<div dir="ltr"><div dir="ltr">On Fri, Apr 16, 2021 at 5:50 AM Nicolas Barral <<a href="mailto:nicolas.barral@math.u-bordeaux.fr">nicolas.barral@math.u-bordeaux.fr</a>> wrote:<br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">On 31/03/2021 21:44, Matthew Knepley wrote:<br>
> On Wed, Mar 31, 2021 at 3:36 PM Nicolas Barral <br>
> <<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a> <br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>> wrote:<br>
> <br>
> On 31/03/2021 21:24, Matthew Knepley wrote:<br>
> > Ok so that's worth clarifying, but my problem is that dm has a<br>
> > 0-overlap<br>
> > before DMPlexDistributeOverlap and odm has a 1-overlap even<br>
> though I<br>
> > passed "0". If I understand what you just wrote, adding "0"<br>
> more levels<br>
> > of overlap to 0-overlap, that should still be 0 overlap ?<br>
> ><br>
> > Yet when I look at the code of DMPlexDistributeOverlap,<br>
> you're flagging<br>
> > points to be added to the overlap whatever "k" is.<br>
> ><br>
> ><br>
> > Crap. There is a bug handling 0. Evidently, no one ever asks for<br>
> overlap 0.<br>
> > Will fix.<br>
> ><br>
> ok now I'm sure I understand what you explained :) Thanks Matt.<br>
> <br>
> Now we can look at the other question: I need to be able to pass the<br>
> non-overlapping mesh to the remesher. I can either maintain 2<br>
> plexes, or<br>
> trim the overlapping plex when I create the arrays I pass to the<br>
> remesher. I'm not sure which is the best/worst ?<br>
> <br>
> <br>
> I would start with two plexes since it is very easy.<br>
<br>
Hi Matt,<br>
<br>
I've been playing with two plexes, and am running in an unexpected <br>
issue. It seems that the vertices ordering of the new overlapping plex <br>
is not the same as the one of the original plex, which makes converting <br>
a Vec from one plex to the other difficult. Can you please confirm it's <br>
the case, and is there a way to convert the Vecs out of the box ?<br></blockquote><div><br></div><div>Okay, we should get all the new cells at the end of the current cells, but then we automatically create</div><div>the renumbering for the cones using the global vertex numbering. Thus it looks like they could get</div><div>renumbered if the vertex of a new cell has a lower global number than some existing vertex.</div><div><br></div><div>Whenever we move things around, we give back the PetscSF we built to do the moving. The idea is</div><div>that you can use the returned SF to move anything that we did not, using the same method we used to</div><div>move the internal things. For example, DMMigrate() takes an SF and moves the internal mesh data,</div><div>cones + labels + coordinates. It calls DMPlexDistributeField() to move the coordinate data. You can</div><div>call the same thing. If you have your two vectors+sections already created, and you just want to go</div><div>back and forth, you can use PetscSFCreateSectionSF() (which you can store) and SFBcast(). This is</div><div>done inside DMPlexDistributeField().</div><div><br></div><div>Does this make sense?</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
Else filtering the plex may be easier.<br>
<br>
Thanks<br>
<br>
-- <br>
Nicolas<br>
<br>
> <br>
> Trimming the plex would essentially make another plex anyway, but it is <br>
> not hard using DMPlexFilter().<br>
> <br>
> Thanks,<br>
> <br>
> Matt<br>
> <br>
> Thanks<br>
> <br>
> -- <br>
> Nicolas<br>
> <br>
> <br>
> > Thanks,<br>
> ><br>
> > Matt<br>
> ><br>
> > Sample code:<br>
> > static char help[] = "Tests plex distribution and overlaps.\n";<br>
> ><br>
