On 03/07/2018 12:19 PM, RAJAT ARORA wrote:


I want to do the following thing: I have a scalar quantity available
only at the Gauss points of a cell. (cell = 2d rectangular element)
I want to get the derivative of this quantity at the center of the cell.

One way to do this is to locally project the gauss point variable to the nodes
of the element using compute_projection_from_quadrature_points_matrix
and then take the derivative.

What I want to do is the following: Think of the 4 gauss points as a new rectangular element. Then, these 4 vertices become the node and this makes the value of the variable known at the nodes of this element.

Now, I want to take the derivative of the variable wrt to this new cell (vertices of new cell = gauss points of parent cell).

Can someone please help me figure out how can I take the derivative wrt to this new cell?

Some thought: Mapping eulerian may not work here as that mapping applies to the nodes and is continuous. Here, the same node gets mapped to different vertices (gauss point of the cell of which the node is a part of), so a single mapping may not work. Either I use different Euler vector for the different element but will that be expensive?

I think this is too complicated. That's because everything in deal.II always assumed that you have a mesh, so if you did what you suggest, you'd have to actually build a triangulation and everything that lives on it. That does not seem efficient.

What is wrong with the approach using compute_projection_from_quadrature_points_matrix()?

Best
 W.

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

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