[petsc-users] Moving from KSPSetNullSpace to MatSetNullSpace

[Olivier Mesnard]

Hi all,

We develop a CFD code using the PETSc library that solves the Navier-Stokes
equations using the fractional-step method from Perot (1993).
At each time-step, we solve two systems: one for the velocity field, the
other, a Poisson system, for the pressure field.
One of our test-cases is a 2D lid-driven cavity flow (Re=100) on a 20x20
grid using 1 or 2 procs.
For the Poisson system, we usually use CG preconditioned with GAMG.

So far, we have been using PETSc-3.5.4, and we would like to update the
code with the latest release: 3.7.4.

As suggested in the changelog of 3.6, we replaced the routine
`KSPSetNullSpace()` with `MatSetNullSpace()`.

Here is the list of options we use to configure the two solvers:
* Velocity solver: prefix `-velocity_`
  -velocity_ksp_type bcgs
  -velocity_ksp_rtol 1.0E-08
  -velocity_ksp_atol 0.0
  -velocity_ksp_max_it 10000
  -velocity_pc_type jacobi
  -velocity_ksp_view
  -velocity_ksp_monitor_true_residual
  -velocity_ksp_converged_reason
* Poisson solver: prefix `-poisson_`
  -poisson_ksp_type cg
  -poisson_ksp_rtol 1.0E-08
  -poisson_ksp_atol 0.0
  -poisson_ksp_max_it 20000
  -poisson_pc_type gamg
  -poisson_pc_gamg_type agg
  -poisson_pc_gamg_agg_nsmooths 1
  -poissonksp_view
  -poisson_ksp_monitor_true_residual
  -poisson_ksp_converged_reason

With 3.5.4, the case runs normally on 1 or 2 procs.
With 3.7.4, the case runs normally on 1 proc but not on 2.
Why? The Poisson solver diverges because of an indefinite preconditioner
(only with 2 procs).

We also saw that the routine `MatSetNullSpace()` was already available in
3.5.4.
With 3.5.4, replacing `KSPSetNullSpace()` with `MatSetNullSpace()` led to
the Poisson solver diverging because of an indefinite matrix (on 1 and 2
procs).

Thus, we were wondering if we needed to update something else for the KSP,
and not just modifying the name of the routine?

I have attached the output files from the different cases:
* `run-petsc-3.5.4-n1.log` (3.5.4, `KSPSetNullSpace()`, n=1)
* `run-petsc-3.5.4-n2.log`
* `run-petsc-3.5.4-nsp-n1.log` (3.5.4, `MatSetNullSpace()`, n=1)
* `run-petsc-3.5.4-nsp-n2.log`
* `run-petsc-3.7.4-n1.log` (3.7.4, `MatSetNullSpace()`, n=1)
* `run-petsc-3.7.4-n2.log`

Thank you for your help,
Olivier
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