2. Reflecting and absorbing faces

The pulse of the first tutorial, centred in the box, against two kinds of $x$ faces: a perfect conductor that reflects it and a Silver–Müller face that lets it out. The energy history tells them apart.

The changes

Start from src/tests/prism/regression/periodic-pulse-blocks/input.ini and change:

[initial_conditions]
r0 = 0.0             ; the packet starts at the centre, away from the x faces

[bc_x_min]
type = PEC           ; then: Silver_Muller
[bc_x_max]
type = PEC           ; then: Silver_Muller

The $y$ and $z$ faces stay periodic. The two faces of an axis must be both periodic or neither; the accepted kinds and their ghost relations are on the boundary conditions page (Silver_Muller is spelled with an underscore).

PEC: the pulse reflects

A perfect electric conductor sets ${\mathbf{E}}_t=0$ and $B_n=0$ on the face, by odd reflection into the ghosts. The packet's centre reaches $+x$ at step 96; the pulse reflects and travels back. Total energy, $W_D+W_B$ from -energy_history.dat:

step	10	50	100	150	192
$W_D+W_B$ (J)	84628.44	84628.44	84628.43	84628.43	84628.42

The box is closed: the energy is conserved to $2\cdot {10}^{-7}$ over the run.

Silver–Müller: the pulse leaves

The first-order Silver–Müller condition imposes the impedance of an outgoing plane wave, $|{\mathbf{E}}_t|=c_0|{\mathbf{B}}_t|$, on the face ghosts: a wave arriving along the normal passes through.

step	10	50	100	150	192
$W_D+W_B$ (J)	84628.44	84628.16	29704.97	375.70	191.57

The pulse crosses the face between steps 50 and 150; what remains at step 192, $2.3\cdot {10}^{-3}$ of the initial energy, is what the first-order condition does not let out. The next page replaces it with a perfectly matched layer.

What you learned

• A face kind is one key per face; periodic pairs the two faces of an axis.
• PEC reflects and conserves the energy; Silver–Müller transmits a normally incident wave to first order.
• The energy history measures what a boundary lets out.

Previous: 1. A pulse in a periodic box. Next: 3. A perfectly matched layer.