This procedure is often referred to as working in the frequency domain or
Fourier domain as opposed to the
time domain. From the mathematical point of view, the time-harmonic equation is a Fourier transform of the original time-dependent equations and its solution as function of
ω is the Fourier transform of a full transient solution. It is therefore possible to synthesize a time-dependent solution from a frequency-domain simulation by applying an inverse Fourier transform.
The result of a frequency domain analysis is a complex time-dependent field p, which can be interpreted as an amplitude
pamp = abs(
p) and a phase angle
pphase = arg(
p). The actual pressure at any point in time is the real part of the solution
Visualize the amplitudes and phases as well as the solution at a specific angle (time). When using the Solution data sets, the solution at angle (phase) parameter makes this task easy. When plotting the solution, COMSOL Multiphysics multiplies it by
eiϕ, where
is the angle in radians that corresponds to the angle (specified in degrees) in the
Solution at angle field. The plot shows the real part of the evaluated expression:
The angle is available as the variable phase (in radians) and is allowed in plot expressions. Both the frequency
freq and angular frequency
omega are available variables.