Average of shape 3rd derivatives function?

[Sean Carney]

Hello,

I'm in the process of implementing a DG method for a 4th order problem, which requires access to the average of the third derivative of the finite element functions across an interface. I notice that the FEInterfaceValues class has a "jump_in_shape_3rd_derivatives" function, but not the corresponding function for the average.

Any suggestions for how to implement this, specifically in the context of [the face_worker part] the MeshWorker framework?

Any suggestions are appreciated!

Best regards,

-Sean

[Wolfgang Bangerth]

On 6/20/24 22:04, Sean Carney wrote:
>
> I'm in the process of implementing a DG method for a 4th order problem, which
> requires access to the average of the third derivative of the finite element
> functions across an interface. I notice that the FEInterfaceValues class has a
> "jump_in_shape_3rd_derivatives" function, but not the corresponding function
> for the average.
>
> Any suggestions for how to implement this, specifically in the context of [the
> face_worker part] the MeshWorker framework?

Sean:
If you take a look at how the corresponding functions for the second
derivatives (Hessians) are implemented here
https://github.com/dealii/dealii/blob/master/include/deal.II/fe/fe_interface_values.h#L3420-L3445
and here
https://github.com/dealii/dealii/blob/master/include/deal.II/fe/fe_interface_values.h#L3477-L3502
then you will pretty immediately see how the implementation of the jump in
third derivatives in
https://github.com/dealii/dealii/blob/master/include/deal.II/fe/fe_interface_values.h#L3449-L3473
can be extended to compute the average.

It would of course be great if you could make that a patch to deal.II that we
could include in the next release!

Best
Wolfgang

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

[Sean Carney]

Wolfgang,

Thank you for pointing me to these locations in the source code, that is very helpful!

It is quite simple to mimic what is happening in "average_of_shape_hessians" and "jump_in_shape_3rd_derivatives"

to write a function "average_of_shape_3rd_derivatives".

I am re-compling deal.ii right now with the changes I made; when it's done I will test the implementation. 

If and when the function works, I will follow the instructions here for contributing a patch:

https://github.com/dealii/dealii/wiki/Contributing

Best regards,

-Sean

[Wolfgang Bangerth]

On 6/24/24 11:25, Sean Carney wrote:
>
> Thank you for pointing me to these locations in the source code, that is very
> helpful!
>
> It is quite simple to mimic what is happening in "average_of_shape_hessians"
> and "jump_in_shape_3rd_derivatives"
> to write a function "average_of_shape_3rd_derivatives".
>
> I am re-compling deal.ii right now with the changes I made; when it's done I
> will test the implementation.
>
> If and when the function works, I will follow the instructions here for
> contributing a patch:
> https://github.com/dealii/dealii/wiki/Contributing

Fantastic, we look forward to the patch!
Best
W.