Re: [deal.II] FE w/ Gauss Point DoFs

2018-03-07 Thread Jonathan Russ 
Thank you Jean-Paul! That seems to be precisely what I should use assuming 
the number of degrees of freedom per cell is equal to the number of 
quadrature points per cell (which it appears to be). Thanks again!
Jonathan

On Wednesday, March 7, 2018 at 12:54:06 PM UTC-5, Jean-Paul Pelteret wrote:
>
> Dear Jonathan,
>
> Is FE_DGQArbitraryNodes 
>  
> perhaps 
> what you’re looking for? From the documentation:
>
> The primary purpose of this class is to provide an element for which the 
> mass matrix can be made diagonal by choosing basis functions that are not 
> either zero or one at the vertices of the cell, but instead are zero or one 
> at a given set of quadrature points.
>
>
> J-P
>
> On 07 Mar 2018, at 18:09, Jonathan Russ  
> wrote:
>
> Bruno -
>
> Thank you for your help. I see what you are saying. In this way I would 
> need to make sure I have the same number of gauss points as nodes in the 
> finite element since deal.II will assume that the stress degrees of freedom 
> are associated with the nodes. For now I don't believe this is too strict 
> of a limitation for me since I will likely choose the quadrature rule such 
> that the number of quadrature points is equal to the number of nodes 
> anyways. Perhaps there is a better way to handle this situation but I will 
> try this for now. Thanks again!
>
> Jonathan
>
> On Wednesday, March 7, 2018 at 11:04:33 AM UTC-5, Bruno Turcksin wrote:
>>
>> Jonathan,
>>
>> 2018-03-07 10:43 GMT-05:00 Jonathan Russ :
>>
>>>
>>> Thank you for your fast reply. I'm sorry I'm not doing a great job of 
>>> explaining this. Here is an example from elasticity that illustrates what I 
>>> would like:
>>> In this case there are displacement degrees of freedom at the nodes but 
>>> the stress is a quantity typically derived from the displacements. However, 
>>> one could make the stress an independent degree of freedom at the gauss 
>>> points. 
>>>
>>> So, in the element there would be displacement degrees of freedom at the 
>>> nodes and stress degrees of freedom at the gauss points. Does this make 
>>> sense?
>>>
>> I don't think there is a way to do that in deal unless you can split your 
>> finite elements, i.e., you have one FE_Q for the displacement and another 
>> FE_Q for the stress. Then, you can use FESystem. But do I understand 
>> correctly that the stress is not describe by any finite element but you 
>> would like to use dof_handler to help you manage some data. In that case, I 
>> think that using a FESystem should work, you just will never call FEValues 
>> for the stress since you don't care about the associated finite element but 
>> the dof_handler will associate a degree of freedom to each quadrature point.
>>
>> Best,
>>
>> Bruno
>>
>
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Re: [deal.II] FE w/ Gauss Point DoFs

2018-03-07 Thread Jean-Paul Pelteret 
Dear Jonathan,

Is FE_DGQArbitraryNodes 
 
perhaps what you’re looking for? From the documentation:

> The primary purpose of this class is to provide an element for which the mass 
> matrix can be made diagonal by choosing basis functions that are not either 
> zero or one at the vertices of the cell, but instead are zero or one at a 
> given set of quadrature points.


J-P

> On 07 Mar 2018, at 18:09, Jonathan Russ  wrote:
> 
> Bruno -
> 
> Thank you for your help. I see what you are saying. In this way I would need 
> to make sure I have the same number of gauss points as nodes in the finite 
> element since deal.II will assume that the stress degrees of freedom are 
> associated with the nodes. For now I don't believe this is too strict of a 
> limitation for me since I will likely choose the quadrature rule such that 
> the number of quadrature points is equal to the number of nodes anyways. 
> Perhaps there is a better way to handle this situation but I will try this 
> for now. Thanks again!
> 
> Jonathan
> 
> On Wednesday, March 7, 2018 at 11:04:33 AM UTC-5, Bruno Turcksin wrote:
> Jonathan,
> 
> 2018-03-07 10:43 GMT-05:00 Jonathan Russ :
> 
> Thank you for your fast reply. I'm sorry I'm not doing a great job of 
> explaining this. Here is an example from elasticity that illustrates what I 
> would like:
> In this case there are displacement degrees of freedom at the nodes but the 
> stress is a quantity typically derived from the displacements. However, one 
> could make the stress an independent degree of freedom at the gauss points. 
> 
> So, in the element there would be displacement degrees of freedom at the 
> nodes and stress degrees of freedom at the gauss points. Does this make sense?
> I don't think there is a way to do that in deal unless you can split your 
> finite elements, i.e., you have one FE_Q for the displacement and another 
> FE_Q for the stress. Then, you can use FESystem. But do I understand 
> correctly that the stress is not describe by any finite element but you would 
> like to use dof_handler to help you manage some data. In that case, I think 
> that using a FESystem should work, you just will never call FEValues for the 
> stress since you don't care about the associated finite element but the 
> dof_handler will associate a degree of freedom to each quadrature point.
> 
> Best,
> 
> Bruno
> 
> -- 
> The deal.II project is located at http://www.dealii.org/ 
> 
> For mailing list/forum options, see 
> https://groups.google.com/d/forum/dealii?hl=en 
> 
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[deal.II] FE w/ Gauss Point DoFs

2018-03-07 Thread Jonathan Russ 
Hello -

I apologize since this question is likely obvious to most, but a quick 
search didn't reveal the answer to me. 

Is there a FiniteElement in deal.II that allows the addition of degrees of 
freedom at gauss points so that the DoFHandler object also manages them? 
For example, I would like to have just a standard Lagrangian finite element 
interpolated with the plain bilinear shape functions for nodal degrees of 
freedom but I also have a single degree of freedom at each gauss point 
within the element (and, consequently, residual equations at each gauss 
point in each element). Is this possible in deal.II to have degrees of 
freedom not associated with nodes?

Thank you in advance for your help,
Jonathan

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