[petsc-users] Finding NullSpaces of Jacobian and TransposeJacobian

[Ali Berk Kahraman]

Dear All,

I am trying to solve a Poisson problem with a known source function with 
all Neumann BCs. Hence, I know that my problem does not always have a 
solution, at those times it has a transpose nullspace of one vector. If 
I know that vector, I can inform petsc of its existence using a 
MatNullSpace object.

Currently, I am trying to find the nullspace vector by solving a linear 
system where TrJacobian*nullvec = e, but an arbitrary row of the 
TrJacobian (ith row) is replaced with all zeros except for the ith 
column, and every entry of e is 0 except for the ith entry which is 1. 
However, sometimes the KSP that solves this either does not converge, or 
even if it converges the nullvec it creates does not help with the 
original problem's ksp.

Is there a more reliable way to find the transpose nullspace of a matrix?

Best Regards,

Ali Berk Kahraman
M.Sc. Student, Mechanical Eng.
Bogazici Uni. Istanbul, Turkey