cashocs.space_mapping.shape_optimization.SpaceMappingProblem#

class cashocs.space_mapping.shape_optimization.SpaceMappingProblem(
fine_model: FineModel,
coarse_model: CoarseModel,
parameter_extraction: ParameterExtraction,
method: Literal['broyden', 'bfgs', 'lbfgs', 'sd', 'steepest_descent', 'ncg'] = 'broyden',
max_iter: int = 25,
tol: float = 0.01,
use_backtracking_line_search: bool = False,
broyden_type: Literal['good', 'bad'] = 'good',
cg_type: Literal['FR', 'PR', 'HS', 'DY', 'HZ'] = 'FR',
memory_size: int = 10,
verbose: bool = True,
save_history: bool = False,
)[source]#

Bases: object

Space mapping method for shape optimization.

Initializes self.

Parameters:

  • fine_model (FineModel) – The fine model optimization problem

  • coarse_model (CoarseModel) – The coarse model optimization problem

  • parameter_extraction (ParameterExtraction) – The parameter extraction problem

  • method (Literal['broyden', 'bfgs', 'lbfgs', 'sd', 'steepest_descent', 'ncg']) – A string, which indicates which method is used to solve the space mapping. Can be one of “broyden”, “bfgs”, “lbfgs”, “sd”, “steepest descent”, or “ncg”. Default is “broyden”.

  • max_iter (int) – Maximum number of space mapping iterations

  • tol (float) – The tolerance used for solving the space mapping iteration

  • use_backtracking_line_search (bool) – A boolean flag, which indicates whether a backtracking line search should be used for the space mapping.

  • broyden_type (Literal['good', 'bad']) – A string, either “good” or “bad”, determining the type of Broyden’s method used. Default is “good”

  • cg_type (Literal['FR', 'PR', 'HS', 'DY', 'HZ']) – A string, either “FR”, “PR”, “HS”, “DY”, “HZ”, which indicates which NCG variant is used for solving the space mapping. Default is “FR”

  • memory_size (int) – The size of the memory for Broyden’s method and the BFGS method

  • verbose (bool) – A boolean flag which indicates, whether the output of the space mapping method should be verbose. Default is True.

  • save_history (bool) – A boolean flag which indicates, whether the history of the space mapping method should be saved to a .json file. Default is False.

Methods Summary

inject_post_callback(function)

Changes the a-posteriori callback of the OptimizationProblem.

inject_pre_callback(function)

Changes the a-priori callback of the OptimizationProblem.

inject_pre_post_callback(pre_function, ...)

Changes the a-priori (pre) and a-posteriori (post) callbacks of the problem.

output()

Uses the output manager to save / show the current results.

smooth_deformation(a)

Smooths a deformation vector field with a Poincaré-Steklov operator.

solve()

Solves the problem with the space mapping method.

test_for_nonconvergence()

Tests, whether maximum number of iterations are exceeded.

Methods Documentation

inject_post_callback(
function: Callable | None,
) → None[source]#

Changes the a-posteriori callback of the OptimizationProblem.

Parameters:

function (Callable | None) – A custom function without arguments, which will be called after the computation of the gradient(s)

Return type:

None

inject_pre_callback(
function: Callable | None,
) → None[source]#

Changes the a-priori callback of the OptimizationProblem.

Parameters:

function (Callable | None) – A custom function without arguments, which will be called before each solve of the state system

Return type:

None

inject_pre_post_callback(
pre_function: Callable | None,
post_function: Callable | None,
) → None[source]#

Changes the a-priori (pre) and a-posteriori (post) callbacks of the problem.

Parameters:

  • pre_function (Callable | None) – A function without arguments, which is to be called before each solve of the state system

  • post_function (Callable | None) – A function without arguments, which is to be called after each computation of the (shape) gradient

Return type:

None

output() → None[source]#

Uses the output manager to save / show the current results.

Return type:

None

smooth_deformation(
a: list[fenics.Function],
) → list[fenics.Function][source]#

Smooths a deformation vector field with a Poincaré-Steklov operator.

Parameters:

a (list[fenics.Function]) – The deformation vector field

Returns:

A smoothed deformation vector field, for the use in the scalar product.

Return type:

list[fenics.Function]

solve() → None[source]#

Solves the problem with the space mapping method.

Return type:

None

test_for_nonconvergence() → None[source]#

Tests, whether maximum number of iterations are exceeded.

Return type:

None