For the second question, if I'm not mistaken you must first compute the
square root of the eigenvalues of C=F^{T}.F from which you can construct U
or V. Thereafter its trivial to compute R. One way that you can do the
eigenvalue computation is with the GNU scientific library (GSL). Otherwise
you can copy a tensor into a LAPACKFullMatrix
<https://www.dealii.org/8.4.0/doxygen/deal.II/classLAPACKFullMatrix.html>
and do an eigenvalue computation
<https://www.dealii.org/8.4.0/doxygen/deal.II/classLAPACKFullMatrix.html#a7ca147298617207c752833fce44715a4>
with it. Perhaps someone has some preferably alternative to this?
On Friday, June 10, 2016 at 6:18:20 PM UTC+2, Anup Basak wrote:
>
> Hello all,
>
> I have two quires regarding tensor product and polar decomposition.
>
> 1. Suppose I want to multiply two second order tensors with a fourth order
> tensor to get a forth order tensor as follows:
>
> A_{ijkl} = B_{im} C_{mjkn} D_{nl}.
>
> It is clear that we have a single index contraction with B and C, and
> with C and D. If I use the command in the code
>
> A = B* C* D, am I correct (of course I have already defined the tensors in
> the code)? I mean the multiplication with '*'
> does contraction over one index, right?
>
>
> 2. I have another query. How to perform the polar decomposition in dealii,
> like
> F_{ij} = R_{ik} U_{kj} = V_{ik} R_{kj},
>
> where R is an orthogonal tensor and U and V are symmetric tensors.
>
> I shall be thankful if someone can help me in this regard.
>
> Thanks and regards,
> Anup.
>
>
>
>
>
>
>
>
>
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