Reading in vector associated with element (or node)

mesh
1

Dear community,

I’m trying to read a vector which is associated to an element (or could be to a node, too). This is for an anisotropic solid material which has a fiber direction at every cell, which is predefined and should be handed in to Fenics to be read at the element level.

So, the common way I thought this might work is to set a vector attribute in the xdmf file. An abbreviation of my file looks like this:

<Xdmf Version=“3.0”>
<Domain>
<Grid Name=“Grid”>
<Geometry GeometryType=“XYZ”>
<DataItem DataType=“Float” Dimensions=“1199 3” Format=“XML” Precision=“8”>
31.1172078030027 -37.35353365752 23.3608991129423
49.1337819098811 -1.2034305749188e-14 18.5333726269385
…
19.51531616548419 -43.562521374451734 -15.792062807031005
</DataItem>
</Geometry>
<Topology NodesPerElement=“4” NumberOfElements=“3612” TopologyType=“tetrahedron”>
<DataItem DataType=“Int” Dimensions=“3612 4” Format=“XML” Precision=“4”>
780 893 115 324
766 328 949 334
…
214 117 215 1188
</DataItem>
</Topology>
<Attribute AttributeType=“Vector” Center=“Cell” Name=“fibers”>
<DataItem DataType=“Double” Dimensions=“3612” Format=“XML” Precision=“4”>
0.2324 -0.983765 0.7863
-0.1243 -0.283468 0.35235
…
0.1243 0.231324 -0.237467
</DataItem>
</Attribute>
</Grid>
</Domain>

Then, I thought reading the vectors worked as for the scalar attributes for boundary conditions (domain ids):

mvc_fib = MeshValueCollection(“double”, mesh, 3)
with XDMFFile(‘file.xdmf’) as infile:
infile.read(mvc_fib, “fibers”)

mf_fib = cpp.mesh.MeshFunctionDouble(mesh, mvc_fib)

However, it turns out that the mesh value collection only collects scalar values and orders all my vector components in a 1-d array.

So, even if the xdmf format supports attributes that are vector-, tensor- or in general matrix-valued (as I figured out from the xdmf documentation), I’m not able to get this info properly into Fenics.

It would be great if anyone had an idea on how to get a fiber field to the element level and then to have a element-wise 3x1 vector f0 which can be used in a material law.
Basically, I have the fiber vectors in a textfile as a list with each row corresponding to an element (or, alternatively, to a node). Maybe there is another option instead of the xdmf attributes?

Thanks!

Best wishes,
Marc

2

Meanwhile, I figured out how to proceed. Indeed, one has to define mesh functions for each vector component separately, similar to this example:
https://fenicsproject.org/docs/dolfin/2018.1.0/python/demos/tensor-weighted-poisson/documentation.html

Bw,
Marc