[petsc-users] GMRES solver

[Mohamad M. Nasr-Azadani]

Thanks Barry and Matt,

Barry,
  Also if you are really solving the Poisson problem you should use
multigrid; if simple geometry then geometric multigrid if complicated
geometry probably easier to use hypre BoomerAMG. No sane person solves
Poisson problem with anything but a multigrid or FFT based solver.

In my main code, I am actually doing what you suggested, i.e. GMRES +
boomerAMG to solve for my Poisson equation. I have not used the
KSPSetNullSpace() though.
The problem is that my code (CFD, incompressible flow 3D) diverges after a
long time integration and I am trying to find out why.
The system that I have is a fairly big one, i.e. 100 million grid points
and more.
I see that pressure solution (which is obviously coupled to the velocity
field) starts showing strange behavior.
That's why I tried to first double check my pressure solver.

Based on your experience, do you think that not using a nullspace() for the
pressure solver for that linear system size could have caused it to
diverge?


Matt,
1) Matlab could be doing a lot of things. I am betting that they scale the
problem, so -pc_type jacobi.

That could be right. The reason that I relied on the MATLAB's gmres solver
to behave exactly similar to PETSc was just their "help" saying that
************
 X = GMRES(A,B,RESTART,TOL,MAXIT,M1,M2) use preconditioner M or M=M1*M2
    and effectively solve the system inv(M)*A*X = inv(M)*B for X. If M is
    [] then a preconditioner is not applied.
************

Best,
Mohamad

On Sat, Jan 7, 2012 at 5:39 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> On Jan 7, 2012, at 4:00 PM, Mohamad M. Nasr-Azadani wrote:
>
> > Hi guys,
> >
> > I am trying to narrow down an issue with my Poisson solver.
> > I have the following problem setup
> >
> > Laplace(f) = rhs(x,z,y)
> > 0 <= x,y,z <= (Lx,Ly,Lz)
> >
> > I solve the Poisson equation in three dimensions with the analytical
> function f(x,y,z) defined by
> >
> > f(x,z,y) = cos(2*pi*x/Lx)*cos(2*pi*y/Ly)*cos(2*pi*z/Lz) + K
> > where Lx = Ly =Lz = 1.0 and K is a constant I use to set f(Lx,Ly,Lz) =
> 0.0.
> >
> > Second order descritization is used for the Poisson equation.
> > Also, Neumann boundary condition is used everywhere, but I set the
> top-right-front node's value to zero to get rid of the Nullspaced matrix
> manually.
>
>    Please don't do this. That results in a unnecessaryly huge condition
> number. Use KSPSetNullSpace.()
>
>   Also if you are really solving the Poisson problem you should use
> multigrid; if simple geometry then geometric multigrid if complicated
> geometry probably easier to use hypre BoomerAMG. No sane person solves
> Poisson problem with anything but a multigrid or FFT based solver.
>
>   Barry
>
> > I use 20 grid points in each direction.
> >
> > The problem is:
> > I use GMRES(20) without any preconditioners (rtol = 1e-12) to solve the
> linear system.
> > It takes 77,000 iterations to converge!!!!
> >
> > For the size of only 8,000 unknowns, even though the lsys is not
> preconditioned, I guess that is a LOT of iterations.
> > Next, I setup the exact same problem in MATLAB and use their GMRES
> solver function.
> > I set the same parameters and MATLAB tells me that it converges using
> only 3870 iterations.
> >
> > I know that there might be some internal differences between MATLAB and
> PETSc's implementations of this method, but given the fact that these two
> solvers are not preconditioned, I am wondering about this big difference?
> >
> > Any ideas?
> >
> > Best,
> > Mohamad
> >
>
>
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