A bifurcation analysis toolbox built for FreeFEM.
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Table of Contents

1. About The Project
2. Getting Started
   • Prerequisites
   • Installation
3. Usage
4. Roadmap
5. Contributing
6. License
7. Contact
8. Acknowledgments

About The Project

ff-bifbox is a package of scalable and cross-compatible FreeFEM scripts designed for numerical continuation, bifurcation analysis, resolvent analysis, and time-integration of large-scale time-dependent nonlinear PDEs on adaptively refined meshes. The project is built on top of FreeFEM, a free, open-source finite-element software, and PETSc, a scalable scientific computing library.

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Getting Started

Prerequisites

Make sure you have access to a recent FreeFEM installation (version 4.14 or above), compiled with the PETSc and PETSc-complex (with SLEPc) plugins. Guides for compiling FreeFEM with PETSc can be found on the FreeFEM GitHub page or in this tutorial by Pierre Jolivet. More details about the PETSc and SLEPc options used in the solvers may be found in their respective manuals.

Installation

1. Clone the repo

   git clone https://github.com/cmd8/ff-bifbox.git

2. Add ff-bifbox to FreeFEM's filepath

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Usage

See the examples folder.

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Roadmap

• Add linear resolvent analysis framework
• Add time-domain nonlinear simulation framework
• Add support for 3-D problems with multiple symmetries
• Add harmonic balance framework for computation/continuation of periodic orbits
• Add time-domain linear simulation framework
• Add Floquet analysis for periodic orbits
• Add fold/Neimark-Sacker bifurcation computation/continuation for periodic orbits
• Improve documentation and tutorials/examples

See the open issues for a full list of proposed features (and known issues).

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Contributing

Contributions are what make the open source community such an amazing place to learn, inspire, and create. Any contributions you make are greatly appreciated.

If you have a suggestion that would make this better, please fork the repo and create a pull request. You can also simply open an issue with the tag "enhancement". Don't forget to give the project a star! Thanks again!

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
3. Commit your Changes (git commit -m 'Add some AmazingFeature')
4. Push to the Branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

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License

Distributed under the GPL-3.0 License. See LICENSE for more information.

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Contact

Chris Douglas - [email protected]

Project Link: https://github.com/cmd8/ff-bifbox

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Acknowledgments

• Pierre Jolivet

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