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) → float[source]#

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

Returns:

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

Return type:

float

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