Horizontal and vertical transforms about oceananigans.jl HOT 4 CLOSED

Thanks for the info @glwagner!

I decided to go back and build up the spectral solver from the 1D case which now works using rfft and irfft as tested against analytic solutions, and I discovered a couple of bugs with my 3D solver in the process. Working on the 2D solver now and this issue + domains.jl will be quite helpful.

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Great, keep us updated!

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Got the 1D and 2D solvers working and confirmed that they converge spectrally using your 2D wavenumber construction. Here are the tests you've been craving: test_spectral_solvers.jl

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This has been figured out. We have

1. solve_poisson_3d_ppn(f, Nx, Ny, Nz, Δx, Δy, Δz)
2. solve_poisson_3d_ppn!(g::RegularCartesianGrid, f::CellField, ϕ::CellField)
3. solve_poisson_3d_ppn_planned!(ssp::SpectralSolverParameters, g::RegularCartesianGrid, f::CellField, ϕ::CellField)

that work and pass multiple tests. The DCT is slower than the FFT (somewhat expected) and for some reason we couldn't get it to work with FFTW.rfft but those are optimizations we can figure out later.

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