What are the advantages of a blocked Newton Solver?

Hello Everyone,

I have a general questions regarding the blocked assembly of the stiffness matrix, as it is e.g., done here in this tutorial.

I do not understand what the advantages of this technique are compared to e.g. just setting the weak form to zero and giving this term to the newton solver?

Is there some literature which you can recommend where this is described?

Best regards
Martin

Your link only goes to the main page of scores, not a specific tutorial.
For certain problems, such as those involving real spaces, using a block solver is currently the only option, as there is no «real» finite element in basix.ufl.

@mscroggs can comment on if we could/should do this, as all the pieces are in place for dofmap construction, and should be easy to do within dolfinx itself.

You also get a specific dof ordering, that can more easily be used for similar problems with PETSc nest.

Thank you for your fast reply and your explanations, I really appreciate it.

I am sorry for the misplaced link, I meant this tutorial.