Hi everyone!

My math problem is the next

\lambda Mu=Ju, where M is the mass matrix and J is the Jacobian of a non linear operator (Navier-Stokes’s equation).

The boundary condition are

u(u,y)=0 \ \ (x,y)\in \partial \Omega.

Then, my code to solve this is:

```
from fenics import *
from dolfin import *
from petsc4py import PETSc
mesh = UnitSquareMesh(10, 10)
V = VectorFunctionSpace(mesh, "CG", 1)
u=Funtcion(V)
v=TestFunction(V)
a=dot(u,v)*dx
solve(a==0, u, bc)
vm = TestFunction(V)
um = TrialFunction(V)
mass_form = dot(vm,um)*dx
mass_action_form = action(mass_form, Constant((1.0,1.0,1.0)))
J = derivative(a,u)
JM = PETScMatrix()
Mass= PETScMatrix()
dummy = inner(Constant((1.0, 1.0)), v) * dx
assemble_system(J, dummy, bcs_m, A_tensor = JM)
assemble_system(mass_form, dummy, bcs_m, A_tensor = Mass)
eigensolver = SLEPcEigenSolver(JM,Mass)
```

This works for me to solve the direct problem. I need to solve

\lambda^{\dagger} Mu^{*}=J^{\dagger}u^{*} too with the same bcs.

I try

```
JMAux=JM.copy()
petsc_mat = as_backend_type(JMAux).mat()
petsc_mat.transpose()
JMA = PETScMatrix(petsc_mat)
Aeigensolver = SLEPcEigenSolver(JMA,Mass)
```

The problem is, when I do petcs_mat.trnaspose(), the “J^{\dagger}” doesn’t have the boundary condition.

I try to do J.T and then assemble the bcs,like the first problem, but this function doesn’t work (I think that J isn’t a rank 2 tensor, but I’m not sure…)

I try to do

```
petsc_mat = as_backend_type(JDolfin).mat()
petsc_mat.transpose()
JMA = PETScMatrix(petsc_mat)
bcs.apply(JMA)
```

but i obtain the next error

```
Error: Unable to set given (local) rows to identity matrix.
Reason: some diagonal elements not preallocated (try assembler option keep_diagonal).
Where: This error was encountered inside PETScMatrix.cpp.
Process: 0
```

I would like if someone could help me solve this problem with some other way than this or fix it.

Thank you!!