ssWFS is a Python program that calculates the steady-state power density of the wifi signal over the downstairs of my house. The program solves the inhomogeneous two-dimensional vector Helmholtz equation with natural boundary conditions using the finite element method. Both circular wave and approximate Dirac Delta function sources are modeled in detail. ssWFS then generates a filled contour plot of the power density. The relative levels of the plot are correct, but the numerical values are dubious as I was unsure about the scaling of the source term. The script is configured for automatic documentation generation using Python's built-in command line tools.
To run ssWFS, simply enter
$ python ssWFS.py
into any command line interface. The script can also be run from any Python IDE such as IDLE or VS Code. There are dependencies on the following Python libraries, all of which are easily installed from the command line using pip:
Numpy: https://numpy.org/ SciPy: https://www.scipy.org/ Matplotlib: https://matplotlib.org/stable/users/installing.html Triangle: https://rufat.be/triangle/
TDGS.py is a Python program still in beta that calculates the relative instantaneous power density of the WiFi signal over the downstairs of my house. The program solves the inhomogeneous wave equation with point time dependent source with harmonics at 2.4 and 5.0 GHz with natural boundary conditions. TDGS is a 2D finite element version of the 3D finite difference time domain (FDTD) method commonly used in computational electromagnetics. To run TDGS program, simply enter into the command line
$ python TDGS.py
Possible extensions of this program include modifiying the code such that it solves general second order linear elliptic PDEs with Robin boundary conditions as well as including a function that can read in parameters desribing the domain of the problem using a file. Code was tested with Python version 3.9.
Eric Gelphman University of California Irvine Department of Mathematics