Mauro and I are looking into this. We'll let you know. :-)
Luca
> On 21 mag 2016, at 12:34, Praveen C <cprav...@gmail.com> wrote:
>
> Some additional info about the problem I am facing. In the test I sent last,
> I used a divergence-free vector field v on the sphere.
>
> Both the quantities
>
> integral_K (div(v) * dx)
>
> and
>
> integral_{boundary K}( normal * v * ds)
>
> should be zero. But with MappingManifold, both quantities show large value
> while MappingQ(9) gives small values.
>
> Best
> praveen
>
>> On Fri, May 20, 2016 at 11:10 AM, Praveen C <cprav...@gmail.com> wrote:
>> Dear Luca
>>
>> I have created a simple test case to show the problem with MappingManifold
>> for sphere.
>>
>> Please see attached pdf. The code is also attached.
>>
>> Thanks
>> praveen
>>
>>> On Tue, May 17, 2016 at 6:21 PM, Praveen C <cprav...@gmail.com> wrote:
>>> Face normals from opposite sides sum to O(1e-15)
>>>
>>> I run on coarse mesh with MappingQ and MappingManifold, see pictures. I
>>> dont see any discontinuity in the geometry.
>>>
>>> Best
>>> praveen
>>>
>>>> On Tue, May 17, 2016 at 2:16 PM, luca.heltai <luca.hel...@gmail.com> wrote:
>>>> Can you check that the generated normals on the two faces are actually one
>>>> the opposite of the other? I see no other reasons for this to go wrong,
>>>> unless the generated normals/geometry are not actually the same.
>>>>
>>>> Can you output a coarse result, using 10 subdivisions, and MappingManifold
>>>> to generate the output? I’d expect the geometry to be continuous, but this
>>>> may actually not be the case. This test should use the manifold of each
>>>> cell to produce the subdivisions, so if the geometry is wrong, you should
>>>> see a discontinuity (only if you produce more than one subdivision when
>>>> generating the output, and if the subdivision respect the mapping…)
>>>>
>>>> L.
>>>>
>>>> > On 17 May 2016, at 10:38, Praveen C <cprav...@gmail.com> wrote:
>>>> >
>>>> > Dear Luca
>>>> >
>>>> > I am solving shallow water equation on sphere using a DG scheme. With
>>>> > MappingQ, I get decent results, but I want to improve the mapping by
>>>> > using MappingManifold.
>>>> >
>>>> > With MappingManifold based on two charts, after just one time step, I
>>>> > see large velocities at the junction region of the two charts as seen in
>>>> > attached figure.
>>>> >
>>>> > In the DG scheme, I have to assemble fluxes on the edges of the surface
>>>> > mesh.
>>>> >
>>>> > Best
>>>> > praveen
>>>> >
>>>> > On Tue, May 17, 2016 at 1:55 PM, luca.heltai <luca.hel...@gmail.com>
>>>> > wrote:
>>>> > Dear Praveen,
>>>> >
>>>> > yes, I was expecting those numbers. Mapping Manifold should be machine
>>>> > precision. I’d expect Q9 to be a little better though… I’ll try to look
>>>> > into this (when I have some time).
>>>> >
>>>> > What error do you see at the junction? What’s happening? What do you
>>>> > expect to happen?
>>>> >
>>>> > L.
>>>> >
>>>> >
>>>> > > On 17 May 2016, at 10:16, Praveen C <cprav...@gmail.com> wrote:
>>>> > >
>>>> > > So q_point * normal is most accurate with ManifoldMapping of O(1e-15)
>>>> > > while MappingQ(9) is O(1e-9)
>>>> > >
>>>> > > Now the problem is when I use two charts, SphericalManifold and
>>>> > > RotatedSphericalManifold to cover the sphere, I see errors at the
>>>> > > junction region of the two charts.
>>>> > >
>>>> > > Best
>>>> > > praveen
>>>> > >
>>>> > > On Tue, May 17, 2016 at 12:30 PM, luca.heltai <luca.hel...@gmail.com>
>>>> > > wrote:
>>>> > > Then can you verify which ones are correct, by taking the scalar
>>>> > > product with the quadrature points (assuming a sphere centered at the
>>>> > > origin), and check which ones are zero (IF they are zero)?
>>>> > >
>>>> > > Best,
>>>> > >
>>>> > > L.
>>>> > >
>>>> > >
>>>> > > > On 17 May 2016, at 8:53, Praveen C <cprav...@gmail.com> wrote:
>>>> > > >
>>>> > > > Dear Luca
>>>> > > >
>>>> > > > These are not normal to sphere surface, but normal to edges on the
>>>> > > > sphere, which should be tangent to sphere surface.
