From 26db5e757af37d0a726e07eff7f696faf7983ddd Mon Sep 17 00:00:00 2001 From: Jan Petykiewicz Date: Sat, 8 Feb 2020 17:44:13 -0800 Subject: [PATCH] add note about sources --- meanas/fdtd/__init__.py | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/meanas/fdtd/__init__.py b/meanas/fdtd/__init__.py index 3d498a9..2a99f76 100644 --- a/meanas/fdtd/__init__.py +++ b/meanas/fdtd/__init__.py @@ -137,6 +137,23 @@ Note that each value of \\( J \\) contributes to the energy twice (i.e. once per despite only causing the value of \\( E \\) to change once (same for \\( M \\) and \\( H \\)). +Sources +============= + +It is often useful to excite the simulation with an arbitrary broadband pulse and then +extract the frequency-domain response by performing an on-the-fly Fourier transform +of the time-domain fields. + +The Ricker wavelet (normalized second derivative of a Gaussian) is commonly used for the pulse +shape. It can be written + +$$ f_r(t) = (1 - \\frac{1}{2} (\\omega (t - \\tau))^2) e^{-(\\frac{\\omega (t - \\tau)}{2})^2} $$ + +with \\( \\tau > \\frac{2 * \\pi}{\\omega} \\) as a minimum delay to avoid a discontinuity at +t=0 (assuming the source is off for t<0 this gives \\( \\sim 10^{-3} \\) error at t=0). + + + Boundary conditions =================== # TODO notes about boundaries / PMLs