This repository contains minimal code for running the numerical examples in the paper:

D. Pradovera, M. Nonino, and I. Perugia, Geometry-based approximation of waves in complex domains (2023)

Preprint publicly available here!

• numpy and scipy
• matplotlib
• fenics and mshr for 2D FEM tests

The 2D FEM engine relies on FEniCS. If you do not have FEniCS installed, you may want to create an Anaconda3/Miniconda3 environment using the command

conda create -n fenicsenv -c conda-forge numpy=1.21.4=py38he2449b9_0 scipy=1.5.3=py38h828c644_0 matplotlib=3.4.3=py38h578d9bd_1 fenics=2019.1.0=py38_9 mshr=2019.1.0=py38hf9f41d3_3 boost-cpp=1.72.0=h312852a_5

This will create an environment where FEniCS (and all other required modules) can be used. In order to use FEniCS, the environment must be activated through

conda activate fenicsenv

See the Anaconda documentation for more information.

More recent versions of FEniCS and mshr may be preferred, but one should be careful of inconsistent dependencies. If the following code snippet runs successfully, then your environment should have been created correctly:

from mshr import *

The ROM-based simulations can be run via run_rom.py. The FEM-based simulations can be run via run_fem.py.

Code can be run as

python3 run_rom.py $example_tag

or

python3 run_fem.py $example_tag

The placeholder $example_tag can take the values

• wedge_1
• wedge_2
• wedge_3
• wedge_4
• cavity
• room_tol2.5e-2
• room_tol1e-3
• room_harmonic_1
• room_harmonic_5

Otherwise, one can simply run

python3 run_rom.py

or

python3 run_fem.py

and then input $example_tag later.

Part of the funding that made this code possible has been provided by the Austrian Science Fund (FWF) through projects F 65 and P 33477.