Description

This folder contains the sources of the paper

"An adaptive parareal algorithm"

by Y. Maday and O. Mula. Arxiv link

Required software

Python >= 3.7

Required packages: scipy, numpy, matplotlib, pandas

Running the adaptive and classical parareal algorithm

You can run the adaptive and classical parareal algorithm by calling

python3 run_parareal.py -ode odename -T 200 -N 10 -eps 1.e-8 -eps_g 0.1 -fn foldername

The parameters are the following:

• ode: type of ODE. Supported keys={Brusselator, VDP, Oregonator, SEIR}
• T: final time
• N: Number of processors
• eps: final target accuracy
• eps_g: accuracy of the coarse solver
• fn: data and plots about the results of the run are stored in odename/fn

All parameters are optional and the default values are:

• ode: Brusselator
• T: 10
• N: 10
• eps: $10^{-6}$
• eps_g: $10^{-1}$
• fn: default

How to reproduce the results of the paper

You can run the following command in a cluster using PBS for job scheduling

./run_bulk_test_brusselator.sh
./run_bulk_test_vdp.sh

This is an intensive operation that calls multiple times the file run_parareal.py for different parameters T, N, eps and stores each run in a folder, e.g., Brusselator/T_10-N_20-eps_1.0e-08.

Once this is done, you can build the performance plots of the paper by calling

python3 study_performance.py -ode odename -fn foldername

How to test other ODEs

• Add a class MY_NEW_ODE in ode.py following the already existing examples.
• Add a keyword for the new ode in ode_dict at the end of the file ode.py.

Licence

Licensing information can be found in the accompanying file COPYING.md. Copyright (c) 2019, Olga Mula (Paris Dauphine University).