[petsc-users] DMPlex overlap
Matthew Knepley
knepley at gmail.com
Wed Mar 31 14:44:10 CDT 2021
On Wed, Mar 31, 2021 at 3:36 PM Nicolas Barral <
nicolas.barral at math.u-bordeaux.fr> wrote:
> On 31/03/2021 21:24, Matthew Knepley wrote:
> > Ok so that's worth clarifying, but my problem is that dm has a
> > 0-overlap
> > before DMPlexDistributeOverlap and odm has a 1-overlap even though I
> > passed "0". If I understand what you just wrote, adding "0" more
> levels
> > of overlap to 0-overlap, that should still be 0 overlap ?
> >
> > Yet when I look at the code of DMPlexDistributeOverlap, you're
> flagging
> > points to be added to the overlap whatever "k" is.
> >
> >
> > Crap. There is a bug handling 0. Evidently, no one ever asks for overlap
> 0.
> > Will fix.
> >
> ok now I'm sure I understand what you explained :) Thanks Matt.
>
> Now we can look at the other question: I need to be able to pass the
> non-overlapping mesh to the remesher. I can either maintain 2 plexes, or
> trim the overlapping plex when I create the arrays I pass to the
> remesher. I'm not sure which is the best/worst ?
>
I would start with two plexes since it is very easy.
Trimming the plex would essentially make another plex anyway, but it is not
hard using DMPlexFilter().
Thanks,
Matt
> Thanks
>
> --
> Nicolas
>
>
> > Thanks,
> >
> > Matt
> >
> > Sample code:
> > static char help[] = "Tests plex distribution and overlaps.\n";
> >
> > #include <petsc/private/dmpleximpl.h>
> >
> > int main (int argc, char * argv[]) {
> >
> > DM dm, odm;
> > MPI_Comm comm;
> > PetscErrorCode ierr;
> >
> > ierr = PetscInitialize(&argc, &argv, NULL, help);if (ierr)
> > return ierr;
> > comm = PETSC_COMM_WORLD;
> >
> > ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE, NULL, NULL, NULL,
> > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);
> > ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
> >
> >
> >
> > ierr = PetscObjectSetName((PetscObject) dm, "DM
> > before");CHKERRQ(ierr);
> > ierr = DMViewFromOptions(dm, NULL,
> "-before_dm_view");CHKERRQ(ierr);
> > DMPlexDistributeOverlap(dm, 0, NULL, &odm);
> > ierr = PetscObjectSetName((PetscObject) odm, "DM
> > after");CHKERRQ(ierr);
> > ierr = DMViewFromOptions(odm, NULL,
> "-after_dm_view");CHKERRQ(ierr);
> >
> >
> > ierr = DMDestroy(&dm);CHKERRQ(ierr);
> > ierr = DMDestroy(&odm);CHKERRQ(ierr);
> > ierr = PetscFinalize();
> > return ierr;
> > }
> >
> > % mpiexec -n 2 ./test_overlapV3 -dm_plex_box_faces 5,5 -dm_distribute
> > -before_dm_view -after_dm_view
> > DM Object: DM before 2 MPI processes
> > type: plex
> > DM before in 2 dimensions:
> > 0-cells: 21 21
> > 1-cells: 45 45
> > 2-cells: 25 25
> > Labels:
> > depth: 3 strata with value/size (0 (21), 1 (45), 2 (25))
> > celltype: 3 strata with value/size (0 (21), 1 (45), 3 (25))
> > marker: 1 strata with value/size (1 (21))
> > Face Sets: 1 strata with value/size (1 (10))
> > DM Object: DM after 2 MPI processes
> > type: plex
> > DM after in 2 dimensions:
> > 0-cells: 29 29
> > 1-cells: 65 65
> > 2-cells: 37 37
> > Labels:
> > depth: 3 strata with value/size (0 (29), 1 (65), 2 (37))
> > celltype: 3 strata with value/size (0 (29), 1 (65), 3 (37))
> > marker: 1 strata with value/size (1 (27))
> > Face Sets: 1 strata with value/size (1 (13))
> >
> >
> >
> > >
> > > Thanks,
> > >
> > > Matt
> > >
> > > Thanks,
> > >
> > > --
> > > Nicolas
> > >
> > > >
> > > > Thanks,
> > > >
> > > > Matt
> > > >
> > > > if (!dm) {printf("Big problem\n"); dm = odm;}
> > > > else {DMDestroy(&odm);}
> > > > ierr = PetscObjectSetName((PetscObject) dm,
> "Initial
> > > > DM");CHKERRQ(ierr);
> > > > ierr = DMViewFromOptions(dm, NULL,
> > > > "-initial_dm_view");CHKERRQ(ierr);
> > > >
> > > >
> > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);
> > > > ierr = PetscFinalize();
> > > > return ierr;
> > > > }
> > > >
> > > > called with mpiexec -n 2 ./test_overlapV3
> -initial_dm_view
> > > > -dm_plex_box_faces 5,5 -dm_distribute
> > > >
> > > > gives:
> > > > DM Object: Initial DM 2 MPI processes
> > > > type: plex
> > > > Initial DM in 2 dimensions:
> > > > 0-cells: 29 29
> > > > 1-cells: 65 65
> > > > 2-cells: 37 37
> > > > Labels:
> > > > depth: 3 strata with value/size (0 (29), 1 (65), 2
> > (37))
> > > > celltype: 3 strata with value/size (0 (29), 1
> > (65), 3 (37))
> > > > marker: 1 strata with value/size (1 (27))
> > > > Face Sets: 1 strata with value/size (1 (13))
> > > >
> > > > which is not what I expect ?