> > #include <petsc/private/dmpleximpl.h><br>
> ><br>
> > int main (int argc, char * argv[]) {<br>
> ><br>
> > DM dm, odm;<br>
> > MPI_Comm comm;<br>
> > PetscErrorCode ierr;<br>
> ><br>
> > ierr = PetscInitialize(&argc, &argv, NULL, help);if (ierr)<br>
> > return ierr;<br>
> > comm = PETSC_COMM_WORLD;<br>
> ><br>
> > ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL,<br>
> NULL, NULL,<br>
> > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);<br>
> > ierr = DMSetFromOptions(dm);CHKERRQ(ierr);<br>
> ><br>
> ><br>
> ><br>
> > ierr = PetscObjectSetName((PetscObject) dm, "DM<br>
> > before");CHKERRQ(ierr);<br>
> > ierr = DMViewFromOptions(dm, NULL,<br>
> "-before_dm_view");CHKERRQ(ierr);<br>
> > DMPlexDistributeOverlap(dm, 0, NULL, &odm);<br>
> > ierr = PetscObjectSetName((PetscObject) odm, "DM<br>
> > after");CHKERRQ(ierr);<br>
> > ierr = DMViewFromOptions(odm, NULL,<br>
> "-after_dm_view");CHKERRQ(ierr);<br>
> ><br>
> ><br>
> > ierr = DMDestroy(&dm);CHKERRQ(ierr);<br>
> > ierr = DMDestroy(&odm);CHKERRQ(ierr);<br>
> > ierr = PetscFinalize();<br>
> > return ierr;<br>
> > }<br>
> ><br>
> > % mpiexec -n 2 ./test_overlapV3 -dm_plex_box_faces 5,5<br>
> -dm_distribute<br>
> > -before_dm_view -after_dm_view<br>
> > DM Object: DM before 2 MPI processes<br>
> > type: plex<br>
> > DM before in 2 dimensions:<br>
> > 0-cells: 21 21<br>
> > 1-cells: 45 45<br>
> > 2-cells: 25 25<br>
> > Labels:<br>
> > depth: 3 strata with value/size (0 (21), 1 (45), 2 (25))<br>
> > celltype: 3 strata with value/size (0 (21), 1 (45), 3 (25))<br>
> > marker: 1 strata with value/size (1 (21))<br>
> > Face Sets: 1 strata with value/size (1 (10))<br>
> > DM Object: DM after 2 MPI processes<br>
> > type: plex<br>
> > DM after in 2 dimensions:<br>
> > 0-cells: 29 29<br>
> > 1-cells: 65 65<br>
> > 2-cells: 37 37<br>
> > Labels:<br>
> > depth: 3 strata with value/size (0 (29), 1 (65), 2 (37))<br>
> > celltype: 3 strata with value/size (0 (29), 1 (65), 3 (37))<br>
> > marker: 1 strata with value/size (1 (27))<br>
> > Face Sets: 1 strata with value/size (1 (13))<br>
> ><br>
> ><br>
> ><br>
> > ><br>
> > > Thanks,<br>
> > ><br>
> > > Matt<br>
> > ><br>
> > > Thanks,<br>
> > ><br>
> > > --<br>
> > > Nicolas<br>
> > ><br>
> > > ><br>
> > > > Thanks,<br>
> > > ><br>
> > > > Matt<br>
> > > ><br>
> > > > if (!dm) {printf("Big problem\n"); dm = odm;}<br>
> > > > else {DMDestroy(&odm);}<br>
> > > > ierr = PetscObjectSetName((PetscObject) dm,<br>
> "Initial<br>
> > > > DM");CHKERRQ(ierr);<br>
> > > > ierr = DMViewFromOptions(dm, NULL,<br>
> > > > "-initial_dm_view");CHKERRQ(ierr);<br>
> > > ><br>
> > > ><br>
> > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);<br>
> > > > ierr = PetscFinalize();<br>
> > > > return ierr;<br>
> > > > }<br>
> > > ><br>
> > > > called with mpiexec -n 2 ./test_overlapV3<br>
> -initial_dm_view<br>
> > > > -dm_plex_box_faces 5,5 -dm_distribute<br>
> > > ><br>
> > > > gives:<br>
> > > > DM Object: Initial DM 2 MPI processes<br>
> > > > type: plex<br>
> > > > Initial DM in 2 dimensions:<br>
> > > > 0-cells: 29 29<br>
> > > > 1-cells: 65 65<br>
> > > > 2-cells: 37 37<br>
> > > > Labels:<br>
> > > > depth: 3 strata with value/size (0 (29), 1<br>
> (65), 2<br>
> > (37))<br>
> > > > celltype: 3 strata with value/size (0 (29), 1<br>
> > (65), 3 (37))<br>
> > > > marker: 1 strata with value/size (1 (27))<br>
> > > > Face Sets: 1 strata with value/size (1 (13))<br>
> > > ><br>
> > > > which is not what I expect ?<br>
> > > ><br>
> > > > Thanks,<br>
> > > ><br>
> > > > --<br>
> > > > Nicolas<br>
> > > ><br>
> > > > On 31/03/2021 19:02, Matthew Knepley wrote:<br>
