[firedrake] Possible bug with perturbed extruded mesh?

Wed Apr 15 11:56:30 BST 2015

Also works with 'bendy' (non-affine support):

atm112 at ubuntu:~$ python tuomas.py
pyop2:INFO Solving linear variational problem...
pyop2:INFO Solving linear variational problem...done
a == L: 0.999999885647 1.00000011385
pyop2:INFO Solving linear variational problem...
pyop2:INFO Solving linear variational problem...done
a == L2: 0.999999999999 1.0

Do you want more details?  It's a small-to-moderate PITA to enable this
functionality, depending on exactly which repositories you've checked out
and which ones you've only pip-installed.

On 15 April 2015 at 02:11, Tuomas Karna <tuomas.karna at gmail.com> wrote:

>  OK, had to pip install petsc and petsc4py to fix that.
>
> Yes, the test works on deformed tetrahedral mesh:
> a == L: 0.99999977445 1.00000019589
> a == L2: 0.999999999998 1.0
>
> - Tuomas
>
> On 04/14/2015 05:04 PM, Tuomas Karna wrote:
>
> Hmm, just updated all the components, still seeing the same. I'm using the
> mapdes firedrake branches for petsc and petsc4py. Could be linking to old
> petsc4py or some other lib...
>
> - Tuomas
>
> On 04/14/2015 02:15 PM, Andrew McRae wrote:
>
>    WTF?
>
>  Is your PETSc (and everything else) up to date?
>
>  I just opened an ipython session and typed
>  from firedrake import *
>  mesh = UnitCubeMesh(10, 10, 6)
>
>  and all was fine.
>
> On 14 April 2015 at 21:51, Tuomas Karna <tuomas.karna at gmail.com> wrote:
>
>> Hi Andrew,
>>
>> I see, that could indeed be the reason.
>>
>> Tried UnitCubeMesh, results in an error:
>>
>> File "test_integration.py", line 77, in <module>
>>     mesh = UnitCubeMesh(10, 10, 6)
>>   File
>> "/home/tuomas/.local/lib/python2.7/site-packages/firedrake/utility_meshes.py",
>> line 508, in UnitCubeMesh
>>     return CubeMesh(nx, ny, nz, 1, reorder=reorder)
>>   File
>> "/home/tuomas/.local/lib/python2.7/site-packages/firedrake/utility_meshes.py",
>> line 488, in CubeMesh
>>     return BoxMesh(nx, ny, nz, L, L, L, reorder=reorder)
>>   File
>> "/home/tuomas/.local/lib/python2.7/site-packages/firedrake/utility_meshes.py",
>> line 440, in BoxMesh
>>     plex = PETSc.DMPlex().generate(boundary)
>>   File "PETSc/DMPlex.pyx", line 438, in petsc4py.PETSc.DMPlex.generate
>> (src/petsc4py.PETSc.c:215426)
>> petsc4py.PETSc.Error: error code 77
>> [0] DMPlexGenerate() line 1080 in
>> /home/tuomas/sources/petsc/firedrake/src/dm/impls/plex/plexgenerate.c
>> [0] DMPlexGenerate_CTetgen() line 834 in
>> /home/tuomas/sources/petsc/firedrake/src/dm/impls/plex/plexgenerate.c
>> [0] TetGenTetrahedralize() line 21483 in
>> /home/tuomas/sources/petsc/firedrake/arch-linux2-c-debug/externalpackages/ctetgen/ctetgen.c
>> [0] TetGenMeshDelaunizeVertices() line 12113 in
>> /home/tuomas/sources/petsc/firedrake/arch-linux2-c-debug/externalpackages/ctetgen/ctetgen.c
>> [0] TetGenMeshDelaunayIncrFlip() line 12046 in
>> /home/tuomas/sources/petsc/firedrake/arch-linux2-c-debug/externalpackages/ctetgen/ctetgen.c
>> [0] TetGenMeshInsertVertexBW() line 11321 in
>> /home/tuomas/sources/petsc/firedrake/arch-linux2-c-debug/externalpackages/ctetgen/ctetgen.c
>> [0] TetGenMeshPreciseLocate() line 5781 in
>> /home/tuomas/sources/petsc/firedrake/arch-linux2-c-debug/externalpackages/ctetgen/ctetgen.c
>> [0] Petsc has generated inconsistent data
>> [0] This is wrong
>>
