On 1/13/23 05:59, 王昆 wrote:
Happy new year! I am a DealII amateur from China and need your help!
Recently, I want to perform the polar decomposition for a Tensor<2,dim> using
DealII. I have searched all the methods provided in Tensor
and Physics::Elasticity::Kinematics. But no method could directly perform such
operation. It is known that the singular value decomposition could be used for
such operation. However, I cannot find similar method for the Tensor, too.
Could you give me some tips on how to solve this problem?
Dear K. Wang:
if I understand you right, for a given d x d tensor A, you want to find
factors U and P so that
A = UP
? That might indeed not be implemented so far, but it should not be very
difficult to do. You will need to write something like this:
// 1d case
std::pair<Tensor<2,1>,Tensor<2,1>>
polar_decomposition (const Tensor<2,1> &A) {
const Tensor<2,1> U = {{ (A[0][0]>0 ? 1 : -1) }};
const Tensor<2,1> P = {{ std::fabs(A[0][0]) }};
return {U,P};
}
// 2d case
std::pair<Tensor<2,2>,Tensor<2,2>>
polar_decomposition (const Tensor<2,2> &A) {
Tensor<2,2> U;
Tensor<2,2> P;
...compute U, P...
return {U,P};
}
// 3d case
std::pair<Tensor<2,3>,Tensor<2,3>>
polar_decomposition (const Tensor<2,3> &A) {
Tensor<2,3> U;
Tensor<2,3> P;
...compute U, P...
return {U,P};
}
I don't know what algorithms exist for the 2d and 3d cases, but I assume that
there is literature.
If you were interested in implementing these functions above, we would be very
happy to add them to the library!
Best
Wolfgang
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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