Gradient of the shape function wrt natural coordinate system?

[Yuxiang Wang]

Dear all,

While I can use the shape_grad function to get the gradient of the shape function with respect to the real cell coordinates, would there be a way to get the shape_grad with respect to the reference natural coordinates? For example, for shell element (that I'm working on), I have the global coordinates (x, y, z) for a point and also a natural coordinate system (r, s, t). 

One possibility is that I can use the chain rule and the jacobian matrix to get that value, but it'll be very computationally inefficient. Could anyone please help?

Best,

Shawn

[Wolfgang Bangerth]

I think you are asking for the *unmapped* shape functions as they are defined
on the reference cell. That's something you can get from the finite element
itself via the
FiniteElement::shape_grad()
function or its implementation in derived classes.

The gradient of the shape functions mapped to a particular cell in a mesh can
be obtained via FEValues::shape_grad(), which I think is what you are
referring to above.

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Yuxiang Wang]

Exactly what I was looking for! Thank you so much Professor Bangerth.

Have a great one,

Shawn

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Yuxiang "Shawn" Wang, PhD

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