> > > >
> > > > Thanks,
> > > >
> > > > --
> > > > Nicolas
> > > >
> > > > On 31/03/2021 19:02, Matthew Knepley wrote:
> > > > > Alright, I think the problem had to do with keeping
> > track
> > > of what
> > > > DM you
> > > > > were looking at. This code increases the overlap of
> an
> > > initial DM:
> > > > >
> > > > > static char help[] = "Tests plex distribution and
> > > overlaps.\n";
> > > > >
> > > > > #include <petsc/private/dmpleximpl.h>
> > > > >
> > > > > int main (int argc, char * argv[]) {
> > > > >
> > > > > DM dm, dm2;
> > > > > PetscInt overlap;
> > > > > MPI_Comm comm;
> > > > > PetscErrorCode ierr;
> > > > >
> > > > > ierr = PetscInitialize(&argc, &argv, NULL,
> > help);if (ierr)
> > > > return ierr;
> > > > > comm = PETSC_COMM_WORLD;
> > > > >
> > > > > ierr = DMPlexCreateBoxMesh(comm, 2, PETSC_TRUE,
> > NULL,
> > > NULL, NULL,
> > > > > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);
> > > > > ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
> > > > > ierr = PetscObjectSetName((PetscObject) dm,
> "Initial
> > > > DM");CHKERRQ(ierr);
> > > > > ierr = DMViewFromOptions(dm, NULL,
> > > > "-initial_dm_view");CHKERRQ(ierr);
> > > > >
> > > > > ierr = DMPlexGetOverlap(dm,
> &overlap);CHKERRQ(ierr);
> > > > > ierr = DMPlexDistributeOverlap(dm, overlap+1,
> NULL,
> > > > &dm2);CHKERRQ(ierr);
> > > > > ierr = PetscObjectSetName((PetscObject) dm2,
> > "More Overlap
> > > > > DM");CHKERRQ(ierr);
> > > > > ierr = DMViewFromOptions(dm2, NULL,
> > > > "-over_dm_view");CHKERRQ(ierr);
> > > > >
> > > > > ierr = DMDestroy(&dm2);CHKERRQ(ierr);
> > > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);
> > > > > ierr = PetscFinalize();
> > > > > return ierr;
> > > > > }
> > > > >
> > > > > and when we run it we get the expected result
> > > > >
> > > > > master *:~/Downloads/tmp/Nicolas$
> > > /PETSc3/petsc/apple/bin/mpiexec
> > > > -n 2
> > > > > ./test_overlap -initial_dm_view -dm_plex_box_faces
> 5,5
> > > > -dm_distribute
> > > > > -dm_distribute_overlap 1 -over_dm_view
> > > > > DM Object: Initial DM 2 MPI processes
> > > > > type: plex
> > > > > Initial DM in 2 dimensions:
> > > > > 0-cells: 29 29
> > > > > 1-cells: 65 65
> > > > > 2-cells: 37 37
> > > > > Labels:
> > > > > depth: 3 strata with value/size (0 (29), 1 (65),
> > 2 (37))
> > > > > celltype: 3 strata with value/size (0 (29), 1
> > (65), 3 (37))
> > > > > marker: 1 strata with value/size (1 (27))
> > > > > Face Sets: 1 strata with value/size (1 (13))
> > > > > DM Object: More Overlap DM 2 MPI processes
> > > > > type: plex
> > > > > More Overlap DM in 2 dimensions:
> > > > > 0-cells: 36 36
> > > > > 1-cells: 85 85
> > > > > 2-cells: 50 50
> > > > > Labels:
> > > > > depth: 3 strata with value/size (0 (36), 1 (85),
> > 2 (50))
> > > > > celltype: 3 strata with value/size (0 (36), 1
> > (85), 3 (50))
> > > > > marker: 1 strata with value/size (1 (40))
> > > > > Face Sets: 1 strata with value/size (1 (20))
> > > > >
> > > > > Thanks,
> > > > >
> > > > > Matt
> > > > >
> > > > > On Wed, Mar 31, 2021 at 12:57 PM Matthew Knepley
