Extend `derivative_block()` to derive residuals from functionals

[jhale]

Describe new/missing feature

Many common variational problems (e.g. elasticity) are most naturally written as energy minimisation problems. The new 'derivative_block()` function takes block residuals to block Jacobians, but not functionals defined on multiple Functions to block residuals.

Suggested user interface

No change to current interface to derivate_block, just extend it to handle the functional case.

[Joseabcd]

Hello @jhale, I am new to the project and if this is still current I would like to work on it

If I understand, the new proposed functionality assumes that only one functional would be given to F, recognizable as a ufl.Form with zero ufl.Arguments. Then there would be two cases:

Case 1
u is a single Function, and du is a single test function (i.e. an ufl.Argument with du.number()==0)

Case 2
u contains multiple Functions, and du contains as many test functions

I would implement these conditions using new isinstance statements under the current condition isinstance(F, ufl.Form).

Could you let me know if this sounds good, and I could implement it in a PR?

[jorgensd]

Describe new/missing feature

Many common variational problems (e.g. elasticity) are most naturally written as energy minimisation problems. The new 'derivative_block()` function takes block residuals to block Jacobians, but not functionals defined on multiple Functions to block residuals.

Suggested user interface

No change to current interface to derivate_block, just extend it to handle the functional case.

You can already do this with ufl:
ufl.extract_blocks(ufl.derivative(J, [u, psi], [du, dpsi])) as far as I’m aware (given that you use ufl.MixedFunctionSpace` for the testfunctions)

[Joseabcd]

Hello @jorgensd

you mean that derivative_block no longer needs this enhancement, and hence this issue should be closed as obsolete?

Or that the functions you quote can be used to implement this enhancement to derivative_block?

[schnellerhase]

derivative_block currently does not support rank 0 forms. @jorgensd is right that this is all possible from an ufl point of view. What is missing is the support for rank 0 functionals, so energy to first variation, i.e. integral to linear form as output (derivative_block only supports rank 1 to rank 2, so linear form to bilinear form atm.).

Have a look at this, which already implements the necessary logic in a different context. The objective there corresponds to the energy here, the jaobian to the residual and hessian to the variation of the residual, respectively.