Lagrange Multiplier for the Poisson equation with pure Neumann boundary conditions about dolfinx HOT 10 OPEN

If others agree this is a good idea to include as a demo, I can help you with the matrix assembly.

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I think this would be a good idea if we can come up with an efficient linear solve (using PETSc Schur complement fieldsplit ?)

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I think this would be a good idea if we can come up with an efficient linear solve (using PETSc Schur complement fieldsplit ?)
Yes, I think the solver is the main concern that need consideration. I have tried to define the operator as nested matrix and then solve it with PC-Type : "fieldsplit" and some KSP solvers like "gmres" and "cg", but the performance is not as good as "LU".

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@WjjSteve I wouldn't necessarily expect the performance (runtime) to be as good as LU, particularly small problems. Instead the key questions are:

1. Does it solve in a reasonable number of inner and outer iterations -ksp_view? Reasonable would be e.g. 50, not many 100s or 1000s.
2. Does the number of iterations stay roughly bounded on mesh refinement?

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Also, does your example work when running using MPI?

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@WjjSteve I wouldn't necessarily expect the performance (runtime) to be as good as LU, particularly small problems. Instead the key questions are:

1. Does it solve in a reasonable number of inner and outer iterations -ksp_view? Reasonable would be e.g. 50, not many 100s or 1000s.
2. Does the number of iterations stay roughly bounded on mesh refinement?

I'm not sure I fully understand your question or not. I tried it with "gmres" and "hypre" and the mesh size is 100 by 100, I used the function KSP.getIterationNumber(), and the result is just 1. Maybe I didn't check it in the correct way, please let me know if you want me to test anyting else.

Also, does your example work when running using MPI?

Unfortunately no, this is just a serier code.

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You'll need to post your example in full for the preconditioners - could you open a pull request with your example as a demo_*.py file?

We can't accept features/demos that do not work using MPI. Perhaps there are ways to get this approach working, it would need some thought.

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We're going to take a look at the MPI aspect of this this for you @WjjSteve.

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We're going to take a look at the MPI aspect of this this for you @WjjSteve.

Sure I understand.
Maybe it is easier to use MPI when nested operators are applied, I will make a demo for that and open a pull.

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We're going to take a look at the MPI aspect of this this for you @WjjSteve.
Hello, I have made a demo using nested matrix and vector for the above algorithm, should I make a pull request as a new branch? There are a lot of branchs and tags, and I don't want to mess anything.

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