I didn't specify a tolerance, it was using the default tolerance. Doesn't the asymptoting norm implies finer grid won't help to get finer solution?
Mark Adams <mfad...@lbl.gov> 于2018年10月2日周二 下午4:11写道： > > > On Tue, Oct 2, 2018 at 5:04 PM Weizhuo Wang <weizh...@illinois.edu> wrote: > >> Yes I was using one norm in my Helmholtz code, the example code used 2 >> norm. But now I am using 2 norm in both code. >> >> /* >> Check the error >> */ >> ierr = VecAXPY(x,-1.0,u); CHKERRQ(ierr); >> ierr = VecNorm(x,NORM_1,&norm); CHKERRQ(ierr); >> ierr = KSPGetIterationNumber(ksp,&its); CHKERRQ(ierr); >> ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations >> %D\n",(double)norm/(m*n),its); CHKERRQ(ierr); >> >> I made a plot to show the increase: >> > > > FYI, this is asymptoting to a constant. What solver tolerance are > you using? > > >> >> [image: Norm comparison.png] >> >> Mark Adams <mfad...@lbl.gov> 于2018年10月2日周二 下午2:27写道： >> >>> >>> >>> On Tue, Oct 2, 2018 at 2:24 PM Weizhuo Wang <weizh...@illinois.edu> >>> wrote: >>> >>>> The example code and makefile are attached below. The whole thing >>>> started as I tried to build a Helmholtz solver, and the mean error >>>> (calculated by: sum( | numerical_sol - analytical_sol | / analytical_sol ) >>>> ) >>>> >>> >>> This is a one norm. If you use max (instead of sum) then you don't need >>> to scale. You do have to be careful about dividing by (near) zero. >>> >>> >>>> increases as I use finer and finer grids. >>>> >>> >>> What was the rate of increase? >>> >>> >>>> Then I looked at the example 12 (Laplacian solver) which is similar to >>>> what I did to see if I have missed something. The example is using 2_norm. >>>> I have made some minor modifications (3 places) on the code, you can search >>>> 'Modified' in the code to see them. >>>> >>>> If this helps: I configured the PETSc to use real and double precision. >>>> Changed the name of the example code from ex12.c to ex12c.c >>>> >>>> Thanks for all your reply! >>>> >>>> Weizhuo >>>> >>>> >>>> Smith, Barry F. <bsm...@mcs.anl.gov> >>>> >>>> >>>>> Please send your version of the example that computes the mean norm >>>>> of the grid; I suspect we are talking apples and oranges >>>>> >>>>> Barry >>>>> >>>>> >>>>> >>>>> > On Oct 1, 2018, at 7:51 PM, Weizhuo Wang <weizh...@illinois.edu> >>>>> wrote: >>>>> > >>>>> > I also tried to divide the norm by m*n , which is the number of >>>>> grids, the trend of norm still increases. >>>>> > >>>>> > Thanks! >>>>> > >>>>> > Weizhuo >>>>> > >>>>> > Matthew Knepley <knep...@gmail.com> >>>>> > On Mon, Oct 1, 2018 at 6:31 PM Weizhuo Wang <weizh...@illinois.edu> >>>>> wrote: >>>>> > Hi! >>>>> > >>>>> > I'm recently trying out the example code provided with the KSP >>>>> solver (ex12.c). I noticed that the mean norm of the grid increases as I >>>>> use finer meshes. For example, the mean norm is 5.72e-8 at m=10 n=10. >>>>> However at m=100, n=100, mean norm increases to 9.55e-6. This seems >>>>> counter >>>>> intuitive, since most of the time error should decreases when using finer >>>>> grid. Am I doing this wrong? >>>>> > >>>>> > The norm is misleading in that it is the l_2 norm, meaning just the >>>>> sqrt of the sum of the squares of >>>>> > the vector entries. It should be scaled by the volume element to >>>>> approximate a scale-independent >>>>> > norm (like the L_2 norm). >>>>> > >>>>> > Thanks, >>>>> > >>>>> > Matt >>>>> > >>>>> > Thanks! >>>>> > -- >>>>> > Wang Weizhuo >>>>> > >>>>> > >>>>> > -- >>>>> > 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 >>>>> > >>>>> > https://www.cse.buffalo.edu/~knepley/ >>>>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__www.cse.buffalo.edu_-7Eknepley_&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=hsLktHsuxNfF6zyuWGCN8x-6ghPYxhx4cV62Hya47oo&m=KjmDEsZ6w8LEry7nlv3Bw7-pczqWbKGueFU59VoIWZg&s=tEv9-AHhL2CIlmmVos0gFa5PAY9oMG3aTQlnfi62ivA&e=> >>>>> > >>>>> > >>>>> > -- >>>>> > Wang Weizhuo >>>>> >>>>> >>>> >>>> -- >>>> Wang Weizhuo >>>> >>> >> >> -- >> Wang Weizhuo >> > -- Wang Weizhuo
