[petsc-users] neumann failure in my version of snes ex12

[Geoffrey Irving]

On Sun, Nov 24, 2013 at 4:10 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Sun, Nov 24, 2013 at 6:06 PM, Geoffrey Irving <irving at naml.us> wrote:
>>
>> On Sun, Nov 24, 2013 at 5:41 AM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>> > On Sat, Nov 23, 2013 at 5:44 PM, Geoffrey Irving <irving at naml.us> wrote:
>> >>
>> >> On Sat, Nov 23, 2013 at 12:20 PM, Matthew Knepley <knepley at gmail.com>
>> >> wrote:
>> >> > On Sat, Nov 23, 2013 at 2:04 PM, Geoffrey Irving <irving at naml.us>
>> >> > wrote:
>> >> >>
>> >> >> On Sat, Nov 23, 2013 at 10:11 AM, Matthew Knepley
>> >> >> <knepley at gmail.com>
>> >> >> wrote:
>> >> >> > On Sat, Nov 23, 2013 at 12:07 PM, Geoffrey Irving <irving at naml.us>
>> >> >> > wrote:
>> >> >> >>
>> >> >> >> On Sat, Nov 23, 2013 at 4:43 AM, Matthew Knepley
>> >> >> >> <knepley at gmail.com>
>> >> >> >> wrote:
>> >> >> >> > On Fri, Nov 22, 2013 at 6:42 PM, Geoffrey Irving
>> >> >> >> > <irving at naml.us>
>> >> >> >> > wrote:
>> >> >> >> >>
>> >> >> >> >> On Fri, Nov 22, 2013 at 4:25 PM, Matthew Knepley
>> >> >> >> >> <knepley at gmail.com>
>> >> >> >> >> wrote:
>> >> >> >> >> > On Fri, Nov 22, 2013 at 6:09 PM, Geoffrey Irving
>> >> >> >> >> > <irving at naml.us>
>> >> >> >> >> > wrote:
>> >> >> >> >> >>
>> >> >> >> >> >> On Fri, Nov 22, 2013 at 3:41 PM, Matthew Knepley
>> >> >> >> >> >> <knepley at gmail.com>
>> >> >> >> >> >> wrote:
>> >> >> >> >> >> > On Fri, Nov 22, 2013 at 5:36 PM, Geoffrey Irving
>> >> >> >> >> >> > <irving at naml.us>
>> >> >> >> >> >> > wrote:
>> >> >> >> >> >> >>
>> >> >> >> >> >> >> I have a duplicate of snes ex12 (FEM Poisson) which
>> >> >> >> >> >> >> works
>> >> >> >> >> >> >> with
>> >> >> >> >> >> >> Dirichlet boundary conditions, but it's breaking for me
>> >> >> >> >> >> >> with
>> >> >> >> >> >> >> Neumann
>> >> >> >> >> >> >> conditions.  In particular, with Neumann conditions I
>> >> >> >> >> >> >> get
>> >> >> >> >> >> >> results
>> >> >> >> >> >> >> which explode even though I believe I am setting a
>> >> >> >> >> >> >> constant
>> >> >> >> >> >> >> nullspace.
>> >> >> >> >> >> >>
>> >> >> >> >> >> >> For example, if I use two first order elements (the unit
>> >> >> >> >> >> >> square
>> >> >> >> >> >> >> divided into two triangles), the resulting solution has
>> >> >> >> >> >> >>
>> >> >> >> >> >> >>     L2 error = 1.75514e+08
>> >> >> >> >> >> >>     u = [-175513825.75680602, -175513825.66302037,
>> >> >> >> >> >> >> -175513825.48390722, -175513824.84436429]
>> >> >> >> >> >> >>
>> >> >> >> >> >> >> This looks rather a lot like the null space isn't
>> >> >> >> >> >> >> getting
>> >> >> >> >> >> >> through.
>> >> >> >> >> >> >> I
>> >> >> >> >> >> >> am creating the constant nullspace with
>> >> >> >> >> >> >>
>> >> >> >> >> >> >>       MatNullSpace null;
>> >> >> >> >> >> >>
>> >> >> >> >> >> >> CHECK(MatNullSpaceCreate(comm(),PETSC_TRUE,0,0,&null));
>> >> >> >> >> >> >>       CHECK(MatSetNullSpace(m,null));
>> >> >> >> >> >> >>       CHECK(MatNullSpaceDestroy(&null));
>> >> >> >> >> >> >>
>> >> >> >> >> >> >> If I pass "-ksp_view -mat_view", I get the following.
>> >> >> >> >> >> >> The
>> >> >> >> >> >> >> matrix
>> >> >> >> >> >> >> entries seem right (they do indeed have the constant
>> >> >> >> >> >> >> nullspace),
>> >> >> >> >> >> >> and
>> >> >> >> >> >> >> ksp_view shows that a nullspace is attached.  Is
>> >> >> >> >> >> >> attaching
>> >> >> >> >> >> >> the
>> >> >> >> >> >> >> nullspace to the matrix with MatSetNullSpace enough, or
>> >> >> >> >> >> >> do
>> >> >> >> >> >> >> I
>> >> >> >> >> >> >> need
