May I know more about tensor calculation?

aki_yafuji · July 2, 2011, 14:53

Hello, everyone!

How do I calculate partial derivative dA/dx (= (dAxx/dx, dAxy/dx, dAxz/dx, dAyy/dx, dAyz/dx, dAzz/dx)) of a symmetric tensor A (= (Axx, Axy, Axz, Ayy, Ayz, Azz))?
I tried to use "grad(A)" but failed. I am at a loss of what to do...
If anyone has information concerning this, please let me know!

Sincerely yours

aki

kathrin_kissling · July 4, 2011, 03:05

Hi Aki,

fvc::grad(A) should do the trick

Best

Kathrin

deepsterblue · July 4, 2011, 23:51

Kathrin,

I don't think that would work... The gradient of a tensor would contain 27 components, which Foam doesn't cater for at the moment. It can be done, just that the templates need to be instantiated, but that wouldn't be trivial.

Cheers,
Sandeep

kathrin_kissling · July 5, 2011, 03:05

Sandeep,

you are totally right. I overlooked A being a tensor. I feel a little embarrassed about it.

Thank you for letting me know!

Aki,

for what do you need this?
Do you just need the single components?

Best Kathrin

deepsterblue · July 5, 2011, 14:53

A simple workaround would be to store the gradient of each row of the tensor as another tensor, and manipulating that as necessary.

kathrin_kissling · July 6, 2011, 03:33

A not so simple way would be to use the VectorN library, which would make possible to have this huge tensor as a whole and add the fvc::grad for this special case. But for me it seems to be overengineered, as least as long as Aki doesn't need the complete tensor.
The question really is for what it is needed...

July 2, 2011, 14:53	May I know more about tensor calculation?	#1
aki_yafuji New Member yafuji aki Join Date: Jul 2010 Location: Japan Posts: 14 Rep Power: 16	Hello, everyone! How do I calculate partial derivative dA/dx (= (dAxx/dx, dAxy/dx, dAxz/dx, dAyy/dx, dAyz/dx, dAzz/dx)) of a symmetric tensor A (= (Axx, Axy, Axz, Ayy, Ayz, Azz))? I tried to use "grad(A)" but failed. I am at a loss of what to do... If anyone has information concerning this, please let me know! Sincerely yours aki

July 4, 2011, 23:51		#3
deepsterblue Senior Member Sandeep Menon Join Date: Mar 2009 Location: Amherst, MA Posts: 403 Rep Power: 25	Kathrin, I don't think that would work... The gradient of a tensor would contain 27 components, which Foam doesn't cater for at the moment. It can be done, just that the templates need to be instantiated, but that wouldn't be trivial. Cheers, Sandeep __________________ Sandeep Menon University of Massachusetts Amherst https://github.com/smenon

July 5, 2011, 14:53		#5
deepsterblue Senior Member Sandeep Menon Join Date: Mar 2009 Location: Amherst, MA Posts: 403 Rep Power: 25	A simple workaround would be to store the gradient of each row of the tensor as another tensor, and manipulating that as necessary. __________________ Sandeep Menon University of Massachusetts Amherst https://github.com/smenon

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July 4, 2011, 03:05		#2
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	Hi Aki, fvc::grad(A) should do the trick Best Kathrin

July 5, 2011, 03:05		#4
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	Sandeep, you are totally right. I overlooked A being a tensor. I feel a little embarrassed about it. Thank you for letting me know! Aki, for what do you need this? Do you just need the single components? Best Kathrin

July 6, 2011, 03:33		#6
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	A not so simple way would be to use the VectorN library, which would make possible to have this huge tensor as a whole and add the fvc::grad for this special case. But for me it seems to be overengineered, as least as long as Aki doesn't need the complete tensor. The question really is for what it is needed...