On Thu, May 22, 2014 at 12:47 PM, Jean-Arthur Louis Olive <[email protected]>wrote:
> Hi Barry, > sorry about the late reply- > We indeed use structured grids (DMDA 2d) - but do not ever provide a > Jacobian for our non-linear stokes problem (instead just rely on petsc's FD > approximation). I understand "snes_type test" is meant to compare petsc’s > Jacobian with a user-provided analytical Jacobian. > Are you saying we should provide an exact Jacobian for our simple linear > test and see if there’s a problem with the approximate Jacobian? > The Jacobian computed by PETSc uses a finite-difference approximation, and thus is only accurate to maybe 1.0e-7 depending on the conditioning of your system. Are you trying to compare things that are more precise than that? You can provide an exact Jacobian to get machine accuracy. Matt > Thanks, > Arthur & Eric > > > > > If you are using DMDA and either DMGetColoring or the SNESSetDM > approach and dof is 4 then we color each of the 4 variables per grid point > with a different color so coupling between variables within a grid point is > not a problem. This would not explain the problem you are seeing below. > > > > Run your code with -snes_type test and read the results and follow the > directions to debug your Jacobian. > > > > Barry > > > > > > On May 13, 2014, at 1:20 PM, Jean-Arthur Louis Olive <[email protected]> > wrote: > > > >> Hi all, > >> we are using PETSc to solve the steady state Stokes equations with > non-linear viscosities using finite difference. Recently we have realized > that our true residual norm after the last KSP solve did not match next > SNES function norm when solving the linear Stokes equations. > >> > >> So to understand this better, we set up two extremely simple linear > residuals, one with no coupling between variables (vx, vy, P and T), the > other with one coupling term (shown below). > >> > >> RESIDUAL 1 (NO COUPLING): > >> for (j=info->ys; j<info->ys+info->ym; j++) { > >> for (i=info->xs; i<info->xs+info->xm; i++) { > >> f[j][i].P = x[j][i].P - 3000000; > >> f[j][i].vx= 2*x[j][i].vx; > >> f[j][i].vy= 3*x[j][i].vy - 2; > >> f[j][i].T = x[j][i].T; > >> } > >> > >> RESIDUAL 2 (ONE COUPLING TERM): > >> for (j=info->ys; j<info->ys+info->ym; j++) { > >> for (i=info->xs; i<info->xs+info->xm; i++) { > >> f[j][i].P = x[j][i].P - 3; > >> f[j][i].vx= x[j][i].vx - 3*x[j][i].vy; > >> f[j][i].vy= x[j][i].vy - 2; > >> f[j][i].T = x[j][i].T; > >> } > >> } > >> > >> > >> and our default set of options is: > >> > >> > >> OPTIONS: mpiexec -np $np ../Stokes -snes_max_it 4 -ksp_atol 2.0e+2 > -ksp_max_it 20 -ksp_rtol 9.0e-1 -ksp_type fgmres -snes_monitor > -snes_converged_reason -snes_view -log_summary -options_left 1 > -ksp_monitor_true_residual -pc_type none -snes_linesearch_type cp > >> > >> > >> With the uncoupled residual (Residual 1), we get matching KSP and SNES > norm, highlighted below: > >> > >> > >> Result from Solve - RESIDUAL 1 > >> 0 SNES Function norm 8.485281374240e+07 > >> 0 KSP unpreconditioned resid norm 8.485281374240e+07 true resid norm > 8.485281374240e+07 ||r(i)||/||b|| 1.000000000000e+00 > >> 1 KSP unpreconditioned resid norm 1.131370849896e+02 true resid norm > 1.131370849896e+02 ||r(i)||/||b|| 1.333333333330e-06 > >> 1 SNES Function norm 1.131370849896e+02 > >> 0 KSP unpreconditioned resid norm 1.131370849896e+02 true resid norm > 1.131370849896e+02 ||r(i)||/||b|| 1.000000000000e+00 > >> 2 SNES Function norm 1.131370849896e+02 > >> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 2 > >> > >> > >> With the coupled residual (Residual 2), the norms do not match, see > below > >> > >> > >> Result from Solve - RESIDUAL 2: > >> 0 SNES Function norm 1.019803902719e+02 > >> 0 KSP unpreconditioned resid norm 1.019803902719e+02 true resid norm > 1.019803902719e+02 ||r(i)||/||b|| 1.000000000000e+00 > >> 1 KSP unpreconditioned resid norm 8.741176309016e+01 true resid norm > 8.741176309016e+01 ||r(i)||/||b|| 8.571428571429e-01 > >> 1 SNES Function norm 1.697056274848e+02 > >> 0 KSP unpreconditioned resid norm 1.697056274848e+02 true resid norm > 1.697056274848e+02 ||r(i)||/||b|| 1.000000000000e+00 > >> 1 KSP unpreconditioned resid norm 5.828670868165e-12 true resid norm > 5.777940247956e-12 ||r(i)||/||b|| 3.404683942184e-14 > >> 2 SNES Function norm 3.236770473841e-07 > >> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 2 > >> > >> > >> Lastly, if we add -snes_fd to our options, the norms for residual 2 get > better - they match after the first iteration but not after the second. > >> > >> > >> Result from Solve with -snes_fd - RESIDUAL 2 > >> 0 SNES Function norm 8.485281374240e+07 > >> 0 KSP unpreconditioned resid norm 8.485281374240e+07 true resid norm > 8.485281374240e+07 ||r(i)||/||b|| 1.000000000000e+00 > >> 1 KSP unpreconditioned resid norm 2.039607805429e+02 true resid norm > 2.039607805429e+02 ||r(i)||/||b|| 2.403700850300e-06 > >> 1 SNES Function norm 2.039607805429e+02 > >> 0 KSP unpreconditioned resid norm 2.039607805429e+02 true resid norm > 2.039607805429e+02 ||r(i)||/||b|| 1.000000000000e+00 > >> 1 KSP unpreconditioned resid norm 2.529822128436e+01 true resid norm > 2.529822128436e+01 ||r(i)||/||b|| 1.240347346045e-01 > >> 2 SNES Function norm 2.549509757105e+01 [SLIGHTLY DIFFERENT] > >> 0 KSP unpreconditioned resid norm 2.549509757105e+01 true resid norm > 2.549509757105e+01 ||r(i)||/||b|| 1.000000000000e+00 > >> 3 SNES Function norm 2.549509757105e+01 > >> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 3 > >> > >> > >> Does this mean that our Jacobian is not approximated properly by the > default “coloring” method when it has off-diagonal terms? > >> > >> Thanks a lot, > >> Arthur and Eric > > > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
