refactor: Green function that can be fast with SVector or Zygote-differentiable with Vectors

[mancellin]

Replaces #1.

If the elements are built with SVectors, the evaluation is state-of-the-art fast.
If they are Vectors, it is a bit slower, but the code is Zygote-differentiable.

Performance of some of the gradients with Zygote seems slightly worse than before. I'm not sure how to really interpret that.

WITH STATIC VECTORS

Evaluation
 Rankine
  140.250 ns (0 allocations: 0 bytes)
  162.703 ns (0 allocations: 0 bytes)
 GFWu
  68.591 ns (0 allocations: 0 bytes)
  106.808 ns (0 allocations: 0 bytes)

WITH VECTORS

Evaluation
 Rankine
  1.313 μs (33 allocations: 2.58 KiB)
  2.415 μs (70 allocations: 5.47 KiB)
 GFWu
  70.861 ns (0 allocations: 0 bytes)
  222.322 ns (4 allocations: 416 bytes)

Gradients
 Rankine
  661.467 μs (2696 allocations: 81.56 KiB)
  5.365 ms (14671 allocations: 436.78 KiB)
 GFWu
  48.893 μs (424 allocations: 19.31 KiB)
  525.291 μs (2598 allocations: 84.78 KiB)

Benchmark code

using BEM
using BenchmarkTools
using StaticArrays
using Zygote

wavenumber = 1.0

println("WITH STATIC VECTORS")
element_1 = (center=SVector(0.0, 0.0, -1.0),)
element_2 = (
    center=SVector(1.0, 1.0, -2.0),
    vertices= @SMatrix([-0.5 -0.5 0.0; 0.5 -0.5 0.0; 0.5 0.5 0.0; -0.5 0.5 0.0]) .+ SVector(1.0, 1.0, -2.0)',
    normal=SVector(0.0, 0.0, 1.0),
    radius=sqrt(2)/2,
    area=1.0,
)

println("Evaluation")
println(" Rankine")
@btime BEM.integral($(Rankine()), $element_1, $element_2)
@btime BEM.integral_gradient($(Rankine()), $element_1, $element_2)

println(" GFWu")
@btime BEM.integral($(GFWu()), $element_1, $element_2, $wavenumber)
@btime BEM.integral_gradient($(GFWu()), $element_1, $element_2, $wavenumber)

println("WITH VECTORS")
element_1 = (center=[0.0, 0.0, -1.0],)
element_2 = (
    center=[1.0, 1.0, -2.0],
    vertices= [-0.5 -0.5 0.0; 0.5 -0.5 0.0; 0.5 0.5 0.0; -0.5 0.5 0.0] .+ [1.0, 1.0, -2.0]',
    normal=[0.0, 0.0, 1.0],
    radius=sqrt(2)/2,
    area=1.0,
)

println("Evaluation")
println(" Rankine")
@btime BEM.integral($(Rankine()), $element_1, $element_2)
@btime BEM.integral_gradient($(Rankine()), $element_1, $element_2)

println(" GFWu")
@btime BEM.integral($(GFWu()), $element_1, $element_2, $wavenumber)
@btime BEM.integral_gradient($(GFWu()), $element_1, $element_2, $wavenumber)

println("Gradients")
println(" Rankine")
S(z) = BEM.integral(Rankine(), (center=[0.0, 0.0, z],), element_2)
@btime Zygote.gradient($S, $(-1.0))
D(z) = BEM.integral_gradient(Rankine(), (center=[0.0, 0.0, z],), element_2)
@btime Zygote.jacobian($D, $(-1.0))

println(" GFWu")
S(z) = real(BEM.integral(GFWu(), (center=[0.0, 0.0, z],), element_2, wavenumber))
@btime Zygote.gradient($S, $(-1.0))
D(z) = real.(BEM.integral_gradient(GFWu(), (center=[0.0, 0.0, z],), element_2, wavenumber))
@btime Zygote.jacobian($D, $(-1.0))

nothing

[KapilKhanal]

oopsie I merged in wrong sequence. This will have to updated to use MarineHydro.jl instead

[KapilKhanal]

what will be the best way to merge now? I did not realize the problem it will have not merging in order especially with the file name changed