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/ >> > >> > >> > -- >> > Wang Weizhuo >> >> > > -- > Wang Weizhuo >