spectralETD

spectralETD is a Python library which combines Exponential Time Differencing and Pseudo-spectral Methods for Phase-Field Model Equation in three dimensions in a GPU-accelerated framework.

Requirements

• Python 3.10 or later
• NumPy is the fundamental package for scientific computing with Python.
• SciPy is a collection of fundamental algorithms for scientific computing in Python.
• Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python.
• PyTorch is a high-level library for machine learning, with multidimensional tensors that can also be operated on a CUDA-capable NVIDIA GPU.

Optional

• SciencePlots is a Matplotlib styles complement for scientific figures

Time Integration Methods

• 'IMEX': implicit-explicit Euler method;
• 'IF': Integrating Factor method
• 'ETD': Exponential Time Differencing

Installation

The easiest way to install spectralETD is by using pip:

pip install spectralETD

To install the development version:

pip install git+https://github.com/elvissoares/spectralETD.git

or

git clone https://github.com/elvissoares/spectralETD
cd spectralETD
pip install -e .

Examples

• 1D Advection-Diffusion equation (DiffusionAdvection1d.ipynb);
• 1D Burgers equations (Burgers1d.ipynb);
• 2D Cahn-Hilliard equation (CH2d.ipynb);
• 3D Cahn-Hilliard equation (CH3d.ipynb);

You can also see some plots and movies of the examples in the examples's folder in the github repository.

Citing spectralETD

If you use spectralETD in your work, please consider to cite it using the following reference:

Soares, E. do A., Barreto, A. G. & Tavares, F. W. Exponential Integrators for Phase-Field Equations using Pseudo-spectral Methods: A Python Implementation. 1–12 (2023). ArXiv: 2305.08998

Bibtex:

@article{Soares2023,
archivePrefix = {arXiv},
arxivId = {2305.08998},
author = {Soares, Elvis do A. and Barreto, Amaro G. and Tavares, Frederico W},
eprint = {2305.08998},
month = {may},
pages = {1--12},
title = {{Exponential Integrators for Phase-Field Equations using Pseudo-spectral Methods: A Python Implementation}},
url = {http://arxiv.org/abs/2305.08998},
year = {2023}
}

Contact

Prof. Elvis do A. Soares

e-mail: elvis@peq.coppe.ufrj.br

Chemical Engineering Program - COPPE

Universidade Federal do Rio de janeiro (UFRJ)

Brazil