Why is my code converging in 4 steps? Linear PDE

[dokken]

@raboynics

solver.convergence_criterion = "incremental"

Start by changing the convergence criterion from «incremental» to residual.

@raboynics

When I simply remove the Dirichlet boundary condition, the problem is physically exactly the same (because voltage is defined up to a constant, and here I let the solver fix it instead of enforcing it myself)

The solver should then know about the null-space, Which you can enforce through options, see for instance

@dokken

problem = LinearProblem(a, L, bcs=[], petsc_options={
                            "ksp_type": "preonly", "pc_type": "lu",
                            "pc_factor_mat_solver_type": "mumps",
                            "mat_mumps_icntl_24": 1,  # Option to support solving a singular matrix
                            "mat_mumps_icntl_25": 0  # Option to support solving a singular matrix
                            })
    nullspace = PETSc.NullSpace().create(constant=True)  # type: ignore
    PETSc.Mat.setNearNullSpace(problem.A, nullspace)

    uh = problem.solve()

in

How to obtain coordinates of nodes? How to work with dofmap?

The rotation vector is -y, x, i.e. from mpi4py import MPI import ufl import dolfinx mesh = dolfinx.mesh.create_unit_square( MPI.COMM_WORLD, 10, 10, cell_type=dolfinx.mesh.CellType.quadrilateral) Ve = ufl.VectorElement("S", mesh.ufl_cell(), 2) V = dolfinx.fem.functionspace(mesh, Ve) u = dolfinx.fem.Function(V) u.interpolate(lambda x: (-x[1], x[0])) V_out = dolfinx.fem.FunctionSpace( mesh, ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)) u_out = dolfinx.fem.Function(V_out) u_out.in…