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cg_op

outram_foam_basic_lib::linear_operator

Function cg_op 

Source 
pub fn cg_op<A, M>(
    a: &A,
    b: &[f64],
    x0: Option<&[f64]>,
    precond: &M,
    settings: &KrylovSettings,
) -> (Vec<f64>, KrylovResult)
where
    A: LinearOperator + ?Sized,
    M: OperatorPreconditioner + ?Sized,
Expand description

Preconditioned conjugate gradients for a symmetric positive-definite operator.

The right solver for a finite-element stiffness matrix, which is symmetric by construction (K = integral of B^T D B with D symmetric), and for the finite-volume pressure Poisson equation.

§Not a replacement for [crate::ldu_matrix::solvers::conjugate_gradient]

That function is the finite-volume path and keeps its DIC preconditioner and its &LduMatrix signature unchanged. This one is generic over the operator and takes the preconditioner from the caller. Neither calls the other.

§Arguments

  • a — the SPD system operator. Behaviour on a non-symmetric or indefinite operator is undefined (CG may stagnate or diverge); use gmres_op or bicgstab_op there.
  • b — right-hand side, length a.n_rows(), caller’s units.
  • x0 — optional initial guess; None means the zero vector. Pass the previous Newton iterate to warm-start.
  • precond — SPD preconditioner M^{-1}.
  • settings — tolerance (relative, on ||b - A x||_2 / ||b||_2) and max_iter. restart is ignored.

§Returns

(x, result). result.final_residual is the true relative residual of the returned iterate, recomputed from a and b, never an internal estimate. An exactly-zero b returns x = 0, converged, 0 iterations.

§Cost

One LinearOperator::apply and one OperatorPreconditioner::apply per iteration, plus O(n) vector work. Storage O(n).