[petsc-users] MatSOR and GaussSeidel

[Matthew Knepley]

On Tue, Sep 27, 2016 at 6:48 AM, Cyrill Vonplanta <cyrill.von.planta at usi.ch>
wrote:

> I am finished with what I set up to do and I just want to leave this note
> to other potential PETSc-newbies that browse the mailing list:
>
> The important thing to point out here, is that PETSc (with the
> configuration below) in general does NOT do a Gauss-Seidel step. Instead it
> might do a block (!) Gauss-Seidel step using the inodes of the matrix. This
> leads to iterates that look different from what you would expect if the
> SOR-step is done coordinate-wise and you get a different convergence
> history.
>

Note that you can disable this using

  -mat_no_inodes

  Thanks,

     Matt


> (It’s mentioned on the documentation page, but one quickly overreads it)
>
> Cyrill
>
> > On 23 Aug 2016, at 16:54, Jed Brown <jed at jedbrown.org> wrote:
> >
> > Cyrill Vonplanta <cyrill.von.planta at usi.ch> writes:
> >
> >> Dear PETSc-Users,
> >>
> >> I am debugging a smoother of ours and i was wondering what settings of
> MatSOR exactly form one ordinary Gauss Seidel smoothing step. Currently I
> use:
> >>
> >> ierr = MatSOR(A,b,1.0,(MatSORType)(SOR_ZERO_INITIAL_GUESS |
> SOR_FORWARD_SWEEP),0,1,1,x); CHKERRV(ierr);
> >
> > Yes, this is a standard forward sweep of GS.  Note that your code below
> > computes half zeros (because the vector starts as 0), but that it
> > handles the diagonal incorrectly if you were to use a nonzero initial
> > guess.
> >
> >> I expect this to be the same as this naïve Gauss-Seidel step:
> >>
> >>
> >> for (int i=0;i<m;i++){
> >>
> >>      sum_i = 0;
> >>
> >>      sum_i += ps_b_values[i];
> >>
> >>      for (int j=0;j<m;j++){
> >>
> >>        sum_i -= ps_A_values[i+j*m]*ps_x_values[j];
> >>
> >>      }
> >>
> >>      ps_x_values[i] += sum_i/ps_A_values[i*m +i];
> >>
> >> }
> >>
> >> The ps_* refer to the data parts of PETSc types (everything is serial
> and dense in my toy example. Initial x is zero.m is dimension of A).
> However the convergence history looks different. Am I missing something
> here?
> >>
> >> Best Cyrill
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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