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? 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 >
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