[petsc-users] GMRES solver

[Jed Brown]

Missing the null space can definitely cause problems.

I suggest checking unpreconditioned residuals.
On Jan 8, 2012 5:13 PM, "Mohamad M. Nasr-Azadani" <mmnasr at gmail.com> wrote:

> 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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