> > > > <knepley at gmail.com <mailto:knepley at gmail.com>
> > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>>
> > > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>
> > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>>>
> > > > > <mailto:knepley at gmail.com
> > <mailto:knepley at gmail.com> <mailto:knepley at gmail.com
> > <mailto:knepley at gmail.com>>
> > > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>
> > <mailto:knepley at gmail.com <mailto:knepley at gmail.com>>>>> wrote:
> > > > >
> > > > > Okay, let me show a really simple example that
> > gives
> > > the expected
> > > > > result before I figure out what is going wrong
> for
> > > you. This code
> > > > >
> > > > > static char help[] = "Tests plex distribution
> and
> > > overlaps.\n";
> > > > >
> > > > > #include <petsc/private/dmpleximpl.h>
> > > > >
> > > > > int main (int argc, char * argv[]) {
> > > > > DM dm;
> > > > > MPI_Comm comm;
> > > > > PetscErrorCode ierr;
> > > > >
> > > > > ierr = PetscInitialize(&argc, &argv, NULL,
> > help);if
> > > (ierr)
> > > > return
> > > > > ierr;
> > > > > comm = PETSC_COMM_WORLD;
> > > > >
> > > > > ierr = DMPlexCreateBoxMesh(comm, 2,
> > PETSC_TRUE, NULL,
> > > > NULL, NULL,
> > > > > NULL, PETSC_TRUE, &dm);CHKERRQ(ierr);
> > > > > ierr = DMSetFromOptions(dm);CHKERRQ(ierr);
> > > > > ierr = PetscObjectSetName((PetscObject) dm,
> > "Initial
> > > > > DM");CHKERRQ(ierr);
> > > > > ierr = DMViewFromOptions(dm, NULL,
> > > > "-initial_dm_view");CHKERRQ(ierr);
> > > > > ierr = DMDestroy(&dm);CHKERRQ(ierr);
> > > > > ierr = PetscFinalize();
> > > > > return ierr;
> > > > > }
> > > > >
> > > > > can do all the overlap tests. For example, you
> > can run
> > > it naively
> > > > > and get a serial mesh
> > > > >
> > > > > master *:~/Downloads/tmp/Nicolas$
> > > > /PETSc3/petsc/apple/bin/mpiexec -n
> > > > > 2 ./test_overlap -initial_dm_view
> > -dm_plex_box_faces 5,5
> > > > > DM Object: Initial DM 2 MPI processes
> > > > > type: plex
> > > > > Initial DM in 2 dimensions:
> > > > > 0-cells: 36 0
> > > > > 1-cells: 85 0
> > > > > 2-cells: 50 0
> > > > > Labels:
> > > > > celltype: 3 strata with value/size (0 (36),
> > 3 (50),
> > > 1 (85))
> > > > > depth: 3 strata with value/size (0 (36), 1
> > (85), 2
> > > (50))
> > > > > marker: 1 strata with value/size (1 (40))
> > > > > Face Sets: 1 strata with value/size (1 (20))
> > > > >
> > > > > Then run it telling Plex to distribute after
> > creating
> > > the mesh
> > > > >
> > > > > master *:~/Downloads/tmp/Nicolas$
> > > > /PETSc3/petsc/apple/bin/mpiexec -n
> > > > > 2 ./test_overlap -initial_dm_view
> > -dm_plex_box_faces 5,5
> > > > -dm_distribute
> > > > > DM Object: Initial DM 2 MPI processes
> > > > > type: plex
> > > > > Initial DM in 2 dimensions:
> > > > > 0-cells: 21 21
> > > > > 1-cells: 45 45
> > > > > 2-cells: 25 25
> > > > > Labels:
> > > > > depth: 3 strata with value/size (0 (21), 1
> > (45), 2
> > > (25))
> > > > > celltype: 3 strata with value/size (0 (21),
> > 1 (45),
> > > 3 (25))
> > > > > marker: 1 strata with value/size (1 (21))
> > > > > Face Sets: 1 strata with value/size (1 (10))
