Yes I began this project by reviewing step-8 
<https://www.google.com/url?q=https%3A%2F%2Fdealii.org%2F8.4.1%2Fdoxygen%2Fdeal.II%2Fstep_8.html&sa=D&sntz=1&usg=AFQjCNE8fid8PZJVBvCz_Ixx08I0EOi-8A>
 and 
the Handling vector valued problems 
<https://dealii.org/8.4.1/doxygen/deal.II/group__vector__valued.html> module. 
That led me to using extractors.

step-57 
<http://www.google.com/url?q=http%3A%2F%2Fwww.dealii.org%2Fdeveloper%2Fdoxygen%2Fdeal.II%2Fstep_57.html&sa=D&sntz=1&usg=AFQjCNE6vPIRLDSt5O067SsyGpHe2_cctg>
 almost clarifies my problem; but unfortunately I don't see its exact weak 
form, and rather it just references back to the Stokes tutorial. The term 
present_velocity_gradients[q]*phi_u[j]*phi_u[i] from its matrix assembly 
caught my eye. I think this is similar to my v*gradz*w, which per a quick 
test I did is equivalent to gradz*w*v. My understanding is that dealii::
Tensor::operator* automatically transposes (at least in the abstract) rank 1 
tensors 
to make dot products, which makes all of this work. 

Since step-57 
<http://www.google.com/url?q=http%3A%2F%2Fwww.dealii.org%2Fdeveloper%2Fdoxygen%2Fdeal.II%2Fstep_57.html&sa=D&sntz=1&usg=AFQjCNE6vPIRLDSt5O067SsyGpHe2_cctg>
 has 
to assume something about the indexing of present_velocity_gradients[q], 
maybe Timo or Liang Zhao can definitively answer my original question. 
What's the best way to draw a specific person's attention to a question on 
the mailing list? :)


On Thursday, April 6, 2017 at 11:38:33 AM UTC+2, Jean-Paul Pelteret wrote:
>
> Ok great, I'm glad that you're getting somewhere. So lets try to get to 
> the bottom of this indexing issue (as a side note, and in case anyone else 
> is interested, in this issue 
> <https://github.com/dealii/dealii/issues/3646> we've started discussing 
> how to document the index-related functions in a bit more detail). 
>
> Can I ask a quick question: Are you familiar with the step-8 
> <https://dealii.org/8.4.1/doxygen/deal.II/step_8.html> tutorial? This is 
> the tutorial that details how vector-valued shape functions work in 
> deal.II, and also what it means to ask (without the help of an extractor) 
> for the gradient of one (primitive) shape function associated with a vector 
> field. Although the tutorial described an application in solid mechanics, 
> exactly the same concepts apply in your scenario. I think that this should 
> give more insight into how one might go from the weak general form to a 
> explicit assembly pseudo-code for a vector valued field. Its also better 
> explained than anything that I could fit into this text-box, but if you 
> don't find that to be the case then I've also expanded on it in this PDF 
> <https://github.com/jppelteret/code-gallery/blob/353c02d31d76fdd76851a7313681d4d8bd1c42f4/Linear_Elastic_Active_Skeletal_Muscle_Model/doc/theory/theory-linear_elastic_active_muscle_model.pdf>
>  (from 
> page 5 is relevant). 
>
> Using the extractors means that you (typically) don't have to worry about 
> the manual component indexing via calls to
> const unsigned int component_i = fe.system_to_component_index 
> <https://dealii.org/developer/doxygen/deal.II/classFiniteElement.html#a27220a135402b96c7e6eecbb04acda56>
> (i).first;
> This allows one to get, for a primitive vector shape function, its only 
> spatial component that is non-zero. The extractors help by filtering out 
> the shape functions associated with other fields and reinterprets and 
> collects the shape function value/gradient information for the given field. 
>
>

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