>> >> >> >> >> >> >> to
>> >> >> >> >> >> >> additionally attach it to the KSP object?
>> >> >> >> >> >> >
>> >> >> >> >> >> >
>> >> >> >> >> >> > 1) I always run with -ksp_monitor_true_residual now when
>> >> >> >> >> >> > debugging.
>> >> >> >> >> >> > This
>> >> >> >> >> >> > can
>> >> >> >> >> >> > give
>> >> >> >> >> >> >     you an idea whether you have a singular PC, which I
>> >> >> >> >> >> > suspect
>> >> >> >> >> >> > here.
>> >> >> >> >> >> >
>> >> >> >> >> >> > 2) Can you try using -pc_type jacobi? I think ILU might
>> >> >> >> >> >> > go
>> >> >> >> >> >> > crazy
>> >> >> >> >> >> > on a
>> >> >> >> >> >> > deficient matrix.
>> >> >> >> >> >>
>> >> >> >> >> >> Here are results with -ksp_monitor_true_residual -pc_type
>> >> >> >> >> >> none:
>> >> >> >> >> >>
>> >> >> >> >> >>     http://naml.us/random/laplace-rtol.txt # with -ksp_rtol
>> >> >> >> >> >> 1e-5
>> >> >> >> >> >>     http://naml.us/random/laplace-atol.txt # with -ksp_atol
>> >> >> >> >> >> 1e-5
>> >> >> >> >> >
>> >> >> >> >> >
>> >> >> >> >> > Okay, if you have an inconsistent RHS I do not think that
>> >> >> >> >> > true_residual
>> >> >> >> >> > will work
>> >> >> >> >> > since it uses the unprojected b, but the solve should be
>> >> >> >> >> > fine.
>> >> >> >> >>
>> >> >> >> >> I still don't understand why the atol version is able to drift
>> >> >> >> >> so
>> >> >> >> >> far
>> >> >> >> >> away from zero mean, even after tens of thousands of
>> >> >> >> >> iterations.
>> >> >> >> >> If
>> >> >> >> >> KSP sees a null space on the matrix, shouldn't it project that
>> >> >> >> >> null
>> >> >> >> >> space out of the *linear system* residual and also out of
>> >> >> >> >> solution
>> >> >> >> >> on
>> >> >> >> >> each iteration?  Even if it is only projecting out of the
>> >> >> >> >> solution
>> >> >> >> >> delta, how can null space errors be accumulating?
>> >> >> >> >
>> >> >> >> >
>> >> >> >> > Both the KSP and Mat show that the null space is set, so
>> >> >> >> > everything
>> >> >> >> > should
>> >> >> >> > work fine,
>> >> >> >> > and at this point its no longer DMPlex that is in control, its
>> >> >> >> > standard
>> >> >> >> > PETSc.
>> >> >> >> >
>> >> >> >> > We have reached the limit of usefu talking. Something is
>> >> >> >> > obviously
>> >> >> >> > wrong
>> >> >> >> > with the code,
>> >> >> >> > but since this routinely works in PETSc examples. In situations
>> >> >> >> > like
>> >> >> >> > these I think we need
>> >> >> >> > to follow the execution in the debugger to see what is
>> >> >> >> > wrong..You
>> >> >> >> > can
>> >> >> >> > look at Vec values
>> >> >> >> > in the debugger using
>> >> >> >> >
>> >> >> >> >   (gdb) p ((Vec_Seq*) b-.data)->array[0]@v->map.n
>> >> >> >> >
>> >> >> >> > and I look at DMPlex things with
>> >> >> >> >
>> >> >> >> >   (gdb) p ((DM_Plex*) dm->data)->coneSection
>> >> >> >> >
>> >> >> >> > etc.
>> >> >> >>
>> >> >> >> Thanks, I appreciate the help.  It looks like there were at least
>> >> >> >> two
>> >> >> >> different problems:
>> >> >> >>
>> >> >> >> 1. The boundary FE I was creating had the same dimension as the
>> >> >> >> interior FE (instead of codimension 1), due to misreading ex12
>> >> >> >> even
>> >> >> >> though I had correctly refactored it.  I added a dimension
>> >> >> >> consistency
>> >> >> >> check to my code, but I can do this in DMPlexComputeResidualFEM
>> >> >> >> as
>> >> >> >> well to catch future user errors.
>> >> >> >>
>> >> >> >> 2. Even after fixing the dimensions, my boundary functions in
>> >> >> >> PetscFEM
>> >> >> >> are getting x values both inside and completely outside the
>> >> >> >> domain.
