[petsc-users] GMRES solver

Mon Jan 9 00:28:17 CST 2012

Are you using the exact same matrix at each time-step or does the matrix
change?

Pressure lsys does not change over time. However, the diagonal of the
velocity lsys's do change due to the variable time step.

Best,
M

On Sun, Jan 8, 2012 at 10:11 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> On Jan 8, 2012, at 9:33 PM, Mohamad M. Nasr-Azadani wrote:
>
> >    How do you know it is diverging? Because it looks weird? You are
> comparing it to something?
> >
> > While marching in time, it only takes 20-30 iterations to solve for
> pressure.
> > After a very long integrattion in time, all of a sudden the pressure
> lsys does not converge even in 10,000 iterations. So, that's why I am
> saying it is converging.
>
>    Are you using the exact same matrix at each time-step or does the
> matrix change?
>
>
> >
> >    How accurately are you solving the linear system?
> > I tried rtol = 1e-10 and 1e-12.
> >
> >     What strange behavior?  Is the right hand side for the pressure
> solution reasonable but the solution "strange"? How do you know you are not
> giving "bad stuff" to the pressure solve?
> > For my case, I get huge pressure gradients close to the solid
> boundaries. That, indeed, causes very small delta_t's when I keep
> integrating. That should not happen cause at this stage of my simulations,
> nothing is really happening in the flow field. Very small velocities and
> velocity gradients.
> > I am trying to find the problem, since I have only seen this for such
> big problem size, i.e. 100 million grid points. That makes it really hard
> to see if the I am feeding back rhs into the pressure linear system.
> >
> > Best,
> > Mohamad
> >
> >
> >
> >
> >
> >
> > On Sun, Jan 8, 2012 at 6:47 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> > On Jan 8, 2012, at 5:13 PM, Mohamad M. Nasr-Azadani 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
> >
> >    How do you know it is diverging? Because it looks weird? You are
> comparing it to something?
> >
> >
> >    How accurately are you solving the linear system?
> >
> >
> > > 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.
> >
> >     What strange behavior?  Is the right hand side for the pressure
> solution reasonable but the solution "strange"? How do you know you are not
> giving "bad stuff" to the pressure solve?
> >
> >   Barry
> >
> >
> > > 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
> > > >
> > >
> > >
> >
> >
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120108/f3a62899/attachment.htm>