Need introductory examples with pictures!

[arturgower]

ElasticWaves.jl/test/inverse_problems.jl

Lines 98 to 128 in bfcf59c

	ksa = bearing.outer_radius * ω / steel.cs
	# estimate the largest basis_order that a wave scattered from the inner boundary can be measured at the outer boundary
	# basis_order = estimate_basisorder(ω, bearing; tol =1e-5)
	basis_order = 5
	basis_length = basisorder_to_basislength(Acoustic{Float64,2}, basis_order)
	# 0.0 and 2pi are the same point
	θs = LinRange(0.0,2pi, basis_length + 1)[1:end-1]
	# let's create a focused pressure on the inner boundary
	fs = θs .* 0 + θs .* 0im |> collect;
	fp = θs .* 0 + θs .* 0im |> collect;
	# fp[1:3] = 1e5 .* ones(3) - 1e5im .* ones(3)
	fp[1] = 1e5
	θ0 = θs[1]
	x0 = radial_to_cartesian_coordinates([bearing.inner_radius, θ0])
	bd1 = BoundaryData(TractionBoundary(inner = true); θs = θs, fields = hcat(fp,fs))
	bd2 = BoundaryData(TractionBoundary(outer = true); θs = θs, fields = hcat(fs,fs))
	sim = BearingSimulation(ω, bearing, bd1, bd2)
	# let's have a look at the modes that were calculated during the Bearing. This is the field we will actual approximate
	inner_field = fouriermodes_to_fields(θs,sim.boundarydata1.fourier_modes)
	@test norm(inner_field[:,1] - fp) < 1e-10

The code above should form the basis of an introductory example on the landing page of this package. It is easier to explain the method in terms of the traction applied at boundaries rather than the Fourier modes. But can add Fourier mode example too.