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,
    /* private fields */
}

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

Number of multigrid levels (1 = single-grid, higher = deeper V-cycle).

shape: [usize; 3]

Grid dimensions [nx, ny, nz].

dx: [f64; 3]

Cell spacings [dx, dy, dz].

bc: SpatialBoundType

Spatial boundary condition (Periodic or Dirichlet zero).

n_smooth: usize

Number of red-black Gauss-Seidel sweeps per pre/post-smoothing phase.

tolerance: f64

Relative residual convergence tolerance for the iterative V-cycle loop.

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 set_progress(&mut self, p: Arc<StepProgress>)

Register a shared progress handle for intra-step reporting to the TUI.

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 = -∇Φ via second-order centered finite differences.