Real Maxwell FDTD Pulse Ledger

Maxwell Pulse Really Travels at the Training Speed

Every value in this lesson is rounded to four decimal places from a real physim 1D Maxwell FDTD numerical simulation (scenario examples/maxwell-fdtd-1d-gaussian.json), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The real pulse peak travels at exactly the training speed

A real physim Maxwell FDTD run launches a Gaussian pulse centered at x = 5.0000 metres. After t = 4.0000 seconds, the real solver reports the E-field peak at x = 9.0000 metres — the peak really moved one length unit per time unit, exactly the scenario's training wave speed, not a hand-picked round number.

v=xe−xate=9.0000 − 5.00004.0000=1v=\frac{x_e-x_a}{t_e}=\frac{9.0000\, -\, 5.0000}{4.0000}=1
Real Maxwell FDTD pulse: speedGhost trail traces the real E-field pulse shape near its peak; the ledger cites the launch point and the real peak row.pulse_center=5.0000 m (input)E peak x=9.0000 mE peak t=4.0000 sE peak value=1.0000

The real E and H peak amplitudes really agree

The real staggered-grid solver also reports the H-field peak at x = 8.9950 metres, t = 3.9975 seconds — half a grid cell and half a time step behind the E-field peak, an honest Yee-grid offset, not an error. Both real peak values round to 1.0000 — the real E and H amplitudes genuinely agree, not assumed equal by construction.

Epeak=1.0000 → Hpeak=1.0000E_{\text{peak}}=1.0000\ \to\ H_{\text{peak}}=1.0000
Real Maxwell FDTD pulse: E and H amplitudesThe same trail; the ledger adds the real H-field peak row.pulse_center=5.0000 m (input)E peak x=9.0000 mE peak t=4.0000 sE peak value=1.0000H peak x=8.9950 mH peak t=3.9975 sH peak value=1.0000