Grid and particle generation

generate_grid(GridProp, mesh)

Generate a background grid where each element is of type GridProp. The first field of GridProp is designated for mesh, and thus its type must match eltype(mesh). The resulting grid is a StructArray.

Examples

julia> struct GridProp{dim, T}
           x  :: Vec{dim, T}
           m  :: Float64
           mv :: Vec{dim, T}
           f  :: Vec{dim, T}
           v  :: Vec{dim, T}
           vⁿ :: Vec{dim, T}
       end

julia> grid = generate_grid(GridProp{2, Float64}, CartesianMesh(0.5, (0,3), (0,2)));

julia> grid[1]
GridProp{2, Float64}([0.0, 0.0], 0.0, [0.0, 0.0], [0.0, 0.0], [0.0, 0.0], [0.0, 0.0])

julia> grid.x
7×5 CartesianMesh{2, Float64, Vector{Float64}}:
 [0.0, 0.0]  [0.0, 0.5]  [0.0, 1.0]  [0.0, 1.5]  [0.0, 2.0]
 [0.5, 0.0]  [0.5, 0.5]  [0.5, 1.0]  [0.5, 1.5]  [0.5, 2.0]
 [1.0, 0.0]  [1.0, 0.5]  [1.0, 1.0]  [1.0, 1.5]  [1.0, 2.0]
 [1.5, 0.0]  [1.5, 0.5]  [1.5, 1.0]  [1.5, 1.5]  [1.5, 2.0]
 [2.0, 0.0]  [2.0, 0.5]  [2.0, 1.0]  [2.0, 1.5]  [2.0, 2.0]
 [2.5, 0.0]  [2.5, 0.5]  [2.5, 1.0]  [2.5, 1.5]  [2.5, 2.0]
 [3.0, 0.0]  [3.0, 0.5]  [3.0, 1.0]  [3.0, 1.5]  [3.0, 2.0]

julia> grid.v
7×5 Matrix{Vec{2, Float64}}:
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]
 [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]  [0.0, 0.0]

generate_particles([ParticleProp], mesh; alg=PoissonDiskSampling())

Generate particles across the entire mesh domain based on the selected alg algorithm. See also GridSampling and PoissonDiskSampling.

The generated particles is a StructArray where each element is of type ParticleProp. The first field of ParticleProp is designated for particle positions.

julia> ParticleProp = @NamedTuple begin
           x  :: Vec{2, Float64}
           m  :: Float64
           V  :: Float64
           v  :: Vec{2, Float64}
           F  :: SecondOrderTensor{2, Float64, 4}
           σ  :: SymmetricSecondOrderTensor{2, Float64, 3}
       end
@NamedTuple{x::Vec{2, Float64}, m::Float64, V::Float64, v::Vec{2, Float64}, F::Tensor{Tuple{2, 2}, Float64, 2, 4}, σ::SymmetricSecondOrderTensor{2, Float64, 3}}

julia> mesh = CartesianMesh(0.5, (0,3), (0,2));

julia> particles = generate_particles(ParticleProp, mesh; alg=GridSampling());

julia> particles.F[1] = one(eltype(particles.F));

julia> particles[1]
(x = [0.125, 0.125], m = 0.0, V = 0.0, v = [0.0, 0.0], F = [1.0 0.0; 0.0 1.0], σ = [0.0 0.0; 0.0 0.0])

julia> particles.F
96-element Vector{Tensor{Tuple{2, 2}, Float64, 2, 4}}:
 [1.0 0.0; 0.0 1.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 ⋮
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]
 [0.0 0.0; 0.0 0.0]

GridSampling(spacing = 1/2)

The generated particles are aligned with the grid using uniform spacing. Setting spacing = 1/η will produce η^dim particles per cell, where dim is the problem dimension.

PoissonDiskSampling(spacing = 1/2, rng = Random.default_rng())

The particles are generated based on the Poisson disk sampling. The spacing parameter is used to produce a similar number of particles as are generated with GridSampling.