> > > > > Alright, I think the problem had to do with<br>
> keeping<br>
> > track<br>
> > > of what<br>
> > > > DM you<br>
> > > > > were looking at. This code increases the<br>
> overlap of an<br>
> > > initial DM:<br>
> > > > ><br>
> > > > > static char help[] = "Tests plex<br>
> distribution and<br>
> > > overlaps.\n";<br>
> > > > ><br>
> > > > > #include <petsc/private/dmpleximpl.h><br>
> > > > ><br>
> > > > > int main (int argc, char * argv[]) {<br>
> > > > ><br>
> > > > > DM dm, dm2;<br>
> > > > > PetscInt overlap;<br>
> > > > > MPI_Comm comm;<br>
> > > > > PetscErrorCode ierr;<br>
> > > > ><br>
> > > > > ierr = PetscInitialize(&argc, &argv, NULL,<br>
> > help);if (ierr)<br>
> > > > return ierr;<br>
> > > > > comm = PETSC_COMM_WORLD;<br>
> > > > ><br>
> > > > > ierr = DMPlexCreateBoxMesh(comm, 2,<br>
> PETSC_TRUE,<br>
> > NULL,<br>
> > > NULL, NULL,<br>
> > > > > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);<br>
> > > > > ierr = DMSetFromOptions(dm);CHKERRQ(ierr);<br>
> > > > > ierr = PetscObjectSetName((PetscObject)<br>
> dm, "Initial<br>
> > > > DM");CHKERRQ(ierr);<br>
> > > > > ierr = DMViewFromOptions(dm, NULL,<br>
> > > > "-initial_dm_view");CHKERRQ(ierr);<br>
> > > > ><br>
> > > > > ierr = DMPlexGetOverlap(dm,<br>
> &overlap);CHKERRQ(ierr);<br>
> > > > > ierr = DMPlexDistributeOverlap(dm,<br>
> overlap+1, NULL,<br>
> > > > &dm2);CHKERRQ(ierr);<br>
> > > > > ierr = PetscObjectSetName((PetscObject) dm2,<br>
> > "More Overlap<br>
> > > > > DM");CHKERRQ(ierr);<br>
> > > > > ierr = DMViewFromOptions(dm2, NULL,<br>
> > > > "-over_dm_view");CHKERRQ(ierr);<br>
> > > > ><br>
> > > > > ierr = DMDestroy(&dm2);CHKERRQ(ierr);<br>
> > > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);<br>
> > > > > ierr = PetscFinalize();<br>
> > > > > return ierr;<br>
> > > > > }<br>
> > > > ><br>
> > > > > and when we run it we get the expected result<br>
> > > > ><br>
> > > > > master *:~/Downloads/tmp/Nicolas$<br>
> > > /PETSc3/petsc/apple/bin/mpiexec<br>
> > > > -n 2<br>
> > > > > ./test_overlap -initial_dm_view<br>
> -dm_plex_box_faces 5,5<br>
> > > > -dm_distribute<br>
> > > > > -dm_distribute_overlap 1 -over_dm_view<br>
> > > > > DM Object: Initial DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > Initial DM in 2 dimensions:<br>
> > > > > 0-cells: 29 29<br>
> > > > > 1-cells: 65 65<br>
> > > > > 2-cells: 37 37<br>
> > > > > Labels:<br>
> > > > > depth: 3 strata with value/size (0 (29),<br>
> 1 (65),<br>
> > 2 (37))<br>
> > > > > celltype: 3 strata with value/size (0 (29), 1<br>
> > (65), 3 (37))<br>
> > > > > marker: 1 strata with value/size (1 (27))<br>
> > > > > Face Sets: 1 strata with value/size (1 (13))<br>
> > > > > DM Object: More Overlap DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > More Overlap DM in 2 dimensions:<br>
> > > > > 0-cells: 36 36<br>
> > > > > 1-cells: 85 85<br>
> > > > > 2-cells: 50 50<br>
> > > > > Labels:<br>
> > > > > depth: 3 strata with value/size (0 (36),<br>
> 1 (85),<br>
> > 2 (50))<br>
> > > > > celltype: 3 strata with value/size (0 (36), 1<br>
> > (85), 3 (50))<br>
> > > > > marker: 1 strata with value/size (1 (40))<br>
> > > > > Face Sets: 1 strata with value/size (1 (20))<br>
> > > > ><br>
> > > > > Thanks,<br>
> > > > ><br>
> > > > > Matt<br>
> > > > ><br>
> > > > > On Wed, Mar 31, 2021 at 12:57 PM Matthew Knepley<br>
> > > > <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>><br>
> > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>>><br>
> > > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>><br>
> > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>>>><br>
> > > > > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>>><br>
> > > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>><br>
> > <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a> <mailto:<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>>>>>>> wrote:<br>
> > > > ><br>
> > > > > Okay, let me show a really simple<br>
> example that<br>
> > gives<br>
> > > the expected<br>
> > > > > result before I figure out what is going<br>
> wrong for<br>
> > > you. This code<br>
> > > > ><br>
> > > > > static char help[] = "Tests plex<br>
> distribution and<br>
> > > overlaps.\n";<br>
> > > > ><br>
> > > > > #include <petsc/private/dmpleximpl.h><br>
> > > > ><br>
> > > > > int main (int argc, char * argv[]) {<br>
> > > > > DM dm;<br>
> > > > > MPI_Comm comm;<br>
> > > > > PetscErrorCode ierr;<br>
> > > > ><br>
> > > > > ierr = PetscInitialize(&argc, &argv,<br>
> NULL,<br>
> > help);if<br>
> > > (ierr)<br>
> > > > return<br>
> > > > > ierr;<br>
> > > > > comm = PETSC_COMM_WORLD;<br>
> > > > ><br>
> > > > > ierr = DMPlexCreateBoxMesh(comm, 2,<br>
> > PETSC_TRUE, NULL,<br>
> > > > NULL, NULL,<br>
> > > > > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);<br>
> > > > > ierr =<br>
> DMSetFromOptions(dm);CHKERRQ(ierr);<br>
> > > > > ierr =<br>
> PetscObjectSetName((PetscObject) dm,<br>
> > "Initial<br>
> > > > > DM");CHKERRQ(ierr);<br>
> > > > > ierr = DMViewFromOptions(dm, NULL,<br>
> > > > "-initial_dm_view");CHKERRQ(ierr);<br>
> > > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);<br>
> > > > > ierr = PetscFinalize();<br>
> > > > > return ierr;<br>
> > > > > }<br>
> > > > ><br>
> > > > > can do all the overlap tests. For<br>
> example, you<br>
> > can run<br>
> > > it naively<br>
> > > > > and get a serial mesh<br>
> > > > ><br>
> > > > > master *:~/Downloads/tmp/Nicolas$<br>
> > > > /PETSc3/petsc/apple/bin/mpiexec -n<br>
> > > > > 2 ./test_overlap -initial_dm_view<br>
> > -dm_plex_box_faces 5,5<br>
> > > > > DM Object: Initial DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > Initial DM in 2 dimensions:<br>
> > > > > 0-cells: 36 0<br>
> > > > > 1-cells: 85 0<br>
> > > > > 2-cells: 50 0<br>
> > > > > Labels:<br>
> > > > > celltype: 3 strata with value/size (0<br>
> (36),<br>
> > 3 (50),<br>
> > > 1 (85))<br>
> > > > > depth: 3 strata with value/size (0<br>
> (36), 1<br>
> > (85), 2<br>
> > > (50))<br>
> > > > > marker: 1 strata with value/size (1 (40))<br>
> > > > > Face Sets: 1 strata with value/size<br>
> (1 (20))<br>
> > > > ><br>
> > > > > Then run it telling Plex to distribute after<br>
> > creating<br>
> > > the mesh<br>
> > > > ><br>
> > > > > master *:~/Downloads/tmp/Nicolas$<br>
> > > > /PETSc3/petsc/apple/bin/mpiexec -n<br>
> > > > > 2 ./test_overlap -initial_dm_view<br>
> > -dm_plex_box_faces 5,5<br>
> > > > -dm_distribute<br>
> > > > > DM Object: Initial DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > Initial DM in 2 dimensions:<br>
> > > > > 0-cells: 21 21<br>
> > > > > 1-cells: 45 45<br>
> > > > > 2-cells: 25 25<br>
> > > > > Labels:<br>
> > > > > depth: 3 strata with value/size (0<br>
> (21), 1<br>
> > (45), 2<br>
> > > (25))<br>
> > > > > celltype: 3 strata with value/size (0<br>
> (21),<br>
> > 1 (45),<br>
> > > 3 (25))<br>
> > > > > marker: 1 strata with value/size (1 (21))<br>
> > > > > Face Sets: 1 strata with value/size<br>
> (1 (10))<br>
> > > > ><br>
> > > > > The get the same thing back with overlap = 0<br>
> > > > ><br>
> > > > > master *:~/Downloads/tmp/Nicolas$<br>
> > > > /PETSc3/petsc/apple/bin/mpiexec -n<br>