> > > > >
> > > > > The get the same thing back with overlap = 0
> > > > >
> > > > > master *:~/Downloads/tmp/Nicolas$
> > > > /PETSc3/petsc/apple/bin/mpiexec -n
> > > > > 2 ./test_overlap -initial_dm_view
> > -dm_plex_box_faces 5,5
> > > > > -dm_distribute -dm_distribute_overlap 0
> > > > > DM Object: Initial DM 2 MPI processes
> > > > > type: plex
> > > > > Initial DM in 2 dimensions:
> > > > > 0-cells: 21 21
> > > > > 1-cells: 45 45
> > > > > 2-cells: 25 25
> > > > > Labels:
> > > > > depth: 3 strata with value/size (0 (21), 1
> > (45), 2
> > > (25))
> > > > > celltype: 3 strata with value/size (0 (21),
> > 1 (45),
> > > 3 (25))
> > > > > marker: 1 strata with value/size (1 (21))
> > > > > Face Sets: 1 strata with value/size (1 (10))
> > > > >
> > > > > and get larger local meshes with overlap = 1
> > > > >
> > > > > master *:~/Downloads/tmp/Nicolas$
> > > > /PETSc3/petsc/apple/bin/mpiexec -n
> > > > > 2 ./test_overlap -initial_dm_view
> > -dm_plex_box_faces 5,5
> > > > > -dm_distribute -dm_distribute_overlap 1
> > > > > DM Object: Initial DM 2 MPI processes
> > > > > type: plex
> > > > > Initial DM in 2 dimensions:
> > > > > 0-cells: 29 29
> > > > > 1-cells: 65 65
> > > > > 2-cells: 37 37
> > > > > Labels:
> > > > > depth: 3 strata with value/size (0 (29), 1
> > (65), 2
> > > (37))
> > > > > celltype: 3 strata with value/size (0 (29),
> > 1 (65),
> > > 3 (37))
> > > > > marker: 1 strata with value/size (1 (27))
> > > > > Face Sets: 1 strata with value/size (1 (13))
> > > > >
> > > > > Thanks,
> > > > >
> > > > > Matt
> > > > >
> > > > > On Wed, Mar 31, 2021 at 12:22 PM Nicolas Barral
> > > > > <nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>
> > > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>>> wrote:
> > > > >
> > > > >
> > > > >
> > > > > @+
> > > > >
> > > > > --
> > > > > Nicolas
> > > > >
> > > > > On 31/03/2021 17:51, Matthew Knepley wrote:
> > > > > > On Sat, Mar 27, 2021 at 9:27 AM Nicolas
> > Barral
> > > > > > <nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>
> > > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>>
> > > > > >
> > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>
> > > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>
> > > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>
> > > <mailto:nicolas.barral at math.u-bordeaux.fr
> > <mailto:nicolas.barral at math.u-bordeaux.fr>>>>>> wrote:
> > > > > >
> > > > > > Hi all,
> > > > > >
> > > > > > First, I'm not sure I understand
> > what the
> > > overlap
> > > > > parameter in
> > > > > > DMPlexDistributeOverlap does. I
> > tried the
> > > following:
> > > > > generate a small
> > > > > > mesh on 1 rank with
> > DMPlexCreateBoxMesh, then
> > > > distribute
> > > > > it with
> > > > > > DMPlexDistribute. At this point I
> > have two nice
> > > > > partitions, with shared
> > > > > > vertices and no overlapping cells.
> > Then I call
> > > > > DMPlexDistributeOverlap
> > > > > > with the overlap parameter set to 0
> > or 1,
> > > and get the
> > > > > same resulting
> > > > > > plex in both cases. Why is that ?
