1) Run the problem with -ksp_view_mat and -ksp_view_rhs and mail
petsc-ma...@mcs.anl.gov the resulting file produced called binaryoutput
2) By default PCLU does a reordering to reduce fill that could introduce a
zero pivoit, PCILU does not do a reordering by default. You can use
-pc_factor_mat_ordering_type none to force no reordering (PCLU does not do
numerical pivoting for stability so can fail with zero pivots).
3) If you need to solve these tiny 7 by 7 systems many times (presumably you
are solving these to set up a large algebraic system solved afterwards) then
you probably don't want to use KSP to solve them. You can use the low level
kernel PetscKernel_A_gets_inverse_A_7() that does do pivoting followed by a
multiply like
s1 = v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
s2 = v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
s3 = v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
s4 = v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
s5 = v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
s6 = v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
where v is the dense 7 by 7 matrix (stored column oriented like Fortran) an the
x are the seven values of the right hand side.
Barry
> On Mar 10, 2018, at 5:22 AM, Ali Berk Kahraman <aliberkkahra...@yahoo.com>
> wrote:
>
> 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
>
>