> > > > > 2 ./test_overlap -initial_dm_view<br>
> > -dm_plex_box_faces 5,5<br>
> > > > > -dm_distribute -dm_distribute_overlap 0<br>
> > > > > DM Object: Initial DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > Initial DM in 2 dimensions:<br>
> > > > > 0-cells: 21 21<br>
> > > > > 1-cells: 45 45<br>
> > > > > 2-cells: 25 25<br>
> > > > > Labels:<br>
> > > > > depth: 3 strata with value/size (0<br>
> (21), 1<br>
> > (45), 2<br>
> > > (25))<br>
> > > > > celltype: 3 strata with value/size (0<br>
> (21),<br>
> > 1 (45),<br>
> > > 3 (25))<br>
> > > > > marker: 1 strata with value/size (1 (21))<br>
> > > > > Face Sets: 1 strata with value/size<br>
> (1 (10))<br>
> > > > ><br>
> > > > > and get larger local meshes with overlap = 1<br>
> > > > ><br>
> > > > > master *:~/Downloads/tmp/Nicolas$<br>
> > > > /PETSc3/petsc/apple/bin/mpiexec -n<br>
> > > > > 2 ./test_overlap -initial_dm_view<br>
> > -dm_plex_box_faces 5,5<br>
> > > > > -dm_distribute -dm_distribute_overlap 1<br>
> > > > > DM Object: Initial DM 2 MPI processes<br>
> > > > > type: plex<br>
> > > > > Initial DM in 2 dimensions:<br>
> > > > > 0-cells: 29 29<br>
> > > > > 1-cells: 65 65<br>
> > > > > 2-cells: 37 37<br>
> > > > > Labels:<br>
> > > > > depth: 3 strata with value/size (0<br>
> (29), 1<br>
> > (65), 2<br>
> > > (37))<br>
> > > > > celltype: 3 strata with value/size (0<br>
> (29),<br>
> > 1 (65),<br>
> > > 3 (37))<br>
> > > > > marker: 1 strata with value/size (1 (27))<br>
> > > > > Face Sets: 1 strata with value/size<br>
> (1 (13))<br>
> > > > ><br>
> > > > > Thanks,<br>
> > > > ><br>
> > > > > Matt<br>
> > > > ><br>
> > > > > On Wed, Mar 31, 2021 at 12:22 PM Nicolas<br>
> Barral<br>
> > > > > <<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>><br>
> > > > > <br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>>>> wrote:<br>
> > > > ><br>
> > > > ><br>
> > > > ><br>
> > > > > @+<br>
> > > > ><br>
> > > > > --<br>
> > > > > Nicolas<br>
> > > > ><br>
> > > > > On 31/03/2021 17:51, Matthew Knepley<br>
> wrote:<br>
> > > > > > On Sat, Mar 27, 2021 at 9:27 AM<br>
> Nicolas<br>
> > Barral<br>
> > > > > ><br>
> <<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>><br>
> > > > > <br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>>><br>
> > > > > ><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>><br>
> > > > > <br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>><br>
> > > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>><br>
> > > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>><br>
> > <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a><br>
> <mailto:<a href="mailto:nicolas.barral@math.u-bordeaux.fr" target="_blank">nicolas.barral@math.u-bordeaux.fr</a>>>>>>>> wrote:<br>
> > > > > ><br>
> > > > > > Hi all,<br>
> > > > > ><br>
> > > > > > First, I'm not sure I understand<br>
> > what the<br>
> > > overlap<br>
> > > > > parameter in<br>
> > > > > > DMPlexDistributeOverlap does. I<br>
> > tried the<br>
> > > following:<br>
> > > > > generate a small<br>
> > > > > > mesh on 1 rank with<br>
> > DMPlexCreateBoxMesh, then<br>
> > > > distribute<br>
> > > > > it with<br>
> > > > > > DMPlexDistribute. At this point I<br>
> > have two nice<br>
> > > > > partitions, with shared<br>
> > > > > > vertices and no overlapping<br>
> cells.<br>
> > Then I call<br>
> > > > > DMPlexDistributeOverlap<br>
> > > > > > with the overlap parameter<br>
> set to 0<br>
> > or 1,<br>
> > > and get the<br>
> > > > > same resulting<br>
> > > > > > plex in both cases. Why is that ?<br>
> > > > > ><br>
> > > > > ><br>
> > > > > > The overlap parameter says how<br>