>>>> > > >
>>>> > > > I get these normals from
>>>> > > >
>>>> > > > FEFaceValues<2,3> and using update_normal_vectors
>>>> > > >
>>>> > > > Best
>>>> > > > praveen
>>>> > > >
>>>> > > > On Tue, May 17, 2016 at 12:19 PM, luca.heltai
>>>> > > > <luca.hel...@gmail.com> wrote:
>>>> > > > Can you verify which ones are correct? The normal on a sphere of
>>>> > > > radius one, centered at the origin, is the same as the quadrature
>>>> > > > point itself. From your numbers, MappingQ+Manifold seem completely
>>>> > > > off (y direction is always zero?).
>>>> > > >
>>>> > > > Can you produce a minimal test that checks normals VS quadrature
>>>> > > > points?
>>>> > > >
>>>> > > > L.
>>>> > > >
>>>> > > >
>>>> > > > > On 17 May 2016, at 8:43, Praveen C <cprav...@gmail.com> wrote:
>>>> > > > >
>>>> > > > > Dear all
>>>> > > > >
>>>> > > > > There is also a large difference in face normal vectors which I
>>>> > > > > need since I am using a DG scheme for pde on sphere.
>>>> > > > >
>>>> > > > > Here are normal vectors at some face quadrature points
>>>> > > > >
>>>> > > > > With MappingQ(9) + SphericalManifold
>>>> > > > > -0.707107 -1.28795e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -7.374e-10 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.12489e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.08533e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.43344e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.52226e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.78585e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.81086e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.9384e-09 0.707107
>>>> > > > >
>>>> > > > > -0.707107 -1.80885e-09 0.707107
>>>> > > > >
>>>> > > > > With MappingManifold + SphericalManifold
>>>> > > > >
>>>> > > > > -0.649511 -0.103732 0.753243
>>>> > > > >
>>>> > > > > -0.652465 -0.101169 0.751036
>>>> > > > >
>>>> > > > > -0.659029 -0.0948727 0.74611
>>>> > > > >
>>>> > > > > -0.668238 -0.0844748 0.739136
>>>> > > > >
>>>> > > > > -0.678651 -0.0700161 0.731116
>>>> > > > >
>>>> > > > > -0.727853 0.06925 0.682227
>>>> > > > >
>>>> > > > > -0.730142 0.0918833 0.677089
>>>> > > > >
>>>> > > > > -0.730699 0.11164 0.67351
>>>> > > > >
>>>> > > > > -0.730325 0.125663 0.671442
>>>> > > > >
>>>> > > > >
>>>> > > > > -0.729954 0.131967 0.670636
>>>> > > > >
>>>> > > > >
>>>> > > > > The difference seems rather large.
>>>> > > > >
>>>> > > > > Best
>>>> > > > > praveen
>>>> > > > >
>>>> > > > > On Mon, May 16, 2016 at 9:08 PM, Praveen C <cprav...@gmail.com>
>>>> > > > > wrote:
>>>> > > > > Dear Luca
>>>> > > > >
>>>> > > > > I need a Manifold<2,3> object but I could not succeed in composing
>>>> > > > > SphericalManifold with a rotation. There were many dimensions
>>>> > > > > involved in the composition which I have not understood.
>>>> > > > >
>>>> > > > > But I think I understood what it is supposed to do, so I modified
>>>> > > > > Spherical Manifold by adding in a 90 deg rotation. I use
>>>> > > > > RotatedSphericalManifold for north/south faces and
>>>> > > > > SphericalManifold for the other faces.
>>>> > > > >
>>>> > > > > When I run my code with this, I find large errors arising in the
>>>> > > > > region where north/south faces meet the other faces.
>>>> > > > >
>>>> > > > > Is there some incompatibility in my mapping ? Will the face normal
>>>> > > > > vectors (which lie in tangent plane) be correct at the junction of
>>>> > > > > the two manifolds ?
>>>> > > > >
>>>> > > > > The RotatedSphericalManifold is attached.
>>>> > > > >
>>>> > > > > Thanks
>>>> > > > > praveen
>>>> > > > >
>>>> > > > > On Mon, May 16, 2016 at 4:20 PM, luca.heltai
>>>> > > > > <luca.hel...@gmail.com> wrote:
>>>> > > > >
>>>> > > > > > On 16 May 2016, at 12:37, Praveen C <cprav...@gmail.com> wrote:
>>>> > > > > >
>>>> > > > > > Dear Luca
>>>> > > > > >
>>>> > > > > > Thanks for clarifying this issue. I need tangent vector in my
>>>> > > > > > code.
>>>> > > > > >
>>>> > > > > > So I first define a ChartManifold which rotates by 90 deg about
>>>> > > > > > x-axis, say RotateX. Then I compose it with SphericalManifold
>>>> > > > > > and use
>>>> > > > > >
>>>> > > > > > SphericalManifold * RotateX
>>>> > > > > >
>>>> > > > > > Is this what you meant ?
