Re: [deal.II] evaluating basis functions at random points

[Wolfgang Bangerth]

On 12/15/21 10:51, Andrea Bonito wrote:


Thanks, seems to do exactly what I want... except it is not implemented 
for co-dim = 1
(by the way, I do not see where the dimensions are relevant for this 
process).


We'd gladly see a patch that fixes this :-)

The challenge is that in the codim>0 case, a point isn't unambiguously 
going to lie in a cell: You need to extend the pull-back to points that 
aren't on the manifold, and then project back onto the dim-dimensional 
reference manifold. I don't think this is *particularly* difficult, but 
it needs to be done.


Best
 W.

--

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

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Re: [deal.II] evaluating basis functions at random points

[Andrea Bonito]

Daniel:

Thanks, seems to do exactly what I want... except it is not implemented for 
co-dim = 1 
(by the way, I do not see where the dimensions are relevant for this 
process).

Anyway, it looks likes this function is doing what I was planning to do (in 
an optimized way), i.e. for each location point, find the active cell 
iterator containing the point and the associated the reference point.
I can then use this info to create a quadrature / fe_value and assemble the 
matrix as usual. 

Best,
Andrea
On Monday, December 13, 2021 at 3:55:14 PM UTC-6 d.arnd...@gmail.com wrote:

> Andrea,
>
> have a look at GridTools::compute_point_locations(
> https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a8e8bb9211264d2106758ac4d7184117e
> ).
> Step-60 demonstrates its use.
>
> Best,
> Daniel
>
> Am Mo., 13. Dez. 2021 um 16:14 Uhr schrieb Andrea Bonito  >:
>
>> Howdy:
>>
>> this might be a simple question but I do not seem to find a way to 
>> efficiently evaluate basis functions at random points. More precisely, I am 
>> given random points in my computational domain and I need to assemble the 
>> terms 
>>
>> phi_i(p) phi_j(p)  for all random points p and all i,j =1,..., n_dofs. 
>>
>> As of now, I am going cell by cell and check whether p is inside the cell 
>> (including the boundary). If it is, I am creating a quadrature with one 
>> point in the reference cell (using the mapping).
>>
>> I am sure one of you has a better way... any help would be appreciated.
>>
>> Andrea
>>
>> -- 
>> 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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>>  
>> 
>> .
>>
>

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Re: [deal.II] evaluating basis functions at random points

[Daniel Arndt]

Andrea,

have a look at GridTools::compute_point_locations(
https://www.dealii.org/developer/doxygen/deal.II/namespaceGridTools.html#a8e8bb9211264d2106758ac4d7184117e
).
Step-60 demonstrates its use.

Best,
Daniel

Am Mo., 13. Dez. 2021 um 16:14 Uhr schrieb Andrea Bonito :

> Howdy:
>
> this might be a simple question but I do not seem to find a way to
> efficiently evaluate basis functions at random points. More precisely, I am
> given random points in my computational domain and I need to assemble the
> terms
>
> phi_i(p) phi_j(p)  for all random points p and all i,j =1,..., n_dofs.
>
> As of now, I am going cell by cell and check whether p is inside the cell
> (including the boundary). If it is, I am creating a quadrature with one
> point in the reference cell (using the mapping).
>
> I am sure one of you has a better way... any help would be appreciated.
>
> Andrea
>
> --
> 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
> ---
> You received this message because you are subscribed to the Google Groups
> "deal.II User Group" group.
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> To view this discussion on the web visit
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> 
> .
>

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[deal.II] evaluating basis functions at random points

[Andrea Bonito]

Howdy:

this might be a simple question but I do not seem to find a way to 
efficiently evaluate basis functions at random points. More precisely, I am 
given random points in my computational domain and I need to assemble the 
terms 

phi_i(p) phi_j(p)  for all random points p and all i,j =1,..., n_dofs. 

As of now, I am going cell by cell and check whether p is inside the cell 
(including the boundary). If it is, I am creating a quadrature with one 
point in the reference cell (using the mapping).

I am sure one of you has a better way... any help would be appreciated.

Andrea

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