POD-RBF NIROM

A collection of high-fidelity (HFM) snapshots are generated that sufficiently capture the time-dynamics of the simulation. POD is adopted to define a reduced basis space for the high-fidelity snaphosts. Radial basis function (RBF) interpolation is employed to approximate the time dynamics in the reduced space spanned by the POD modes. A family of greedy algorithms are proposed to select an optimal set of RBF collocation points for the construction of the interpolant.

Citation

If you find this repo useful for your research, please consider citing:

A greedy non-intrusive reduced order model for shallow water equations,

S. Dutta, M. Farthing, E. Perracchione, G. Savant, M. Putti, (2021),

Journal of Computational Physics, Journal Link

ArXiV preprint.

@article{DUTTA2021,
title = {A greedy non-intrusive reduced order model for shallow water equations},
journal = {Journal of Computational Physics},
pages = {110378},
year = {2021},
issn = {0021-9991},
doi = {https://doi.org/10.1016/j.jcp.2021.110378},
author = {Sourav Dutta and Matthew W. Farthing and Emma Perracchione and Gaurav Savant and Mario Putti},
}

Getting Started

The core modules are in the podrbf subdirectory. The notebooks subdirectory contains a jupyter notebook that implements two different shallow water examples using AdH as the high-fidelity solver. The data subdirectory contains high-fidelity snapshots and mesh files for the shallow water example problems. Some additional data files are available at Link.

Dependencies

• python 2.x or 3.x
• matplotlib
• numpy
• scipy
• jupyter

Installation

• Install the dependencies
• Clone this repo

git clone [email protected]:erdc/podrbf_nirom.git
cd podrbf_nirom

Examples

cd notebooks
jupyter notebook

Shallow water equations (Red River) :-----:

p-greedy centers :-----:

f-greedy centers :-----:

psr-greedy centers :-----:

Authors

• Sourav Dutta - [email protected] - ERDC-CHL
• Matthew Farthing - [email protected] - ERDC-CHL

License

This project is licensed under the MIT License - see the LICENSE.md file for details

Acknowledgments

• Thank you to all the co-authors, Dr. Stacey Howington, Dr. Hwai-Ping Cheng, Dr. Corey Trahan, and the reviewers for the valuable suggestions.
• Thank you to ERDC-HPC facilities for support with valuable computational infrastructure
• Thank you to ORISE for support with appointment to the Postgraduate Research Participation Program.