Galerkin POD for PDEs with Uncertainties

This is the code of the numerical experiments in our paper

Benner, Heiland (2020): Space and Chaos-expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification

in the third version from December 2022.

Installation

Install dolfin and gmesh.

Then clone this repo and install the package with dependencies via

pip install -e .  # make sure you use Python 3

if the installation of multim-galerkin-pod fails because of scikit-sparse try pip install --no-deps multidim-galerkin-pod==1.1.0 instead.

The source are in gen_pod_uq and the files for the simulations are in scripts.

Rerun the simulations

NOTE: For reproduction of the results, use version 1.1.4 of the package to be installed like

pip install gen-pod-uq==1.1.4

from the pypi repo

Generate the mesh

cd mesh
mkdir 3D-mshs
source maketheme-3D.sh

Results of the PCE and POD approximations

To reproduce the results of the manuscript

cd scripts
source runitall.sh

You may want to comment out some parts.

Post Processing

The raw data of our simulations is provided in the folder rawdata. In order to postprocess copy it to the scripts/cached-data folder

# ## caution: this may replace computed data
# cp rawdata/*json scripts/cached-data/
# ## caution: this may replace computed data

cd scripts
source postprocess.sh

Evaluating the Kolmogorov Metric

# ## caution: this may replace computed data
# cp rawdata/ysoltens-for-kolmogorov-metric-evaluation/*npy scripts/cached-data/
# ## caution: this may replace computed data

cd scripts
python3 kolmogorov-metrix.py

In order to (only) compute the plots, one may run a reduced experiment by setting

onlyplots = True

in kolmogorov-metrix.py.