cycle_jump

gripyth.solving.cycle_jump

Helper functions for the implementation of cycle jumps.

CLASS	DESCRIPTION
History	History variables used for the system state prediction.
Method	Available cycle-jump methods.
Parameters	Parameters for cycle jumps.
Restore	Stores state prior to cycle jump in case trial-cycle not accepted.
Variables	Variables for cycle jumps.

FUNCTION	DESCRIPTION
backward_finite_difference	Approximates the p-th derivative of a function f.
extrapolate	Extrapolate system state variables based on backward finite differences.

History dataclass

History variables used for the system state prediction.

Method

Bases: Enum

Available cycle-jump methods.

Parameters dataclass

Parameters for cycle jumps.

ATTRIBUTE	DESCRIPTION
active	whether to jump cycles or not TYPE: bool
fixed_cycle_jump	cycles to jump if "fixed" method is used TYPE: int
max_Dn	maximum allowable cycles to jump if "relative" method is used TYPE: int
max_rel_error	maximum allowable relative error if "relative" method is used TYPE: float
method	approach to determine the number of cycles to jump TYPE: Method
n_stencil	number of cycles computed in between the individual cycle jumps, TYPE: int
prediction_error_estimation	whether to estimate prediction error for postprocessing purposes TYPE: bool
stage2_scale	Scales allowed increment in stage II if "adaptive" method is used. TYPE: float
stage3_scale	Scales allowed increment in stage III if "adaptive" method is used. TYPE: float

active class-attribute instance-attribute

active: bool = False

whether to jump cycles or not

fixed_cycle_jump class-attribute instance-attribute

fixed_cycle_jump: int = 10

cycles to jump if "fixed" method is used

max_Dn class-attribute instance-attribute

max_Dn: int = 1000

maximum allowable cycles to jump if "relative" method is used

max_rel_error class-attribute instance-attribute

max_rel_error: float = 1e-06

maximum allowable relative error if "relative" method is used

method class-attribute instance-attribute

method: Method = adaptive

approach to determine the number of cycles to jump

n_stencil class-attribute instance-attribute

n_stencil: int = 4

number of cycles computed in between the individual cycle jumps, used for the extrapolation of the fatigue history variable

prediction_error_estimation class-attribute instance-attribute

prediction_error_estimation: bool = False

whether to estimate prediction error for postprocessing purposes

stage2_scale class-attribute instance-attribute

stage2_scale: float = 1.0

Scales allowed increment in stage II if "adaptive" method is used.

stage3_scale class-attribute instance-attribute

stage3_scale: float = 1.0

Scales allowed increment in stage III if "adaptive" method is used.

Restore dataclass

Stores state prior to cycle jump in case trial-cycle not accepted.

Variables dataclass

Variables for cycle jumps.

METHOD	DESCRIPTION
__init__	Creates cycle-jump variables.

ATTRIBUTE	DESCRIPTION
error_predictions	array to monitor the system state prediction error estimate (if requested) TYPE: NDArray[float64] | None
history	history variables used for the system state prediction TYPE: History | None
jumps	array to monitor the cycle jumps TYPE: NDArray[float64]
n_resolved	number of explicitly computed cycles in total TYPE: int
restore	Stores state prior to cycle jump in case trial-cycle cannot be accepted. TYPE: Restore | None

error_predictions class-attribute instance-attribute

error_predictions: NDArray[float64] | None = None

array to monitor the system state prediction error estimate (if requested)

history class-attribute instance-attribute

history: History | None = None

history variables used for the system state prediction

jumps instance-attribute

jumps: NDArray[float64] = zeros((3, 3))

array to monitor the cycle jumps

n_resolved class-attribute instance-attribute

n_resolved: int = 0

number of explicitly computed cycles in total

restore class-attribute instance-attribute

restore: Restore | None = None

Stores state prior to cycle jump in case trial-cycle cannot be accepted.

__init__

__init__(
    parameters: Parameters,
    mesh: Mesh,
    quadrature: Quadrature,
)

Creates cycle-jump variables.

backward_finite_difference

backward_finite_difference(
    f_i: list[NDArray[float64]], p: int
) -> NDArray[float64]

Approximates the p-th derivative of a function f.

The derivative is computed with respect to x based on n equidistant points f_i, given as a list of arrays such as [f(x-2), f(x-1), f(x)]. Accepts scalars, vectors, or matrices for the points.

Returns the derivative dpf_dxp, i.e. \(\frac{d^p f}{d x^p}\).

extrapolate

extrapolate(
    fatigue: NDArray[float64], n_stencil: int, Dn: int
)

Extrapolate system state variables based on backward finite differences.

Dn is the number of cycles to jump.

Returns Theta_extrap.