Also GCR seems to use and allocate comparatively more vectors, translating to lot more memory. This does make FGMRES more attractive. I will look at the preconditioner and try to find the true cause of the issue.
Cheers, Vijay On Tue, Dec 21, 2010 at 2:52 PM, Barry Smith <bsmith at mcs.anl.gov> wrote: > > ?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 >>>>> >>>>> >>>>> >>> >>> > >
