gridlod-random-perturbations

# This repository is part of the project for "An offline-online strategy for multiscale problems with random defects":
#   https://github.com/BarbaraV/gridlod-random-perturbations
# Copyright holder: Barbara Verfürth 
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)

This repository provides code for the experiments of the paper "An offline-online strategy for multiscale problems with random defects" by Axel Målqvist and Barbara Verfürth. The code is based on the module gridlod which has been developed by Fredrik Hellman and Tim Keil and consists of code for PGLOD. gridlod is provided as a submodule, the files in the subfolder random_perturbations extend the PGLOD with the offline-online strategy for random defects and were written by Barbara Verfürth.

Setup

This setup works with a Ubuntu system. The following packages are required (tested versions):

• python (v3.8.5)
• numpy (v1.17.4)
• scipy (v1.3.3)
• scikit-sparse (v0.4.4)
• matplotlib (v3.1.2)

Please see also the README of the gridlod submodule for required packages and setup. After cloning this repo with git, initialize the submodule via

git submodule update --init --recursive

Now, build and activate a python3 virtual environment with

virtualenv -p python3 venv3
. venv3/bin/activate

and execute the following commands

echo $PWD/gridlod/ > $(python -c 'from distutils.sysconfig import get_python_lib; print(get_python_lib())')/gridlod.pth

Now you can use every file from the subfolders in the virtualenv. Install all the required python packages for gridlod.

Reproduction of experiments

First of all, change into the folder with the experiments

cd experiments

Reproduction of the experiments consists of two steps: (i) generating the data and (ii) visualization.

Generating the data

To reproduce the data of the experiments run

python3 exp1_randcheck1d.py

for the experiments of Section 6.1;

python3 exp2_randcheck2d.py

for the experiments of Section 6.2;

python3 exp3a_randdef2dvalues.py

and

python3 exp3b_randdef2dchanges.py

for the experiments of Section 6.3;

python3 exp4_indicator.py

for the experiments of Section 6.4. Some results, in particular the timings of Section 6.2, will be printed on screen and the data for the figures will be stored as .mat-files. Note that running these experiments may take quite a while.

Visualization

To reproduce the figures with the errors in Section 6 (Figures 6.1, 6.2, 6.4, and 6.5), run

python3 plot_results.py

All data from the experiments are available and stored in the data-folder as .mat-files, so you can skip the step of generating the data to save time.

Apart from the visualization of the errors, you can also reproduce the coefficient visualizations from the paper (Figures 1.1, 3.2, and 6.3) by running

python3 plot_coeffs.py

This is completely independent from the other experiments.

Note

This code is meant to illustrate the numerical methods presented in the paper. It is not optimized in any way, in particular no parallelization is implemented. See gridlod for some further explanations of parallelization of the standard PGLOD with ipyparallel.