neco-stencil

Finite-difference stencil operators for uniform 2D grids on row-major &[f64] / &mut [f64] slices.

Grid operators

The basic operators cover Laplacian, first derivatives, and second derivatives on a uniform 2D grid.

The fused routines reuse work buffers so plate-style biharmonic assembly can stay in flat slices without introducing a matrix type.

Usage

use neco_stencil::laplacian;

let nx = 5;
let ny = 5;
let dx = 0.1;
let mut field = vec![0.0; nx * ny];
field[2 * ny + 2] = 1.0;

let mut out = vec![0.0; nx * ny];
laplacian(&field, nx, ny, dx, &mut out).expect("valid stencil input");

assert!(out[2 * ny + 2] < 0.0);
assert_eq!(out[0], 0.0);

API

Item	Description
`laplacian(u, nx, ny, dx, out)`	Apply the 5-point Laplacian on a uniform grid
`gradient_x(u, nx, ny, dx, out)`	Compute the central-difference x-gradient
`gradient_y(u, nx, ny, dx, out)`	Compute the central-difference y-gradient
`d2_dx2(u, nx, ny, dx, out)`	Compute the second x-derivative
`d2_dy2(u, nx, ny, dx, out)`	Compute the second y-derivative
`d2_dxdy(u, nx, ny, dx, out)`	Compute the mixed second derivative
`w_derivatives(...)`	Compute first and second derivatives of one field in one pass
`uv_gradients(...)`	Compute gradients of two fields in one pass
`biharmonic_pass1_fused(...)`	Compute `D * Laplacian(w)` and derivative work buffers in one pass
`biharmonic(...)`	Apply `Laplacian(D * Laplacian(w))` using work buffers
`bilaplacian_uniform(w, nx, ny, d, dx, bilap)`	Apply the 13-point bilaplacian for uniform stiffness
`bilaplacian_ortho_uniform(...)`	Apply an orthotropic bilaplacian on selected interior cells

Preconditions

Inputs and outputs must have length nx * ny; invalid lengths return StencilError.
Data layout is row-major with index (i, j) -> i * ny + j.
Operators write zeros on boundaries that do not have the required stencil neighborhood.
laplacian, gradient_*, d2_*, w_derivatives, uv_gradients, biharmonic, and bilaplacian_uniform return all zeros when the grid is too small for the required stencil.
bilaplacian_ortho_uniform expects caller-provided interior cells; boundary filtering happens before this call.

Optional features

Feature	Description
`rayon`	Enables internal parallel loops for larger grids only; public results are intended to stay identical to the non-`rayon` build

License

MIT