Example: spectral_3d_poisson
Figure 10.2 — Example: Spectral 3D Poisson
Crate: cfd-suite (workspace root)
Run: cargo run --example spectral_3d_poisson
Source: examples/spectral_3d_poisson.rs
What This Example Demonstrates
Solves ∇²u = f on a 3D unit cube with Dirichlet boundary conditions using the spectral Poisson solver, and compares against the analytical solution.
| Concept | API |
|---|---|
| 3D Poisson solver creation | PoissonSolver::new(nx, ny, nz) |
| Dirichlet boundary specification | PoissonBoundaryCondition::Dirichlet |
| RHS and solution arrays | leto::Array1::zeros([n]) |
Key Code Snippet
use cfd_3d::spectral::{PoissonBoundaryCondition, PoissonSolver};
use leto::Array1;
use std::f64::consts::PI;
let solver = PoissonSolver::new(8, 8, 8)?;
// f(x,y,z) = sin(πx)sin(πy)sin(πz)
// Exact: u = -sin(πx)sin(πy)sin(πz) / (3π²)
let mut rhs = Array1::zeros([8 * 8 * 8]);
for i in 0..8 { for j in 0..8 { for k in 0..8 {
let x = -1.0 + 2.0 * i as f64 / 7.0;
let y = -1.0 + 2.0 * j as f64 / 7.0;
let z = -1.0 + 2.0 * k as f64 / 7.0;
rhs[i*64 + j*8 + k] = (PI*x).sin() * (PI*y).sin() * (PI*z).sin();
}}}Physics Background
The spectral Poisson solver represents u as a truncated Fourier series and solves in wavenumber space via division by −|k|². This achieves spectral convergence (exponential error decay) for smooth f, which makes it the preferred baseline for pressure-Poisson steps in incompressible CFD.
Zero padding: the solver uses Atlas apollo-fft for the forward/inverse
transforms so the convolution is computed exactly without aliasing.