Numerical experiment scripts for the parallel SDC paper#

Python scripts of the numerical experiments of the paper Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections by Čaklović, Lunet, Götschel and Ruprecht (SIAM Journal on Scientific Computing, 2025).

Figures for the manuscript#

See the scripts folder, all python scripts have the fig0[…] prefix, and each script generate several figures from the manuscript. One can run everything with the run.sh script, and crop the pdf figures to the format used in the manuscript with the crop.sh script.

Note that most scripts generate error vs cost figure using a cost modeling of the simulation that counts the number of Newton iterations and RHS evaluation. This can be switched to a estimation of the cost using runtime measurements by :

  • modifying the return statement in the getCost function by return tComp

  • changing the xlabel=”Cost” in the plt.gca().set call into xlabel=”Computation time [s]”

  • commenting the xlim argument in the plt.gca().set call

Experimental scripts#

For several problem probName, there is two scripts :

  • {probName}_setup.py : runs the problem with specific parameters and one given SDC configuration

  • {probName}_accuracy.py : generate error vs dt and error vs cost figures for different SDC configurations

In addition, there is those generic scripts for analysis :

  • convergence.py : generate convergence graph for specific SDC configurations, using Dahlquist

  • nilpotency.py : look at nilpotency of stiff and non-stiff limit of the SDC iteration matrix

  • stability.py : generate stability contours for specific SDC configurations

Finally, all those scripts use the utility module utils.py.

Papers#

The results of this project are published in:

  • Gayatri Čaklović, Thibaut Lunet, Sebastian Götschel, Daniel Ruprecht, Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections, SIAM Journal on Scientific Computing 47(1), A430–A453, 2025, https://doi.org/10.1137/24M1649800

    BibTeX
    @article{čaklović2025improving,
    author = {Čaklović, Gayatri and Lunet, Thibaut and Götschel, Sebastian and Ruprecht, Daniel},
    title = {Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections},
    journal = {SIAM Journal on Scientific Computing},
    volume = {47},
    number = {1},
    pages = {A430--A453},
    year = {2025},
    doi = {10.1137/24M1649800}
}