Struct PdeOperator 

pub struct PdeOperator {
    pub terms: Vec<(f64, Vec<usize>)>,
    pub dim: usize,
}

A linear PDE operator: L[u](x) = Σ_k c_k · ∂^{α_k} u(x)

Each term is a pair (coefficient, multi_index) where multi_index[d] is the order of differentiation with respect to the d-th coordinate.

Fields

terms: Vec<(f64, Vec<usize>)>

List of (coefficient, derivative_order_per_dim) terms.

dim: usize

Spatial dimension of the input space.

Implementations

impl PdeOperator

pub fn laplacian(dim: usize) -> Self

Create the Laplacian operator in dim dimensions: L = Σ_{i=0}^{dim-1} ∂²/∂x_i².

pub fn advection_1d(speed: f64) -> Self

Create a 1D advection operator: L = speed · ∂/∂x.

pub fn custom( terms: Vec<(f64, Vec<usize>)>, dim: usize, ) -> InterpolateResult<Self>

Create a custom linear combination of derivative terms.

Each element of terms is (coefficient, order_per_dim) where order_per_dim must have length dim.

Errors

Returns InvalidInput if any multi-index has the wrong length.

pub fn apply_fd( &self, center: &[f64], f_at: impl Fn(&[f64]) -> f64, h: f64, ) -> f64

Evaluate L[f] at center by applying finite differences.

Supports derivative orders 0 (identity), 1 (central difference), and 2 (second central difference) per dimension. Mixed partials of total order ≤ 2 are handled by composing 1-D stencils.

For a term with multi-index [α₀, α₁, …] the stencil approximation is:

• Order 0 in dim d → evaluate at center
• Order 1 in dim d → (f(c + h*eₐ) - f(c - h*eₐ)) / (2h)
• Order 2 in dim d → (f(c + h*eₐ) - 2f(c) + f(c - h*eₐ)) / h²

Mixed partials of order (1,1) in two different dimensions use the cross-difference stencil: (f(++)-f(+-)-f(-+)+f(--)) / (4h²).

Higher-order mixed partials (total order > 2) raise NotImplemented.

Arguments

• center – Point at which the operator is evaluated; length must equal dim.
• f_at – Function to apply the operator to.
• h – Finite-difference step size.

pub fn try_apply_fd( &self, center: &[f64], f_at: impl Fn(&[f64]) -> f64, h: f64, ) -> InterpolateResult<f64>

Like apply_fd but returns an error on unsupported stencil orders instead of panicking.

Trait Implementations

impl Clone for PdeOperator

fn clone(&self) -> PdeOperator

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for PdeOperator

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.