juliawavescattering / effectivewaves.jl

A package to calculate ensemble averaged waves in heterogeneous materials. The focus is on wave propagation, scattering, and reflection, from particulate and porous materials.

EffectiveWaves

A Julia package for calculating, processing and plotting waves travelling in heterogeneous materials. The focus is on ensemble averaged waves.

Documentation	Build Status

At present, the package focuses on materails filled with randomly placed particles. You can calculate effective wavenumbers for 2D [1] and 3D [4] acoustics, wave transimission and wave reflection in 2D [1,2,3] and 3D [4], and scattering from an inhomogenious sphere [4]. See these notes for brief formulas on effective wavenumbers.

Together with MultipleScattering.jl, this package has been setup to easily extend to other dimensions, materials, and types of waves, such as elastic and electromagnetic waves.

Documentation

• Stable — documentation of the most recently tagged version.
• Develpment — documentation of the in-development version.

More examples

For more examples and details go to docs/src/examples/.

Acknowledgements and contributing

This library was originally written by Artur L Gower. Contributions are very welcome.

The implementation of the Percus-Yevick pair correlation was based these notes [5].

The low frequency effective properties was based on these notes.

References

[1] Gower AL, Smith MJ, Parnell WJ, Abrahams ID. "Reflection from a multi-species material and its transmitted effective wavenumber". Proc. R. Soc. A. 2018 Apr 1;474(2212):20170864.

[2] Gower, Artur L., William J. Parnell, and I. David Abrahams. "Multiple waves propagate in random particulate materials". SIAM Journal on Applied Mathematics 79.6 (2019): 2569-2592.

[3] Gower, Artur L., I. David Abrahams, and William J. Parnell. "A proof that multiple waves propagate in ensemble-averaged particulate materials". Proceedings of the Royal Society A 475.2229 (2019): 20190344.

[4] Artur L. Gower and Gerhard Kristensson. "Effective Waves for Random Three-dimensional Particulate Materials". New Journal of Physics (2021).

[5] Gerhard Kristensson. "The Percus-Yevick approximation". github.com/JuliaWaveScattering/EffectiveWaves.jl (2022).

effectivewaves.jl's Issues

The SetupSymmetry types should have fields to fully describe setup.

At present, the subtypes of SetupSymmetry are used only to distinguish what methods to run. They are chosen by analysing the symmetry between the types Source and Material. The code would however be more elegant and easier to generalise if subtypes, such as WithoutSymmetry, had the fields Material, Source, basis_order, basis_field_order. At present several of these are carried with kws, which leads to more hidden behaviour, and some complications with dispatching to different WaveModes.

EffectiveWaves.jl/src/material_types.jl

Lines 10 to 30 in cf5123f

	struct WithoutSymmetry{Dim} <: AbstractSetupSymmetry{Dim} end
	"""
	An incident plane-wave and halfspace material will result in all fields being plane-waves.
	"""
	abstract type AbstractPlanarSymmetry{Dim} <: AbstractSetupSymmetry{Dim} end
	struct PlanarSymmetry{Dim} <: AbstractPlanarSymmetry{Dim} end
	"""
	For spatial dimension > 2, we can consider problems that have azimuthal symmetry. For example, a plane-wave incident on a sphere.
	"""
	abstract type AbstractAzimuthalSymmetry{Dim} <: AbstractSetupSymmetry{Dim} end
	struct AzimuthalSymmetry{Dim} <: AbstractAzimuthalSymmetry{Dim} end
	AzimuthalSymmetry() = AzimuthalSymmetry{3}()
	"""
	For example, a plane-wave with direct incidence on a halfspace will have both azimuthal and plane-wave symmetry.
	"""
	struct PlanarAzimuthalSymmetry{Dim} <: AbstractPlanarSymmetry{Dim} end
	PlanarAzimuthalSymmetry() = PlanarAzimuthalSymmetry{3}()

All effective waves should have the same structure

The effective wave types should have the same structure. For example see EffectivePlaneWaves

EffectiveWaves.jl/src/wave_types.jl

Lines 39 to 45 in c6ad025

	struct EffectivePlaneWaveMode{T<:AbstractFloat,Dim} <: AbstractWaveMode{T,Dim}
	ω::T
	wavenumber::Complex{T}
	basis_order::Int
	direction::SVector{Dim,Complex{T}} # the effective direction where sum(direction.^2) == 1
	eigenvectors::Array{Complex{T}} # the effective ampliudes
	end

Each effective wave type should have only enough information for fully describe the value of this wave at some point in space.

The necessary fields are the eigenvectors, basis_order, wavenumber, and ω. Extra fields should be used sparring and only when necessary. This is certainly not the case for:

EffectiveWaves.jl/src/wave_types.jl

Lines 88 to 96 in c6ad025

	struct EffectiveRegularWaveMode{T<:AbstractFloat,Dim,P<:PhysicalMedium{T,Dim},S<:AbstractSetupSymmetry{Dim}} <: AbstractRegularWaveMode{T,Dim}
	ω::T
	wavenumber::Complex{T}
	medium::P
	material::Material{Dim}
	eigenvectors::Array{Complex{T}} # the effective eigenvectors, each column is one eigenvector
	basis_order::Int
	basis_field_order::Int
	function EffectiveRegularWaveMode(ω::T, wavenumber::Complex{T}, source::AbstractSource{T}, material::Material{Dim}, eigenvectors::Array{Complex{T}};

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Need non-dimensional dispersion equations

A non-dimensional version of dispersion equations would help make the whole optimisation part more numerically robust.

Effective angle and analytic split inconsistent

The branch-cuts for the effective angle and wavenumber are different for the wiener-hopf method, in comparison for other methods. See code 1 and 2.

Need to go back to the paper and adjust.

material scattering coefficients should return a wave

There are several functions that return the coefficients of a wave basis as a final result. For example, scattering coefficients from a sphere, or the reflection coefficient from a halfspace. Instead, these functions should return a canonical wave which is the scattered wave. This would questions like: what phase should the reflected wave have? What kind of basis should these coefficients have (may potential have azimuth symmetry).

EffectiveWaves.jl/src/acoustics/effective_wave/regular/material_scattering_coefficients.jl

Line 3 in c6ad025

function material_scattering_coefficients(wavemode::EffectiveRegularWaveMode{T,3,Acoustic{T,3},WithoutSymmetry{3}}) where T

EffectiveWaves.jl/src/acoustics/effective_wave/planewaves/material_scattering_coefficients.jl

Line 8 in c6ad025

function reflection_coefficient(ω::T, wave_eff::EffectivePlaneWaveMode{T}, psource::PlaneSource{T,2,1,Acoustic{T,2}}, material::Material{2,Halfspace{T,2}};