# [petsc-users] KSPSolve convergence and norms

Torquil Macdonald Sørensen torquil at gmail.com
Fri Oct 25 11:33:56 CDT 2013

```Hi!

I'm using PETSc 3.4.3, with only default runtime settings, to solve Ax=b,
for complex numbers (I have used --with-scalar-type=complex).

After reading sections 4.3.1, 4.3.2, 4.3.3 in the manual, I decided to
investigate the convergence in my program, since I'm having some problems
when the system is larger. So, I'm running it with the options

-ksp_monitor_true_residual -ksp_converged_reason -ksp_view

The output shows that the relative tolerance required for convergence is
1e-5, but none of the reported norms are that small. Despite this,
convergence is reported (CONVERGED_RTOL).

I though that CONVERGED_RTOL should indicate that ||r||_2/||b||_2 < 1e-5,
where r is the preconditioned residual?

Here is the output of my program (which includes some code to compute the
l_2 norm of b, just before KSPSolve is run):

*************************************************************
Norm of b: 0.179829
0 KSP preconditioned resid norm 2.508789303280e+04 true resid norm
1.798290175843e-01 ||r(i)||/||b|| 1.000000000000e+00
1 KSP preconditioned resid norm 1.856991132478e+00 true resid norm
3.186462510386e-01 ||r(i)||/||b|| 1.771940120227e+00
2 KSP preconditioned resid norm 1.704678606994e-01 true resid norm
4.004071321891e-02 ||r(i)||/||b|| 2.226599119363e-01
Linear solve converged due to CONVERGED_RTOL iterations 2
KSP Object: 1 MPI processes
type: gmres
GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
GMRES: 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: ilu
ILU: out-of-place factorization
0 levels of fill
tolerance for zero pivot 2.22045e-14
using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
matrix ordering: natural
factor fill ratio given 1, needed 1
Factored matrix follows:
Matrix Object:         1 MPI processes
type: seqaij
rows=18, cols=18
package used to perform factorization: petsc
total: nonzeros=144, allocated nonzeros=144
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 9 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object:   1 MPI processes
type: seqaij
rows=18, cols=18
total: nonzeros=144, allocated nonzeros=360
total number of mallocs used during MatSetValues calls =18
using I-node routines: found 9 nodes, limit used is 5
************************************************************************************************

Here is the code I used to get the l_2 norm of b:

PetscReal val;
VecNorm(b, NORM_2, &val);
PetscPrintf(PETSC_COMM_WORLD, "Norm of b: %G\n", val);

Best regards
Torquil Sørensen
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20131025/3ac04d74/attachment.html>
```