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 >
