Struct Multigrid 

pub struct Multigrid {
    pub levels: usize,
    pub shape: [usize; 3],
    pub dx: [f64; 3],
    pub bc: SpatialBoundType,
    pub n_smooth: usize,
    pub tolerance: f64,
}

Geometric multigrid Poisson solver.

Uses V-cycles with red-black Gauss-Seidel smoothing, full-weighting restriction, and trilinear prolongation. Supports periodic and Dirichlet zero boundary conditions.

Fields

levels: usize

shape: [usize; 3]

dx: [f64; 3]

bc: SpatialBoundType

n_smooth: usize

tolerance: f64

Implementations

impl Multigrid

pub fn new(domain: &Domain, levels: usize, smoothing_steps: usize) -> Self

Create a new multigrid solver.

• domain: the computational domain (provides shape, dx, boundary type)
• levels: requested number of multigrid levels (will be capped so the coarsest grid has at least 2 cells per dimension)
• smoothing_steps: number of Gauss-Seidel sweeps per pre/post-smoothing phase

Trait Implementations

impl PoissonSolver for Multigrid

fn solve(&self, density: &DensityField, g: f64) -> PotentialField

Solve ∇²Φ = 4πGρ using multigrid V-cycles.

Iterates V-cycles until the relative residual drops below tolerance or the maximum iteration count (100) is reached. For periodic BC, the mean of phi is subtracted after solving (since the solution is only determined up to a constant).

fn compute_acceleration(&self, potential: &PotentialField) -> AccelerationField

Compute gravitational acceleration g = -nabla Phi via finite differences.