[firedrake] Nullspace & VectorSpaceBasis

[Anna Kalogirou]

Dear all,

I am experiencing again the same error I reported in December, when 
trying to solve an equation only on the boundary of a domain (the code 
is the same as the one in my email below dated 11 December 12:46). The 
problem was fixed back then but after all these months and after various 
updates, I get it again.

Basically PETSc is complaining about Object being in wrong state and 
Matrix missing a diagonal entry. The error arises when trying to solve 
this VP:

a = v*phi*ds(4)
L = (v*phi0 - g*dt*v*eta0)*ds(4)


Note that I get two different errors on two different computers (on the 
other computer I get a Zero pivot error in LU factorization, on row 0), 
but the one I am reporting here is based on the computer with the latest 
petsc/pyop2/firedrake update.

Thank you!

Best.

Anna.


On 12/12/14 12:32, Lawrence Mitchell wrote:
> On 11 Dec 2014, at 19:17, Anna Kalogirou <a.kalogirou at leeds.ac.uk> wrote:
>
>> Thanks Andrew. About your comment 1), how can I fix this?
> This required a change in PyOP2 (https://github.com/OP2/PyOP2/pull/417) to always create matrices with (at least) zeros in all diagonal entries.
>
> Further comments in line below.
>
>> The two equations valid on one of the boundaries can actually be combined into one by paying the price of a higher time derivative. This is not a problem for this simple system, so if I use
>>
>> aphi = v*phi*ds(4) + g*dt**2*inner(grad(v),grad(phi))*dx
>> Lphi = v*(2*phi1-phi0)*ds(4)
>>   
>> phi_problem = LinearVariationalProblem(aphi,Lphi,phi2)
>> phi_solver = LinearVariationalSolver(phi_problem)
>>
>> is equivalent to what I had before, and this time the code works and gives a good result (compared to the exact solution).
>>
>> However, I need to understand why the other case doesn't work because that will later be generalised to become nonlinear.
> Hopefully with that change, the problem will go away again.
>>
>> On 11/12/14 13:04, Andrew McRae wrote:
>>> Four comments:
>>>
>>> 1)  If I understand correctly, PETSc insists that the diagonal entries of the sparse matrix are filled in.  Usually, the LHS form will cause this to happen; however, that obviously isn't the case for your form!
>>>
>>> 2)  It should be possible to build the nullspace you want, but I'm clueless on the actual syntax.  This wouldn't get around (1) without further fixes from our end.
>>>
>>> 3)  Could the equations given not be included in the weak form for the rest of the problem?
>>>
>>> 4)  If not, there might be a hacky "add-a-weighted-mass-matrix-to-the-LHS" fix you could use?....
>>>
>>> Andrew
>>>
>>> On 11 December 2014 at 12:46, Anna Kalogirou <a.kalogirou at leeds.ac.uk> wrote:
>>> Dear all,
>>>
>>> I am trying to solve a simple problem (linear water wave equations),
>>> where I have the Laplace equation in a square domain with Neumann
>>> boundary conditions on the three sides and on the top boundary two
>>> equations are satisfied.
>>>
>>> I have the following code:
>>> --------------------------------------
>>> V = FunctionSpace(mesh,"CG",1)
>>>
>>> eta0 = Function(V).interpolate(Expression("cos(2*pi*x[0])"))
>>> phi0 = Function(V)
>>> eta1 = Function(V)
>>> phi1 = Function(V)
>>> eta = TrialFunction(V)
>>> phi = TrialFunction(V)
>>> v = TestFunction(V)
>>>
>>> aeta = v*eta*ds(4)
>>> Leta = v*eta0*ds(4) + dt*inner(grad(v),grad(phi0))*dx
>>>
>>> eta_problem = LinearVariationalProblem(aeta,Leta,eta1)
>>> eta_solver = LinearVariationalSolver(eta_problem)
>>>
>>> aphi = v*phi*ds(4)
>>> Lphi = (v*phi0 - g*dt*v*eta1)*ds(4)
>>>
>>> phi_problem = LinearVariationalProblem(aphi,Lphi,phi1)
>>> phi_solver = LinearVariationalSolver(phi_problem)
>>> --------------------------------------
>>>
>>> The error I get tells me that Object is in wrong state, and Matrix is
>>> missing diagonal entry 39.
>>>
>>> I thought this had to do with the problem being singular, so I tried to
>>> build the nullspace but I don't know how to define the VectorSpaceBasis.
>>> Any help would be appreciated.
> So this operator certainly has a nullspace, which you can build, but it's quite large.  Since any Function orthogonal to the boundary dofs is in the space.
>
> Can you describe how the documentation for the vector space basis is insufficient?
>
> To build it, you must provide a list of orthonormal Functions spanning the null space of the operator:
>
> basis = []
> for i in range(nbasis):
>      f = Function(V)
>      f.interpolate(...)
>      basis.append(f)
>
> nullspace = VectorSpaceBasis(basis)
>
> solve(...., nullspace=nullspace)
>
> This is the left null space of the operator (used to orthogonalise the solution).  You need to arrange that your right hand side is consistent (i.e. orthogonal to the right null space of the operator [if the operator is symmetric this is the same as the left null space]).
>
> Lawrence

-- 
  
  Dr Anna Kalogirou
  Research Fellow
  School of Mathematics
  University of Leeds

  http://www1.maths.leeds.ac.uk/~matak/