[petsc-users] PCLU diverges where PCILU converges on Dense Matrix

[Ali Berk Kahraman]

Hello All,

I am trying to get the finite difference coefficients for a given 
irregular grid. For this, I follow the following webpage, which tells me 
to solve a linear system.

http://web.media.mit.edu/~crtaylor/calculator.html

I solve a 7 unknown linear system with a 7x7 dense matrix to get the 
finite difference coefficients. Since I will call this code many many 
many times in my overall project, I need it to be as fast, yet as exact 
as possible. So I use PCLU. I make sure that there are no zero diagonals 
on the matrix, I swap required rows for it. However, PCLU still diverges 
with the output at the end of this e-mail. It indicates 
"FACTOR_NUMERIC_ZEROPIVOT" , but as I have written above I make sure 
there are no zero main diagonal entries on the matrix. When I use PCILU 
instead, it converges pretty well.

So my question is, is PCILU the same thing mathematically as PCLU when 
applied on a small dense matrix? I need to know if I get the exact 
solution with PCILU, because my whole project will depend on the 
accuracy of the finite differences.

Best Regards,

Ali Berk Kahraman
M.Sc. Student, Mechanical Engineering Dept.
Boğaziçi Uni., Istanbul, Turkey

Linear solve did not converge due to DIVERGED_PCSETUP_FAILED iterations 0
                PCSETUP_FAILED due to FACTOR_NUMERIC_ZEROPIVOT
KSP Object: 1 MPI processes
   type: gmres
     restart=30, using Classical (unmodified) Gram-Schmidt 
Orthogonalization with no iterative refinement
     happy breakdown tolerance 1e-30
   maximum iterations=10000, initial guess is zero
   tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
   left preconditioning
   using PRECONDITIONED norm type for convergence test
PC Object: 1 MPI processes
   type: lu
     out-of-place factorization
     tolerance for zero pivot 2.22045e-14
     matrix ordering: nd
     factor fill ratio given 5., needed 1.
       Factored matrix follows:
         Mat Object: 1 MPI processes
           type: seqaij
           rows=7, cols=7
           package used to perform factorization: petsc
           total: nonzeros=49, allocated nonzeros=49
           total number of mallocs used during MatSetValues calls =0
             using I-node routines: found 2 nodes, limit used is 5
   linear system matrix = precond matrix:
   Mat Object: 1 MPI processes
     type: seqaij
     rows=7, cols=7
     total: nonzeros=49, allocated nonzeros=49
     total number of mallocs used during MatSetValues calls =0
       using I-node routines: found 2 nodes, limit used is 5