EMSim

EMSim is a FDTD (Finite-Difference Time-Domain) solver for the Maxwell equations.

The three scripts are standalone simulations — not a library.

• 1d.py — 1D FDTD, Ey/Hx mode, accelerated with numba
• 2d.py — 2D FDTD, Hz mode, accelerated with numba
• 1d-tensorflow.py — 1D FDTD using the TF2 eager execution API

Run

. venv.sh  # creates .venv, activates it, installs requirements.txt
./1d.py    # run a simulation (opens matplotlib animation window)
./2d.py
./1d-tensorflow.py

Code

Grid and time-step derivation

Simulation parameters (grid size, dt, dz/dx/dy, number of steps) are all derived from physical constants and the material stack at startup. The Courant-Friedrichs-Lewy (CFL) condition governs dt:

dt = n_min * dz / (2 * c0)

Grid spatial resolution is set by the minimum wavelength and dzpmwl (cells per wavelength, default 10).

Material definition

Materials are defined as a list of tuples that overwrite each other in order (last write wins). Free space must be the first entry:

• 1D: (mr, er, start_m, width_m)
• 2D: (mr, er, startx_m, starty_m, widthx_m, widthy_m)

The material arrays (mr, er) are filled by iterating layers and snapping to the grid.

Update coefficients

Precomputed coefficient arrays mkhx and mkey are used in the field update equations to avoid repeated division inside the hot loop:

mkhx = c0 * dt / mr
mkey = c0 * dt / er

Normalized magnetic field

The magnetic field H is stored normalized (multiplied by the impedance of free space). Source injection must account for this with a_corr = -sqrt(er/ur).

@numba.jit() step functions

The inner simulation loop is wrapped with @numba.jit() for performance. The step() function takes field arrays and a range (ifrom, ito) rather than iterating one step at a time. The batch variable controls how many steps run between animation frames.

Absorbing boundaries

Boundaries use a log-linear dampening ramp (LB, RB) applied to both E and H after each update step. Thickness is bsize cells.

Source types

Three source functions are defined in each script (sinc, Gaussian pulse, blip). Sources are injected as soft sources by adding to a specific grid cell index. The Gaussian pulse source is used by default.

TensorFlow variant

1d-tensorflow.py uses TF2 eager execution. E and H are tf.Variables. The inner loop is compiled with @tf.function(input_signature=[...]), which traces the graph once and reuses it for every call. Sequential field update ordering (H before E) is achieved by structuring the Python code sequentially inside the @tf.function body — no tf.control_dependencies needed. Point-source injection uses tf.tensor_scatter_nd_add; interior field updates are written back via tf.concat + Variable.assign. Field values are read back for display with .numpy(). EMSim is a FDTD solver for the Maxwell equations with focus on simulating antennas.