[petsc-users] Null space correction depends on solver?

[Jed Brown]

On Tue, Aug 28, 2012 at 8:19 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:

> > How to interpret the results? For the first case, is the null space
> information forwarded to the preconditioner? And even for using just gmres
> without any preconditioner, the dot product is much closer to zero but
> still far away.
>
>
>     Are you sure the null space you provide is truly the null space of the
> matrix? Call MatNullSpaceTest().
>
>      GMRES uses left preconditioning by default which forces the null
> space into the Krylov space at each iteration. FGMRES uses right
> preconditioning and doesn't  do anything to the null space because it is
> naturally in the Krylov space (since the result with fgmres contains the
> constants this is why I suspect the matrix actually doesn't have the null
> space you think it has). You can try running -ksp_type gmres -ksp_pc_side
> right      my guess is that you will not get near zero for the dot.
>

Barry, it looks like null space removal is not implemented correctly for
right preconditioning:

diff --git a/src/ksp/ksp/examples/tutorials/ex29.c
b/src/ksp/ksp/examples/tutorials/ex29.c
--- a/src/ksp/ksp/examples/tutorials/ex29.c
+++ b/src/ksp/ksp/examples/tutorials/ex29.c
@@ -78,6 +78,12 @@
   ierr = KSPSolve(ksp,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
   ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
   ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
+  {
+    PetscScalar dot;
+    ierr = VecSet(b,1.0);CHKERRQ(ierr);
+    ierr = VecDot(b,x,&dot);CHKERRQ(ierr);
+    ierr = PetscPrintf(PETSC_COMM_WORLD,"dot %g\n",dot);CHKERRQ(ierr);
+  }

   ierr = DMDestroy(&da);CHKERRQ(ierr);
   ierr = KSPDestroy(&ksp);CHKERRQ(ierr);

$ ./ex29 -bc_type neumann -ksp_monitor_true_residual -ksp_test_null_space
-mat_null_space_test_view -pc_type jacobi -ksp_pc_side left
Constants are likely null vector|| A * 1/N || = 0
  0 KSP preconditioned resid norm 1.135199672180e-01 true resid norm
2.319967097991e-01 ||r(i)||/||b|| 1.000000000000e+00
  1 KSP preconditioned resid norm 4.410876553096e-02 true resid norm
1.254974589275e-01 ||r(i)||/||b|| 5.409449945916e-01
  2 KSP preconditioned resid norm 2.255575515098e-02 true resid norm
5.942041105213e-02 ||r(i)||/||b|| 2.561260937863e-01
  3 KSP preconditioned resid norm 9.933310900089e-03 true resid norm
2.093328265899e-02 ||r(i)||/||b|| 9.023094627987e-02
  4 KSP preconditioned resid norm 1.073259860881e-17 true resid norm
1.660357840786e-16 ||r(i)||/||b|| 7.156816328229e-16
dot 1.73472e-16
$ ./ex29 -bc_type neumann -ksp_monitor_true_residual -ksp_test_null_space
-mat_null_space_test_view -pc_type jacobi -ksp_pc_side right
Constants are likely null vector|| A * 1/N || = 0
  0 KSP unpreconditioned resid norm 2.319967097991e-01 true resid norm
2.319967097991e-01 ||r(i)||/||b|| 1.000000000000e+00
  1 KSP unpreconditioned resid norm 1.218421389101e-01 true resid norm
1.218421389101e-01 ||r(i)||/||b|| 5.251890814123e-01
  2 KSP unpreconditioned resid norm 5.897341285066e-02 true resid norm
5.897341285066e-02 ||r(i)||/||b|| 2.541993500758e-01
  3 KSP unpreconditioned resid norm 2.064441965393e-02 true resid norm
2.064441965393e-02 ||r(i)||/||b|| 8.898582946200e-02
  4 KSP unpreconditioned resid norm 8.019849301680e-17 true resid norm
5.101974804388e-17 ||r(i)||/||b|| 2.199158259100e-16
dot 0.0188443

It seems to be caused by this:

#define KSP_RemoveNullSpace(ksp,y) ((ksp->nullsp && ksp->pc_side ==
PC_LEFT) ? MatNullSpaceRemove(ksp->nullsp,y,PETSC_NULL) : 0)
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