Point value at vertices with DG question

[Craig Michoski]

Hey all,

Here'a a question I wanted to ask real quick, which may seem a little odd.  Say I have DG elements, and want to get point values on vertices, then I think VectorTools::point_value gives me the value on the element I am on (in the iterator sense), so that feeding in vertex points would work.  But now I recognize that in DG vertex coordinates correspond in a regular quad mesh to 4 values.  One on the owned cell, 2 on the two neighboring cells, and one on the adjacent cell.  What if I want to average the vertex value over that stencil?  The traditional DG stencil only includes face neighbors, so the adjacent cell may not have support in a distributed mesh.  Does anyone have a simple idea on how you might do this?

Thanks,

Craig

    

    

[Bruno Turcksin]

Craig,

On Friday, April 29, 2016 at 12:16:27 PM UTC-4, Craig Michoski wrote:

Here'a a question I wanted to ask real quick, which may seem a little odd.  Say I have DG elements, and want to get point values on vertices, then I think VectorTools::point_value gives me the value on the element I am on (in the iterator sense), so that feeding in vertex points would work.  But now I recognize that in DG vertex coordinates correspond in a regular quad mesh to 4 values.  One on the owned cell, 2 on the two neighboring cells, and one on the adjacent cell.  What if I want to average the vertex value over that stencil?  The traditional DG stencil only includes face neighbors, so the adjacent cell may not have support in a distributed mesh.  Does anyone have a simple idea on how you might do this?

I am not sure that I understood correctly your question but the adjacent cell is always known but it may be a ghost cell. The partitioning is independent of the discretization that you are using and the adjacent cell is necessary for continuous finite element.

Best,

Bruno

[Timo Heister]

VectorTools::point_value will pick the cell the point is "in" to
evaluate the FE function. So if you hand the function a vertex,
deal.II will randomly (not really, but the choice depends on rounding,
etc.) pick one of the neighboring cells and evaluate the solution. For
a continuous element this doesn't matter, but for a DG element you get
one of the values.
Note that evaluating your solution on faces/vertices is not a
well-defined operation in DG. If you want to do something like
computing an average value, you have to do so manually.

Did you see the following?
https://github.com/dealii/dealii/wiki/Frequently-Asked-Questions#how-do-i-access-values-of-discontinuous-elements-at-vertices

The parallel aspect has been answered by Bruno above.

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Timo Heister
http://www.math.clemson.edu/~heister/

[Jean-Paul Pelteret]

This question, also ask yesterday, provides additional insights into how to solve your problem.

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