>>>> > > > > >
>>>> > > > > > We have the constructor
>>>> > > > > >
>>>> > > > > > CompositionManifold(F, G)
>>>> > > > > >
>>>> > > > > > Does this do F*G or G*F ? The description given in words is a
>>>> > > > > > bit ambiguous.
>>>> > > > >
>>>> > > > >
>>>> > > > > y = G(F(x))
>>>> > > > >
>>>> > > > > "ChartManifold going from the chart of the firstChartManifold to
>>>> > > > > the embedding space of the second ChartManifold"
>>>> > > > >
>>>> > > > > In your case, F is your spherical manifold, while your G is the
>>>> > > > > rotation manifold (to preserve periodicity of the spherical
>>>> > > > > manifold).
>>>> > > > >
>>>> > > > > Best,
>>>> > > > >
>>>> > > > > Luca.
>>>> > > > >
>>>> > > > > >
>>>> > > > > > Thanks
>>>> > > > > > praveen
>>>> > > > > >
>>>> > > > > > On Mon, May 16, 2016 at 2:29 PM, luca.heltai
>>>> > > > > > <luca.hel...@gmail.com> wrote:
>>>> > > > > > Dear Praveen,
>>>> > > > > >
>>>> > > > > > there is a bug in SphericalManifold for dimension 3, which makes
>>>> > > > > > it unusable so far with MappingManifold.
>>>> > > > > >
>>>> > > > > > The issue is with the computation of the tangent vector across
>>>> > > > > > the north and south poles.
>>>> > > > > >
>>>> > > > > > At the moment MappingManifold is the only class using this
>>>> > > > > > computation, so if you don’t use MappingManifold, you don’t see
>>>> > > > > > this issue.
>>>> > > > > >
>>>> > > > > > You can solve it by writing a rotated SphericalManifold
>>>> > > > > > descriptor (one where the poles are east and west respectively),
>>>> > > > > > and associating this Manifold to the north and south faces of
>>>> > > > > > the sphere. You could use, for example, CompositionManifold to
>>>> > > > > > compose a rotation of 90 degree along the x or y axis with
>>>> > > > > > SphericalManifold, and attach the resulting manifold to the
>>>> > > > > > north and south faces.
>>>> > > > > >
>>>> > > > > > This is related to some of the issues here:
>>>> > > > > > https://github.com/dealii/dealii/issues/2530
>>>> > > > > >
>>>> > > > > > What you are hitting is a problem with the geometry, not with
>>>> > > > > > MappingManifold in itself. It is not possible to describe the
>>>> > > > > > surface of a sphere with a single chart without introducing at
>>>> > > > > > least one singularity. We have implemented the standard polar
>>>> > > > > > coordinate mapping, which has two singularities (north and south
>>>> > > > > > poles respectively), and these are the ones introducing nans in
>>>> > > > > > your computation.
>>>> > > > > >
>>>> > > > > > Everything works fine when computing intermediate points, but
>>>> > > > > > not when computing tangents. I’m still thinking of a way to fix
>>>> > > > > > this. The easiest fix is to implement the SphericalManifold
>>>> > > > > > without charts, but I haven’t had much time to sit down and do
>>>> > > > > > some fun stuff lately…
>>>> > > > > >
>>>> > > > > > Though, I can help you with implementing fixes, if you are
>>>> > > > > > willing to help… :)
>>>> > > > > >
>>>> > > > > > L.
>>>> > > > > >
>>>> > > > > > > On 16 May 2016, at 10:35, Praveen C <cprav...@gmail.com> wrote:
>>>> > > > > > >
>>>> > > > > > > Dear all
>>>> > > > > > > I am solving pde on sphere and want to use MappingManifold
>>>> > > > > > >
>>>> > > > > > > My mesh is generated like this.
>>>> > > > > > >
>>>> > > > > > > Point<spacedim> center(0.0, 0.0, 0.0);
>>>> > > > > > > GridGenerator::hyper_sphere(triangulation, center,
>>>> > > > > > > Radius);
>>>> > > > > > > static SphericalManifold<dim,spacedim>
>>>> > > > > > > surface_description;
>>>> > > > > > > triangulation.set_all_manifold_ids(0);
>>>> > > > > > > triangulation.set_manifold (0, surface_description);
>>>> > > > > > > triangulation.refine_global(n_refine);
>>>> > > > > > >
>>>> > > > > > > Changing from MappingQ to MappingManifold leads to blow up,
>>>> > > > > > > with nan.
>>>> > > > > > >
>>>> > > > > > > Before I debug, is there an example I can see of
>>>> > > > > > > MappingManifold usage ?
>>>> > > > > > >
>>>> > > > > > > Thanks
>>>> > > > > > > praveen
>>>> > > > > > >
>>>> > > > > > > --
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