Dolci/schedules application

[Ig-dolci]

No description provided.

[jrmaddison]

Some general comments:

• I think there is an error in the forward residual -- the boundary conditions don't seem to be applied.
• The adjoint derivation is motivated by a continuous adjoint approach, but the later Taylor testing verifies discrete adjoint consistency.
• The displayed adjoint sensitivity is a directional derivative rather than the full gradient.
• I recommend reducing the number of example schedules.
• I recommend removing all the code comments in the example schedules.
• The disk storage schedules don't actually store checkpoints on disk.
• I don't understand the single_storage behaviour.

[jrmaddison]

From checking mass and stiffness matrices:

• There is an off-by-on error in the definition of $h$, which should be model["lx"] / (model["nx"] - 1). This appears in three places.
• The _mass_matrix method returns the mass divided by $h$, which could be noted in a comment.
• The _stiffness_matrix method returns the stiffness matrix multiplied by -\model["nu"] / h. There are sign errors when the result is used in _residual and _jacobian.

[jrmaddison]

Code should also be linted (e.g. using ruff).