> many cell<br>
> > > adjacencies to go<br>
> > > > > out. You<br>
> > > > > > should not get the same<br>
> > > > > > mesh out. We have lots of<br>
> examples that use<br>
> > > this. If<br>
> > > > you send<br>
> > > > > your small<br>
> > > > > > example, I can probably<br>
> > > > > > tell you what is happening.<br>
> > > > > ><br>
> > > > ><br>
> > > > > Ok so I do have a small example on<br>
> that and the<br>
> > > DMClone<br>
> > > > thing I<br>
> > > > > set up<br>
> > > > > to understand! I attach it to the email.<br>
> > > > ><br>
> > > > > For the overlap, you can change the<br>
> overlap<br>
> > > constant at<br>
> > > > the top<br>
> > > > > of the<br>
> > > > > file. With OVERLAP=0 or 1, the<br>
> distributed<br>
> > > overlapping mesh<br>
> > > > > (shown using<br>
> > > > > -over_dm_view, it's DMover) are the<br>
> same, and<br>
> > > different<br>
> > > > from the<br>
> > > > > mesh<br>
> > > > > before distributing the overlap<br>
> (shown using<br>
> > > > -distrib_dm_view). For<br>
> > > > > larger overlap values they're different.<br>
> > > > ><br>
> > > > > The process is:<br>
> > > > > 1/ create a DM dm on 1 rank<br>
> > > > > 2/ clone dm into dm2<br>
> > > > > 3/ distribute dm<br>
> > > > > 4/ clone dm into dm3<br>
> > > > > 5/ distribute dm overlap<br>
> > > > ><br>
> > > > > I print all the DMs after each step.<br>
> dm has a<br>
> > > distributed<br>
> > > > > overlap, dm2<br>
> > > > > is not distributed, dm3 is<br>
> distributed but<br>
> > without<br>
> > > > overlap. Since<br>
> > > > > distribute and distributeOverlap<br>
> create new<br>
> > DMs, I<br>
> > > don't seem<br>
> > > > > have a<br>
> > > > > problem with the shallow copies.<br>
> > > > ><br>
> > > > ><br>
> > > > > > Second, I'm wondering what<br>
> would be<br>
> > a good<br>
> > > way to<br>
> > > > handle<br>
> > > > > two overlaps<br>
> > > > > > and associated local vectors.<br>
> In my<br>
> > adaptation<br>
> > > > code, the<br>
> > > > > remeshing<br>
> > > > > > library requires a<br>
> non-overlapping mesh,<br>
> > > while the<br>
> > > > > refinement criterion<br>
> > > > > > computation is based on hessian<br>
> > > computations, which<br>
> > > > > require a layer of<br>
> > > > > > overlap. What I can do is<br>
> clone the<br>
> > dm before<br>
> > > > > distributing the overlap,<br>
> > > > > > then manage two independent plex<br>
> > objects with<br>
> > > > their own<br>
> > > > > local sections<br>
> > > > > > etc. and copy/trim local vectors<br>
> > manually.<br>
> > > Is there a<br>
> > > > > more automatic<br>
> > > > > > way<br>
> > > > > > to do this ?<br>
> > > > > ><br>
> > > > > ><br>
> > > > > > DMClone() is a shallow copy, so that<br>
> > will not work.<br>
> > > > You would<br>
> > > > > maintain<br>
> > > > > > two different Plexes, overlapping<br>
> > > > > > and non-overlapping, with their<br>
> own sections<br>
> > > and vecs. Are<br>
> > > > > you sure you<br>
> > > > > > need to keep around the<br>
> non-overlapping one?<br>
> > > > > > Maybe if I understood what operations<br>
> > you want<br>
> > > to work, I<br>
> > > > > could say<br>
> > > > > > something more definitive.<br>
> > > > > ><br>
> > > > > I need to be able to pass the<br>
> > non-overlapping mesh<br>
> > > to the<br>
> > > > > remesher. I<br>
> > > > > can either maintain 2 plexes, or<br>
> trim the<br>
> > overlapping<br>
> > > > plex when<br>
> > > > > I create<br>
> > > > > the arrays I give to the remesher.<br>
> I'm not sure<br>
> > > which is the<br>
> > > > > best/worst ?<br>
> > > > ><br>
> > > > > Thanks<br>
