newton_raphson
Newton-Raphson solver.
| FUNCTION | DESCRIPTION |
|---|---|
newton_raphson |
Solves for |
newton_raphson(
assemble: Callable[
[NDArray[float64]],
tuple[NDArray[float64], NDArray[float64]],
],
field: NDArray[float64],
active_dof: NDArray[int32],
i_row: NDArray[int32],
j_col: NDArray[int32],
d_rhs_tract: NDArray[float64] | None = None,
max_iter: int = 500,
min_iter: int = 1,
res_tol: float = 1e-06,
) -> tuple[NDArray[float64], float64, float64]
Solves for field iteratively using the Newton-Raphson method.
assemble is a function object that accepts field and returns
(K_vector, residual), i.e. the vectorized elements of the system
stiffness matrix and the residual vector of the field. It is typically,
if not always, implemented as a closure in the caller's scope, as it
will require knowledge of model attributes, such as mesh and material,
in order to call the actual assembly routine. In other words, the
closure separates what is relevant to the Newton-Raphson method from
everything that is not.
active_dof is an array of indices into field marking the active
degrees of freedom. i_row and j_col are the sparse-matrix indices
corresponding to K_vector. They are thus expected to not change
over Newton-Raphson iterations. d_rhs_tract is an optional right-hand
side of tractions, assumed to be zero if not provided. min_iter
and max_iter restrict the number of Newton-Raphson iterations
to be performed to reach convergence. res_tol is the tolerance for
the norm of the residual vector that determines if convergence has
been reached.
Returns the solution of field as well as residual norms from the
first and last iteration.
Raises ArithmeticError if the Newton-Raphson solver failed to converge.