The GCR algorithm computes the residual and hence the residual norm EXPLICITLY as part of the solution process, it does not use the recursive formula that FGMES uses. I "think" the use of the recursive formula is why FGMRES is cheaper than GCR (and hence much more commonly used).
Barry On Dec 21, 2010, at 2:46 PM, Vijay S. Mahadevan wrote: >> Yes but look at the true residual norm it is huge and indicates the residual >> is not really getting small. > Ah yes. I was reading the output wrongly. Thanks for pointing that > out. So then it is quite possible that my preconditioner is terrible > for this problem. > > Curiously with GCR, the true residual does converge. > > 62 KSP Residual norm 6.845396874593e-10 > 62 KSP preconditioned resid norm 6.845396874593e-10 true resid norm > 6.845396874593e-10 ||Ae||/||Ax|| 1.063128003731e+00 > 63 KSP preconditioned resid norm 4.617426258215e-10 true resid norm > 4.617426258215e-10 ||Ae||/||Ax|| 9.425403350509e-01 > 63 KSP Residual norm 4.617426258215e-10 > 63 KSP preconditioned resid norm 4.617426258215e-10 true resid norm > 4.617426258215e-10 ||Ae||/||Ax|| 9.425403350509e-01 > 64 KSP preconditioned resid norm 3.659090331422e-10 true resid norm > 3.659090331422e-10 ||Ae||/||Ax|| 1.044433624917e+00 > 64 KSP Residual norm 3.659090331422e-10 > 64 KSP preconditioned resid norm 3.659090331422e-10 true resid norm > 3.659090331422e-10 ||Ae||/||Ax|| 1.044433624917e+00 > 65 KSP preconditioned resid norm 2.457005532004e-10 true resid norm > 2.457005532004e-10 ||Ae||/||Ax|| 9.250757590415e-01 > 65 KSP Residual norm 2.457005532004e-10 > 65 KSP preconditioned resid norm 2.457005532004e-10 true resid norm > 2.457005532004e-10 ||Ae||/||Ax|| 9.250757590415e-01 > 66 KSP preconditioned resid norm 1.765446010945e-10 true resid norm > 1.765446010945e-10 ||Ae||/||Ax|| 9.880804659179e-01 > 66 KSP Residual norm 1.765446010945e-10 > 66 KSP preconditioned resid norm 1.765446010945e-10 true resid norm > 1.765446010945e-10 ||Ae||/||Ax|| 9.880804659179e-01 > > Jed, with modified gram schmidt procedure, fgmres yields the > following, which looks like the same as before: > > 49 KSP Residual norm 2.426160176080e-08 > 49 KSP preconditioned resid norm 2.426160176080e-08 true resid norm > 1.864897210364e+02 ||Ae||/||Ax|| 2.696456942624e+02 > 50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm > 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02 > 50 KSP Residual norm 1.864914790828e+02 > 50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm > 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02 > 51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm > 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02 > 51 KSP Residual norm 6.741080961009e+01 > 51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm > 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02 > 52 KSP preconditioned resid norm 5.191621875736e+01 true resid norm > 5.146342142561e+01 ||Ae||/||Ax|| 7.225409161988e+01 > > But I generally see that the true residual of GCR seems to converge to > desired tolerance but for GMRES, the convergence stagnates with > different options on my MG preconditioner. This is puzzling to me > since I spent enough time making sure that the preconditioner was > working correctly but I will look more into this now. Thanks for all > the helpful comments guys ! I will post here if I find any other > curious behavior. > > Vijay > > On Tue, Dec 21, 2010 at 2:30 PM, Barry Smith <bsmith at mcs.anl.gov> wrote: >> >> Yes but look at the true residual norm it is huge and indicates the >> residual is not really getting small. >> >> Barry >> >> On Dec 21, 2010, at 2:26 PM, Vijay S. Mahadevan wrote: >> >>> Barry, I tried with the true_residual_norm option and it gives me the >>> exact same