Hi guys, <div><br></div><div>I am trying to narrow down an issue with my Poisson solver. </div><div>I have the following problem setup</div><div><br></div><div>Laplace(f) = rhs(x,z,y)</div><div>0 <= x,y,z <= (Lx,Ly,Lz)</div>
<div><br></div><div>I solve the Poisson equation in three dimensions with the analytical function f(x,y,z) defined by</div><div><br></div><div>f(x,z,y) = cos(2*pi*x/Lx)*cos(2*pi*y/Ly)*cos(2*pi*z/Lz) + K</div><div>where Lx = Ly =Lz = 1.0 and K is a constant I use to set f(Lx,Ly,Lz) = 0.0. </div>
<div><br></div><div>Second order descritization is used for the Poisson equation. </div><div>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. </div>
<div>I use 20 grid points in each direction. </div><div><br></div><div>The problem is: </div><div>I use GMRES(20) without any preconditioners (rtol = 1e-12) to solve the linear system. </div><div>It takes 77,000 iterations to converge!!!! </div>
<div><br></div><div>For the size of only 8,000 unknowns, even though the lsys is not preconditioned, I guess that is a LOT of iterations. </div><div>Next, I setup the exact same problem in MATLAB and use their GMRES solver function. </div>
<div>I set the same parameters and MATLAB tells me that it converges using only 3870 iterations. </div><div><br></div><div>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? </div>
<div><br></div><div>Any ideas? </div><div><br></div><div>Best, </div><div>Mohamad</div><div><br></div>