Struct dzahui::solvers::fem::diffusion_solver::time_independent::DiffussionSolverTimeIndependent

pub struct DiffussionSolverTimeIndependent {
    pub boundary_conditions: [f64; 2],
    pub(crate) stiffness_matrix: Array2<f64>,
    pub(crate) b_vector: Array1<f64>,
    pub gauss_step: usize,
    pub mu: f64,
    pub b: f64,
}

General Information

A diffusion solver with time-independence abstracts the equation: “- μu_xx + bu_x = 0” and contains boundary conditions along with mesh, “b” and “μ”

Fields

• boundary_conditions - Original boundary conditions (Only Dirichlet is supported for now).
• stiffness_matrix - Left-side matrix of the resulting discrete equation.
• b_vector - Right-side vector of the resulting discrete equation.
• gauss_step - Precision of quadrature.
• mu - First ot two needed constants.
• b - Second of two needed constants.

Fields

boundary_conditions: [f64; 2]

stiffness_matrix: Array2<f64>

b_vector: Array1<f64>

gauss_step: usize

mu: f64

b: f64

Implementations

impl DiffussionSolverTimeIndependent

pub fn new(
    params: &DiffussionParamsTimeIndependent,
    mesh: Vec<f64>,
    gauss_step: usize
) -> Result<Self, Error>

Creates new instance

pub fn gauss_legendre_integration(
    boundary_conditions: [f64; 2],
    mu: f64,
    b: f64,
    mesh: &Vec<f64>,
    gauss_step: usize
) -> Result<(Array2<f64>, Array1<f64>), Error>

General Information

First, it generates the basis for a solver from the linear basis constructor. Then the stiffnes matrix and vector b are generated based on linear basis integration via Gauss-Legendre and returned. Note that vector and matrix will have one on their diagonals’ boundaries and zero on other boundary elements to make boundary conditions permanent.

Parameters

• boundary_conditions - Conditions to guarantee system solution.
• mu - Movement term.
• b - Velocity term.
• mesh - Vector of f64 representing a line.
• gauss_step - How many nodes will be calculated for a given integration.

Returns

A tuple with both the stiffness matrix and the vector b.

Trait Implementations

impl Debug for DiffussionSolverTimeIndependent

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

Formats the value using the given formatter.

impl DiffEquationSolver for DiffussionSolverTimeIndependent

fn solve(&mut self, _time_step: f64) -> Result<Vec<f64>, Error>

Specific implementation

Solving starts by obtaining stiffness matrix and vector b (Ax=b). Then both are used inside function solve_by_thomas to obtain the result vector.