Poisson Solver:

This project contains the files which solve the Maxwell's constraint equation for electric fields:

This is done in the electrostatic limit:

Hence the reduced equation we need to solve is:

Dependencies:

The solver makes use of ArrayFire and requires it to be built and installed on the system of usage in addition to the python interface(arrayfire-python. The following Python packages are also required:

• numpy
• pytest

Once ArrayFire is installed successfully, all other dependencies can be installed using pip install -r requirements.txt

Installation:

• First build ArrayFire from source. Suggested installation folder: ${HOME}/arrayfire
• This code needs Python3 to run. Suggested install : Anaconda for Python3
• After installing Anaconda, type which python in the terminal. Output should show that python from Anaconda is being used.
• Next, inside the Poisson_Solver folder, use: pip install -r requirements.txt to install required Python3 libraries.

Usage:

The function fft_poisson assumes that in the density array, x varies along axis 0, y varies along axis 1, z varies along axis 2. Additionally, we consider cell centered formulation to be used throughout. Hence the density array needs to be passed to the function following these conventions:

from fft_poisson_3d import fft_poisson
potential, Ex, Ey, Ez = fft_poisson(rho, dx, dy, dz)

Testing:

The solver can be tested by running:

py.test test_fft_poisson_3d.py