>> >> >> >> Almost certainly more user error, but hopefully also something I
>> >> >> >> can
>> >> >> >> add a check for in petsc once I localize it.
>> >> >> >
>> >> >> > This could be my bug. The test I have for ex12 is the variable
>> >> >> > coefficient problem
>> >> >> > with div (x + y) grad u = f. This seems to check between the
>> >> >> > analytic
>> >> >> > and field
>> >> >> > versions, meaning that the x coming into f1() matches the x I used
>> >> >> > to
>> >> >> > make the
>> >> >> > field, and my exact solution.
>> >> >>
>> >> >> It does seem to happen with stock snes ex12:
>> >> >>
>> >> >>     branch: irving/assert-ex12-in-box1
>> >> >>
>> >> >>     % mpiexec -host localhost -n 1
>> >> >> /home/irving/petsc/debug/lib/ex12-obj/ex12 -run_type test
>> >> >> -refinement_limit 0.0    -bc_type neumann   -interpolate 1
>> >> >> -petscspace_order 1 -bd_petscspace_order 1 -show_initial
>> >> >> -dm_plex_print_fem 1 -dm_view ::ascii_info_detail
>> >> >>     ...
>> >> >>     [0]PETSC ERROR: evaluation at point outside unit box: 0 1.25
>> >> >>
>> >> >> I'll trace down why this is happening.
>> >> >
>> >> > My first guess is a triangle with backwards edge. This could cause
>> >> > the
>> >> > geometry routines to barf.
>> >>
>> >> I don't think it's edge orientation: it breaks (though at different
>> >> points) regardless of whether I orient all the edges clockwise or
>> >> counterclockwise.  Also, I would expect bad edge orientation to result
>> >> in bad normals but not to produce bad quadrature locations (nor bad
>> >> residuals as long as the user routines don't depend on normal).
>> >>
>> >> Specifically, I think the problem is a sign error in
>> >> DMPlexComputeProjection2Dto1D_Internal.  The following patch seems to
>> >> fix the out of bounds evaluation problem.
>> >> DMPlexComputeProjection2Dto1D is computing a matrix which maps from
>> >> the given segment to the canonical segment, and
>> >> DMPlexComputeLineGeometry_Internal expects a map from the canonical
>> >> segment to the given segment.
>> >>
>> >> snes ex12 passes with and without this change, presumably because the
>> >> only Neumann test has constants along each box side, and is therefore
>> >> invariant to this error.
>> >
>> >
>> > When I replaced my kludge with code using the normal explicitly, I get
>> > the
>> > same
>> > error as you do. You fix is correct, and I checked it into
>> > knepley/fix-fem-bd-integrate
>> >
>> >   https://bitbucket.org/petsc/petsc/branch/knepley/fix-fem-bd-integrate
>> >
>> > along with other fixes that I think get Neumann all the way correct in
>> > ex12.
>> >
>> >>
>> >> Unfortunately, my Laplace test is also invariant to this error, so
>> >> this bug is unrelated to the earlier problem.
>> >
>> > It could be one of the other fixes I made. Could you run again?
>>
>> Much better.  All the points and (inward) normals are right, and now
>> my residuals have zero sum as expected.  There's still something
>> wrong, since I don't get the exact solution with second order
>> elements, but that's probably an independent problem.  I will trace it
>> down.  Thanks for the help and fixes!
>>
>> Why did you choose inward pointing normals, by the way?  I would have
>> though outward pointing normals are the nearly universal convention.
>
> That is a bug fixed in that branch. Did you try next?

Oops, I had misread that commit message as "Use inward pointing
normal" rather than "Used inward pointing normal".  I get outward
normals if I reorient the outer boundary edges in my DMPlex to be
clockwise, which I guess is what you intended.

Closer and closer!

Geoffrey