cashocs.verification.shape_gradient_test

cashocs.verification.shape_gradient_test(

sop: shape_optimization.ShapeOptimizationProblem,

h: list[fenics.Function] | None = None,

rng: np.random.RandomState | None = None,

verbose: bool = True,

) → float

Performs a Taylor test to verify that the computed shape gradient is correct.

Parameters:

• sop (shape_optimization.ShapeOptimizationProblem) – The underlying shape optimization problem.

• h (list[fenics.Function] | None) – The direction used to compute the directional derivative. If this is None, then a random direction is used (default is None).

• rng (np.random.RandomState | None) – A numpy random state for calculating a random direction

• verbose (bool) – Prints the result to the console, if True. Default is True.

Returns:

The convergence order from the Taylor test. If this is (approximately) 2 or larger, everything works as expected.

Return type:

float