[petsc-users] GMRES solver

[Mohamad M. Nasr-Azadani]

Thanks Jed,

Maybe I was not 100% clear, the way that I dealt with the nullspace was to
set the pressure to zero at one node in the entire domain.

Best,
Mohamad


On Sun, Jan 8, 2012 at 3:33 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> 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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