How can I use Block Forms, Multiphenicsx, and Lagrange Multipliers to Solve Poisson's Equation with Pure Neumann Boundary Conditions?

francesco-ballarin · December 1, 2023, 10:53am

Can you discuss where for which part of the code do you plan to use multiphenicsx? (I guess the Lagrange multipliers that are not there yet, but I want to be sure)
As the author of that, I cannot see it being actually used right now [1].

On pure Neumann boundary conditions, you may want to have a look at Singular poisson equation in DOLFINx

Together with @hherlyng in the next few weeks we would like to add a tutorial on pure Neumann BCs in multiphenicsx. Please get in touch with me by email to remind me that you are interested, and to post a link here when we are done.

[1] I do understand that you are indeed using multiphenicsx.fem.petsc.BlockVecSubVectorWrapper. I like that approach, otherwise I wouldn’t have prepared it ;), but just keep in mind that until you actually have restrictions you can do a similar operation using plain dolfinx, see e.g.

github.com

FEniCS/dolfinx/blob/24f86a9ce57df6978070dbee22b3eae8bb77235f/python/demo/demo_stokes.py#L361


      
          
          # We also need to create a block vector, `x`, to store the (full)
          # solution, which we initialize using the block RHS form `L`.
          
          # +
          # Compute solution
          x = A.createVecRight()
          ksp.solve(b, x)
          
          # Create Functions and scatter x solution
          u, p = Function(V), Function(Q)
          offset = V_map.size_local * V.dofmap.index_map_bs
          u.x.array[:offset] = x.array_r[:offset]
          p.x.array[:(len(x.array_r) - offset)] = x.array_r[offset:]
          # -
          
          # We can calculate the $L^2$ norms of u and p as follows:
          
          norm_u_1 = u.x.norm()
          norm_p_1 = p.x.norm()
          if MPI.COMM_WORLD.rank == 0:

As soon as you will have multiphenicsx restrictions, then multiphenicsx.fem.petsc.BlockVecSubVectorWrapper will be the only way to go.

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How can I use Block Forms, Multiphenicsx, and Lagrange Multipliers to Solve Poisson's Equation with Pure Neumann Boundary Conditions?

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