RFC: Include example of vector waves (such as electromagnetism or elasticity)

[jondea]

Currently the machinery should work for acoustics, which is a scalar equation. But we have not yet tested for any physics with a FieldDim > 1. Without a test case it is hard to see what to do. The outer types and structure should be fine, but I expect the inner machinery will break. We also need to be careful that when we generalise the machinery fully that we don't make it slower.

[arturgower]

Much of the inner machinery has now been made more abstract, making it easier to add a new kind of wave, including vectorial waves.

Below is a list of functions and types that need to be implemented. For clarity I will imagine we are trying to implement Electromagnetism:

• A subtype Electromagnetism{T,Dim} <: PhysicalMedium{Dim,2}
• The basis functions of the space including:
  • outgoing_basis_function for outgoing waves
  • regular_basis_function for regular spherical waves
  • outgoing_translation_matrix to translate outgoing waves from one origin to another (addition translation theorem)
  • basisorder_to_basislength and basislength_to_basisorder
• A T-matrix, for example for a sphere we would need to define the function t_matrix(p::Particle{3,Electromagnetism{T,3},Sphere{T,3}}

After this, some small detail in internal working of the functions run and field may need adjusting, but this should be very minor.