gen-pod-uq 0.0.3

Core module for genpod for UQ

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

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==1.0.2 instead.

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

Rerun the simulations

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.

Meshtest

cd scripts
python3 test_the_meshs.py

The small examples of Section 6

cd scripts
python3 test_pce_mc.py

The file test_pce_mc.py has appended the commands that can be processed in Mathematica to compute the reference values.