convergence as the one I have shown before. >>> >>> 45 KSP Residual norm 2.511364148934e-07 >>> 45 KSP preconditioned resid norm 2.511364148934e-07 true resid norm >>> 1.865039278877e+02 ||Ae||/||Ax|| 2.699481989705e+02 >>> 46 KSP preconditioned resid norm 1.307034672896e-07 true resid norm >>> 1.864478183180e+02 ||Ae||/||Ax|| 2.724877015479e+02 >>> 46 KSP Residual norm 1.307034672896e-07 >>> 46 KSP preconditioned resid norm 1.307034672896e-07 true resid norm >>> 1.864478183180e+02 ||Ae||/||Ax|| 2.724877015479e+02 >>> 47 KSP preconditioned resid norm 7.105770015635e-08 true resid norm >>> 1.864563163311e+02 ||Ae||/||Ax|| 2.722662760395e+02 >>> 47 KSP Residual norm 7.105770015635e-08 >>> 47 KSP preconditioned resid norm 7.105770015635e-08 true resid norm >>> 1.864563163311e+02 ||Ae||/||Ax|| 2.722662760395e+02 >>> 48 KSP preconditioned resid norm 4.098578230710e-08 true resid norm >>> 1.864560351328e+02 ||Ae||/||Ax|| 2.690284539995e+02 >>> 48 KSP Residual norm 4.098578230710e-08 >>> 48 KSP preconditioned resid norm 4.098578230710e-08 true resid norm >>> 1.864560351328e+02 ||Ae||/||Ax|| 2.690284539995e+02 >>> 49 KSP preconditioned resid norm 2.426160176080e-08 true resid norm >>> 1.864897210364e+02 ||Ae||/||Ax|| 2.696456942624e+02 >>> 49 KSP Residual norm 2.426160176080e-08 >>> 49 KSP preconditioned resid norm 2.426160176080e-08 true resid norm >>> 1.864897210364e+02 ||Ae||/||Ax|| 2.696456942624e+02 >>> 50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm >>> 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02 >>> 50 KSP Residual norm 1.864914790828e+02 >>> 50 KSP preconditioned resid norm 1.864914790828e+02 true resid norm >>> 1.864914790828e+02 ||Ae||/||Ax|| 2.798875072987e+02 >>> 51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm >>> 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02 >>> 51 KSP Residual norm 6.741080961009e+01 >>> 51 KSP preconditioned resid norm 6.741080961009e+01 true resid norm >>> 6.759768469363e+01 ||Ae||/||Ax|| 1.666964983874e+02 >>> 52 KSP preconditioned resid norm 5.191621875736e+01 true resid norm >>> 5.146342142561e+01 ||Ae||/||Ax|| 7.225409161988e+01 >>> 52 KSP Residual norm 5.191621875736e+01 >>> 52 KSP preconditioned resid norm 5.191621875736e+01 true resid norm >>> 5.146342142561e+01 ||Ae||/||Ax|| 7.225409161988e+01 >>> 53 KSP preconditioned resid norm 4.513782866249e+01 true resid norm >>> 4.546883708687e+01 ||Ae||/||Ax|| 7.426476446334e+01 >>> 53 KSP Residual norm 4.513782866249e+01 >>> 53 KSP preconditioned resid norm 4.513782866249e+01 true resid norm >>> 4.546883708687e+01 ||Ae||/||Ax|| 7.426476446334e+01 >>> 54 KSP preconditioned resid norm 3.320195603375e+01 true resid norm >>> 3.297361634749e+01 ||Ae||/||Ax|| 5.285029509147e+01 >>> >>> >>> Vijay >>> >>> On Tue, Dec 21, 2010 at 2:23 PM, Barry Smith <bsmith at mcs.anl.gov> wrote: >>>> >>>> On Dec 21, 2010, at 2:08 PM, Jed Brown wrote: >>>> >>>>> On Tue, Dec 21, 2010 at 21:04, Barry Smith <bsmith at mcs.anl.gov> wrote: >>>>> This is a sign that the preconditioner is seriously messed up and should >>>>> not be used in its current form. It can happen if the matrix is nearly >>>>> singular and for example you use an incomplete factorization for a >>>>> preconditioner that just screws up the scaling like totally. Run with >>>>> -ksp_monitor_true_residual and you'll see that the solver is not really >>>>> solving the problem even though it thinks it is converging fine. >>>>> >>>>> FGMRES only does right preconditioning so it should be showing the true >>>>> residual. >>>> >>>> No because it uses a recursive formula for "computing" the residual norm >>>> it does not compute it explicitly. So in extreme circumstances the >>>> recursively compute one generates "garbage". >>>> >>>> Barry >>>> >>>> >>>> >> >>