>>
>> On 04/14/2015 12:08 PM, Andrew McRae wrote:
>>
>>     Hi Tuomas,
>>
>>  It's possible that you're hitting a non-affine issue here.  At the
>> moment, the Jacobian, dx_i/dX_j, of the coordinate transformation from the
>> reference cell to the physical cell, x(X), is treated as being constant
>> over the cell.  For non-simplex cells (i.e. quadrilaterals, triangular
>> prisms, tetrahedra), this is only an approximation.  The Jacobian matrix is
>> used when replacing the measure (dx == |det J|*dX) and in derivatives
>> (d/dx_i == sum_j dX_j/dx_i d/dX_j).
>>
>>  I have some work in progress, hopefully landing in the next few weeks,
>> after which the Jacobian will be calculated separately at each quadrature
>> point.  This is currently spread across branches in different components of
>> Firedrake.  I'll try your code tomorrow to see if the results come out the
>> same (or at least much closer!).
>>
>>  Just checking, I assume that doing the problem on tetrahedra gives
>> matching results, even with a deformed mesh?  (If so, this suggests further
>> that it's a non-affine approximation issue).  I.e., replace the first four
>> lines of code with
>>
>>  from firedrake import *
>>  mesh = UnitCubeMesh(10, 10, 6)  # mesh of tetrahedra, each of the
>> 10*10*6 cuboids is split into 6 tets
>>
>>  and send it through the same deformation as before.  Replace 'ds_v +
>> ds_t + ds_b' by just ds in the declaration of L2.
>>
>>  Best,
>>  Andrew
>>
>> On 14 April 2015 at 19:29, Tuomas Karna <tuomas.karna at gmail.com> wrote:
>>
>>> Hi all,
>>>
>>> Encountered this issue with extruded mesh where the coordinates have
>>> been deformed. The first form a==L just evaluates div(u), the second
>>> a==L2 is the same but div(u) integrated in parts. Thus the results
>>> should be equivalent, but that's not what I see:
>>>
>>> a == L: 0.999999886488 1.0000001092
>>> a == L2: -0.235329928101 3.47882106918
>>>
>>> Without the mesh deformation the two forms give the correct solution
>>> (1.0). Am I missing something?
>>>
>>> Cheers,
>>>
>>> Tuomas
>>>
>>> ---
>>>
>>> from firedrake import *
>>> mesh2d = UnitSquareMesh(10,10)
>>> layers = 6
>>> mesh = ExtrudedMesh(mesh2d, layers, -1.0/layers)
>>>
>>> P1 = FunctionSpace(mesh, 'CG', 1, vfamily='CG', vdegree=1)
>>> P2 = FunctionSpace(mesh, 'CG', 2, vfamily='CG', vdegree=1)
>>> P1v = VectorFunctionSpace(mesh, 'CG', 1, vfamily='CG', vdegree=1)
>>>
>>> # deform mesh
>>> scalar = Function(P1).interpolate(Expression('1.0+x[0]'))
>>> coords = mesh.coordinates
>>> coords.dat.data[:,2] *= scalar.dat.data[:]
>>>
>>> u = Function(P1v)
>>> w = Function(P2)
>>> u.interpolate(Expression(('x[0]', '0.0', '0.0')))
>>>
>>> tri = TrialFunction(P2)
>>> test = TestFunction(P2)
>>> normal = FacetNormal(mesh)
>>>
>>> a = test*tri*dx
>>> L = div(u)*test*dx
>>> L2 = -dot(u, grad(test))*dx + dot(u, normal)*test*(ds_v+ds_t+ds_b)
>>>
>>> solve(a == L, w)
>>> print 'a == L:', w.dat.data.min(), w.dat.data.max()
>>>
>>> solve(a == L2, w)
>>> print 'a == L2:', w.dat.data.min(), w.dat.data.max()
>>>
>>>
>>> _______________________________________________
>>> firedrake mailing list
>>> firedrake at imperial.ac.uk
>>> https://mailman.ic.ac.uk/mailman/listinfo/firedrake
>>>
>>
>>
>>
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>>
>>
>>
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