[petsc-users] GMRES solver

[Matthew Knepley]

On Sat, Jan 7, 2012 at 4:00 PM, Mohamad M. Nasr-Azadani <mmnasr at gmail.com>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.
> 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.
>

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

2) Why would anyone ever use GMRES without a preconditioner, particularly
for a problem where several
    optimal PCs exist and are present in PETSc.

   Matt


> 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
>
>


-- 
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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