aspcol.planewaves.plane_wave

aspcol.planewaves.plane_wave(pos, direction, wave_num, exp_center=None)

The complex response of a plane wave for a specific frequency for a set of positions.

Implements exp(-ik(r-r_c)^T d) where r is the position, d is the direction of the plane wave. and r_c is the expansion center (the point around which the directions are calculated).

Using the time-harmonic convention of exp(-iwt), the plane wave is defined as exp(ikr^T d) where d is the plane wave propagation direction [martinMultiple2006]. Therefore the direction provided is the direction from which the plane wave is incoming.

posndarray of shape (num_positions, 3)

The positions where the plane wave is evaluated

directionndarray of shape (num_direction, 3)

The directionfrom which the plane wave is incoming. Must be a unit vector

wave_numfloat or ndarray of shape (num_real_freqs,)

The wave number of the plane wave. Defined as 2*pi*f/c where f is the frequency and c is the speed of sound.

Returns:

plane_wave – The complex response of the plane wave at the positions.

Return type:

ndarray of shape (num_positions, num_direction) or (num_real_freqs, num_positions, num_direction)

References

[martinMultiple2006] P. A. Martin, Multiple scattering: Interaction of time-harmonic waves with N obstacles, vol. 107. in Encyclopedia of mathematics and its applications, vol. 107. Cambridge, UK: Cambridge University Press, 2006.