CTG-wave: Continuous Time Galerkin for the (stochastic) wave equation

Continuous-Time Galerkin (CTG) space-time finite element method (FEM) for deterministic and stochastic wave equations.

Space‑time slabs	Solution over space–time

Table of Contents

• Features
• QuickStart
• Installation
• Usage
• Contributing
• License

Features

• Continuous Time Galerkin (CTG) finite element methods for wave equations
• Space-time finite element discretization
• Parametric coefficient handling for uncertainty quantification
• Brownian motion coefficient implementation
• Efficient sparse matrix assembly for space-time operators
• Multiple examples and convergence studies
• Support for various boundary and initial conditions
• Post-processing and error analysis tools

QuickStart

For those who have no time to lose:

# create and activate the conda environment
mamba env create -f environment.yml
conda activate ctg-wave

# install
pip install -e .

# Run default example (uses data in ctg/presets/swe.yaml)
ctg

# Or run with new custom data:
ctg --config-path examples/data_examples/data_swe.yaml

# run tests
pytest -q

The command produces results under results/<timestamp>/ containing:

• meta.json: Simulation metadata and simple metrics on the output
• config_used.yaml: A copy of the configuration file containing problem data and solver parameters
• numerical outputs / plots

Detailed Installation

1. Clone the repository

git clone git@github.com:andreascaglioni/CTG_wave.git

2. Install the dependencies with Mamba

mamba env create -f environment.yml
conda activate ctg-wave

Note: This package has only been tested with dolfinx v0.9.0.

3. Install the package + hooks

pip install -e .
pre-commit install

4. Run the CLI script with default parameters

python -m ctg.cli

5. Run Pytest tests (options set in pyproject.toml)

pytest

Usage

The program can be run from the command line with a YAML file containing the physics and numerics data:

ctg --config-path [data/your_config.yaml]

If no YAML file is provided, the program will use a default file ctg/default_data/data_swe.yaml.

Give a look to it to understand how it is structured. Note that in the same directory there is a file data_swe_functions.py containing the callables referenced in data_swe.yaml (e.g., initial and boundary data functions).

More examples are available in the examples/ directory:

• examples/SWE_CTG_example.py - Basic parametric wave equation example, similar to the CLI script
• examples/WE_CTG_conv_dt.py - Time step convergence study
• examples/SWE_example_ensamble.py - Ensemble simulation example

Documentation

The documentation contains detailed API reference and mathematical background. Find it at https://andreascaglioni.github.io/ctg-wave/

Contributing

Contributions are welcome! Please open an issue or submit a pull request.

License

Distributed under the MIT License. See LICENSE for more information.

Contact

Andrea Scaglioni - Get in touch on my website