Low-level FFT brick: PoissonFFT (spectral periodic Poisson solver, slab-distributed) plus 1D radix-2 FFT primitives (fft1d) and a direct DFT fallback (dft1d_direct). More...

#include <pops/parallel/comm.hpp>
#include <cmath>
#include <complex>
#include <numbers>
#include <utility>
#include <vector>

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Classes
class	pops::PoissonFFT

Namespaces
namespace	pops

Typedefs
using	pops::cplx = std::complex< double >

Functions
bool	pops::is_pow2 (int n)

void	pops::dft1d_direct (cplx *a, int n, bool inv)

void	pops::fft1d (cplx *a, int n, bool inv)

Detailed Description

Low-level FFT brick: PoissonFFT (spectral periodic Poisson solver, slab-distributed) plus 1D radix-2 FFT primitives (fft1d) and a direct DFT fallback (dft1d_direct).

Layer: include/pops/numerics/elliptic/poisson. Role: solve EXACTLY the discrete periodic Laplacian lap_h phi = rho with phi of zero mean, in ONE transform (no iteration, no tolerance). Works on slabs (flat per-rank vectors, NOT MultiFab): this is the brick wrapped by PoissonFFTSolver/DistributedFFTSolver (poisson_fft_solver.hpp). 2D FFT = local FFT-x -> parallel transpose (MPI_Alltoall) -> local FFT-y -> division by the Laplacian eigenvalue -> inverse. Contract: each rank owns Ny/np rows (full x); solve(rho_local, phi_local) with rho_local and phi_local of size nyl_ x Nx_ (row-major). The ctor takes spectral (false = DISCRETE 5-point stencil eigenvalue, bit-identical default; true = CONTINUOUS symbol -(kx^2+ky^2), signed frequencies).

Invariants:

the slab transpose requires Nx and Ny divisible by np (n_ranks);
power-of-two lengths use the radix-2 FFT; any other size falls back to the correct O(n^2) direct DFT (the radix-2 butterfly would overflow the buffer on an arbitrary n), so single-rank accepts any n;
mode kx=ky=0: zero eigenvalue -> phi_hat=0 (zero mean enforced);
alltoall is the identity when np==1 (and without MPI).

include/pops/numerics/elliptic/poisson/poisson_fft.hpp File Reference¶

Classes

Namespaces

Typedefs

Functions

Detailed Description