Struct LaplaceEquationSolver 

pub struct LaplaceEquationSolver { /* private fields */ }

Laplace equation solver implementing PDESolver trait

Implementations

impl LaplaceEquationSolver

pub fn new() -> Self

pub fn with_max_terms(max_terms: usize) -> Self

pub fn solve_laplace_equation_2d( &self, pde: &Pde, boundary_conditions: &[BoundaryCondition], ) -> Result<LaplaceSolution, PDEError>

Solves the 2D Laplace equation on a rectangle

For the Laplace equation: ∂²u/∂x² + ∂²u/∂y² = 0 on a rectangular domain [0,a] × [0,b] with Dirichlet boundary conditions

Mathematical Background

Eigenvalues for rectangular domain with Dirichlet BCs:

• x-direction: λₙ = nπ/a for n = 1, 2, 3, …
• y-direction: μₘ = mπ/b for m = 1, 2, 3, …

Solution form: u(x,y) = Σ Cₙ sin(λₙx) sinh(λₙy)

Trait Implementations

impl Default for LaplaceEquationSolver

fn default() -> Self

Returns the “default value” for a type.

impl PDESolver for LaplaceEquationSolver

fn solve(&self, pde: &Pde) -> PDEResult

Attempts to solve the given PDE

fn can_solve(&self, pde_type: PdeType) -> bool

Returns true if this solver can handle the given PDE type

fn priority(&self) -> u8

Priority for this solver (higher = try first)

fn name(&self) -> &'static str

Solver name for diagnostics

fn description(&self) -> &'static str

Solver description