> > > > > >
> > > > > >
> > > > > > The overlap parameter says how many cell
> > > adjacencies to go
> > > > > out. You
> > > > > > should not get the same
> > > > > > mesh out. We have lots of examples that
> use
> > > this. If
> > > > you send
> > > > > your small
> > > > > > example, I can probably
> > > > > > tell you what is happening.
> > > > > >
> > > > >
> > > > > Ok so I do have a small example on that and
> the
> > > DMClone
> > > > thing I
> > > > > set up
> > > > > to understand! I attach it to the email.
> > > > >
> > > > > For the overlap, you can change the overlap
> > > constant at
> > > > the top
> > > > > of the
> > > > > file. With OVERLAP=0 or 1, the distributed
> > > overlapping mesh
> > > > > (shown using
> > > > > -over_dm_view, it's DMover) are the same,
> and
> > > different
> > > > from the
> > > > > mesh
> > > > > before distributing the overlap (shown using
> > > > -distrib_dm_view). For
> > > > > larger overlap values they're different.
> > > > >
> > > > > The process is:
> > > > > 1/ create a DM dm on 1 rank
> > > > > 2/ clone dm into dm2
> > > > > 3/ distribute dm
> > > > > 4/ clone dm into dm3
> > > > > 5/ distribute dm overlap
> > > > >
> > > > > I print all the DMs after each step. dm has
> a
> > > distributed
> > > > > overlap, dm2
> > > > > is not distributed, dm3 is distributed but
> > without
> > > > overlap. Since
> > > > > distribute and distributeOverlap create new
> > DMs, I
> > > don't seem
> > > > > have a
> > > > > problem with the shallow copies.
> > > > >
> > > > >
> > > > > > Second, I'm wondering what would be
> > a good
> > > way to
> > > > handle
> > > > > two overlaps
> > > > > > and associated local vectors. In my
> > adaptation
> > > > code, the
> > > > > remeshing
> > > > > > library requires a non-overlapping
> mesh,
> > > while the
> > > > > refinement criterion
> > > > > > computation is based on hessian
> > > computations, which
> > > > > require a layer of
> > > > > > overlap. What I can do is clone the
> > dm before
> > > > > distributing the overlap,
> > > > > > then manage two independent plex
> > objects with
> > > > their own
> > > > > local sections
> > > > > > etc. and copy/trim local vectors
> > manually.
> > > Is there a
> > > > > more automatic
> > > > > > way
> > > > > > to do this ?
> > > > > >
> > > > > >
> > > > > > DMClone() is a shallow copy, so that
> > will not work.
> > > > You would
> > > > > maintain
> > > > > > two different Plexes, overlapping
> > > > > > and non-overlapping, with their own
> sections
> > > and vecs. Are
> > > > > you sure you
> > > > > > need to keep around the non-overlapping
> one?
> > > > > > Maybe if I understood what operations
> > you want
> > > to work, I
> > > > > could say
> > > > > > something more definitive.
> > > > > >
> > > > > I need to be able to pass the
> > non-overlapping mesh
> > > to the
> > > > > remesher. I
> > > > > can either maintain 2 plexes, or trim the
> > overlapping
> > > > plex when
> > > > > I create
> > > > > the arrays I give to the remesher. I'm not
> sure
> > > which is the
> > > > > best/worst ?
> > > > >
> > > > > Thanks
> > > > >
> > > > > --
> > > > > Nicolas
> > > > >
> > > > >
> > > > > > Thanks,
> > > > > >
> > > > > > Matt
> > > > > >
> > > > > > Thanks
> > > > > >
> > > > > > --
> > > > > > Nicolas
> > > > > >
> > > > > >
> > > > > >
> > > > > > --
> > > > > > 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/
> > > > > <http://www.cse.buffalo.edu/~knepley/>
> > > > >
> > > > >
> > > > >
> > > > > --
> > > > > 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/
> > > > > <http://www.cse.buffalo.edu/~knepley/>
> > > > >
> > > > >
> > > > >
> > > > > --
> > > > > 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/
> > > > <http://www.cse.buffalo.edu/~knepley/>
> > > >
> > > >
> > > >
> > > > --
> > > > 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/
> > > <http://www.cse.buffalo.edu/~knepley/>
> > >
> > >
> > >
> > > --
> > > 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/
> > <http://www.cse.buffalo.edu/~knepley/>
> >
> >
> >
> > --
> > 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/ <
> http://www.cse.buffalo.edu/~knepley/>
>
--
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/ <http://www.cse.buffalo.edu/~knepley/>
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