> > > > ><br>
> > > > > --<br>
> > > > > Nicolas<br>
> > > > ><br>
> > > > ><br>
> > > > > > Thanks,<br>
> > > > > ><br>
> > > > > > Matt<br>
> > > > > ><br>
> > > > > > Thanks<br>
> > > > > ><br>
> > > > > > --<br>
> > > > > > Nicolas<br>
> > > > > ><br>
> > > > > ><br>
> > > > > ><br>
> > > > > > --<br>
> > > > > > What most experimenters take for<br>
> granted<br>
> > before<br>
> > > they<br>
> > > > begin their<br>
> > > > > > experiments is infinitely more<br>
> > interesting than any<br>
> > > > results<br>
> > > > > to which<br>
> > > > > > their experiments lead.<br>
> > > > > > -- Norbert Wiener<br>
> > > > > ><br>
> > > > > > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> > > > > <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> > > > ><br>
> > > > ><br>
> > > > ><br>
> > > > > --<br>
> > > > > What most experimenters take for granted<br>
> before<br>
> > they<br>
> > > begin their<br>
> > > > > experiments is infinitely more<br>
> interesting than any<br>
> > > results<br>
> > > > to which<br>
> > > > > their experiments lead.<br>
> > > > > -- Norbert Wiener<br>
> > > > ><br>
> > > > > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> > > > > <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> > > > ><br>
> > > > ><br>
> > > > ><br>
> > > > > --<br>
> > > > > What most experimenters take for granted before<br>
> > they begin<br>
> > > their<br>
> > > > > experiments is infinitely more interesting<br>
> than any<br>
> > > results to which<br>
> > > > > their experiments lead.<br>
> > > > > -- Norbert Wiener<br>
> > > > ><br>
> > > > > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> > > > <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> > > ><br>
> > > ><br>
> > > ><br>
> > > > --<br>
> > > > What most experimenters take for granted before<br>
> they begin<br>
> > their<br>
> > > > experiments is infinitely more interesting than any<br>
> > results to which<br>
> > > > their experiments lead.<br>
> > > > -- Norbert Wiener<br>
> > > ><br>
> > > > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> > > <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> > ><br>
> > ><br>
> > ><br>
> > > --<br>
> > > What most experimenters take for granted before they begin<br>
> their<br>
> > > experiments is infinitely more interesting than any<br>
> results to which<br>
> > > their experiments lead.<br>
> > > -- Norbert Wiener<br>
> > ><br>
> > > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> > <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> ><br>
> ><br>
> ><br>
> > --<br>
> > What most experimenters take for granted before they begin their<br>
> > experiments is infinitely more interesting than any results to which<br>
> > their experiments lead.<br>
> > -- Norbert Wiener<br>
> ><br>
> > <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
> <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
> <br>
> <br>
> <br>
> -- <br>
> What most experimenters take for granted before they begin their <br>
> experiments is infinitely more interesting than any results to which <br>
> their experiments lead.<br>
> -- Norbert Wiener<br>
> <br>
> <a href="https://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">https://www.cse.buffalo.edu/~knepley/</a> <<a href="http://www.cse.buffalo.edu/~knepley/" rel="noreferrer" target="_blank">http://www.cse.buffalo.edu/~knepley/</a>><br>
<br>
</blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div><div><br></div><div><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br></div></div></div></div></div></div></div></div>