

The code now also offers the possibility to compute the pseudo-spectrum and pseudo-spectral radius of the Parareal iteration matrix. You can also uses these parts in line with the in line with its license. If you do, please also cite the following paper in addition to the one stated above:

tba

How can I reproduce Figures from the paper "Impact of spatial coarsening on Parareal convergence"?

tba

Acknowledgements

This project has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955701 (TIME-X). The JU receives support from the European Union's Horizon 2020 research and innovation programme and Belgium, France, Germany, and Switzerland. This project also received funding from the German Federal Ministry of Education and Research (BMBF) grants 16HPC048.

Who do I talk to?

This code is written by Daniel Ruprecht.