How to add addtional point to enrichment functions (FE_Enriched)

[Edith Sotelo]

Hello,

I would like to implement enrichment functions of this type: f(x-xo) where xo is a user defined point. It could be the center of the cell or the dof coordinate.

I would like a suggestion about how to implement this, because I do not see how to pass it in the constructor since it is not a static point.I think it has to be  during the assembly step, but FE_values call the enrich function with a single argument (the quadrature point). 

What sould be a way to do pass the addtional point?

Thank you for you help.

[Denis Davydov]

Hi Edith,

f(x-x0) is just your enrichment function derived from dealii::Function. So define a class which takes that extra parameter (or any number of them) and use it with FE_Enriched.

Assuming that your bilinear form needs gradients, then you would need to implement gradients of your custom function so that FE_Enriched can work out chain rule for you.

Cheers,

Denis.

[Edith Sotelo]

Hi Denis,

Thank you for your answer but I still need to further understand some things :  

* I think I need to pass the point (xo) during assembly since it will different for different cells ( dof coordinate or center of the cell), and I do not see how I can pass the point when declaring the function (ex. Enrichment <dim> (param1,param2, etc...) ) to create the  FE_Enriched constructor, maybe I am missing something here.

*  The thing is that  during assembly the functions are already encapsulated  in the “enrichments” vector and if I even  create a member function like Enrichment<dim>::get_point(Point<dim> & ) how do I apply it to the functions that are already in the “enrichments” vector ? Maybe I can make  the “enrichments” vector  public?...

Thank you for your help

Edith

--
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 a topic in the Google Groups "deal.II User Group" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/dealii/fFbITWIMW5M/unsubscribe.
To unsubscribe from this group and all its topics, send an email to dealii+un...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

Edith

[Denis Davydov]

2 нояб. 2017 г., в 2:50, Edith Sotelo <eso...@tamu.edu> написал(а):

Hi Denis,

Thank you for your answer but I still need to further understand some things :  

* I think I need to pass the point (xo) during assembly since it will different for different cells ( dof coordinate or center of the cell),

Unless you work with discontinuous Galerkin, then you need to be careful with how you use PUM.

If you take a global view of the shape functions and enrich each of them with a a given function, it will be extremely tedious to pull of. 

I don’t know what you are trying to do, but I suggest to draw a 1D sketch with a global view to linear shape-functions and the enriched functions (shape functions times enrichments), try to number them and see what constraints you should have on DoFs to make your FE space continuous.

and I do not see how I can pass the point when declaring the function (ex. Enrichment <dim> (param1,param2, etc...) ) to create

See below

the  FE_Enriched constructor, maybe I am missing something here.

*  The thing is that  during assembly the functions are already encapsulated  in the “enrichments” vector and if I even  create a member function like Enrichment<dim>::get_point(Point<dim> & ) how do I apply it to the functions that are already in the “enrichments” vector ? Maybe I can make  the “enrichments” vector  public?...

Writing out of head (there could be typos): 

template <int dim>

class MyFavoriteEnrichment : public dealii::Function<dim >

{

public:

   MyFavoriteEnrichment(const Point<dim> &x0);

}

is what u need.

Look at implementation of any dealii’s functions.

[Edith Sotelo]

Hi  Denis,

Thank you for answering my (odd) questions...

I think I meant that I do not see how I could pass a point that is calculated during assembly when constructing the enrichments functions. So to pass the point during assembly I think I need to get to the enrichment functions that are already in the “enrichments” vector,  and this is a protected  member of the FE_Enriched class … so I was thinking to make it public…  maybe you have a different suggestion...

I want to do this to try a couple of things..

* I want to test a function like this : Cos ( z) with  z=sqrt ( (x-xo)^2 + (y-yo)^2), where  (xo, yo) is the point I need to pass..

* I would like to implement the  kronecker delta property: f(x)-f(xi) where xi is the coordinate of the dof

 and I was also thinking that I would probably need to work with DG methods. But I can try the 1D test you suggested first to find out the continuity of my functions

Thank you for your help.

Edith

[Denis Davydov]

Hi Edith,

On 2 Nov 2017, at 15:46, Edith Sotelo <sotelo...@gmail.com> wrote:

Hi  Denis,

Thank you for answering my (odd) questions...

I think I meant that I do not see how I could pass a point that is calculated during assembly when constructing the enrichments functions. So to pass the point during

what do you **have to** calculate this point during assembly? If it’s just a support point of the FE basis or a vertex, surely you can get it prior to assembly.

You can also use pointers to a Point<dim> in your custom function and then modify the value outside.

[Edith Sotelo]

Hey Denis,

I think I was not clear enough in describing what I want to do . I apologize, that’s my bad. I hope the next lines explain it better

I want to implement Ni*F(x-xi) or   Ni*[F(x)-F(xi)]  for the enrichment part

where:

Ni is the i-th standard basis function,

F is a enrichment function ,

xi is the dof coordinate of the i-th standard basis function.

That’s why I think  I need to look for the corresponding xi point  during assembly… 

Thank you for your patience.

[Denis Davydov]

Hi Edith,

On 2 Nov 2017, at 20:08, Edith Sotelo <sotelo...@gmail.com> wrote:

Hey Denis,

I think I was not clear enough in describing what I want to do . I apologize, that’s my bad. I hope the next lines explain it better

I want to implement Ni*F(x-xi) or   Ni*[F(x)-F(xi)]  for the enrichment part

(below I assume you have the same FE for enriched and non-enriched parts).

If you have a FE space spanned by { Ni(x), Ni(x) * F(x-xi) } then it essentially means you have a different enrichment function for each DoF.

You might as well write it as  {Ni(x), Ni(x) * Fi (x) }   where Fi(x) := F(x-xi)

That won’t work with FE_Enriched because a single function F(x) is used to enrich all DoFs on the element.

There is no mechanism to selectively pick up a single DoF. You would have to do this manually.

If you need to enrich only a hand-full of all DoFs (say 10 out of 100000) each with a different function, 

then you can try to work out the chain-rule in your bilinear forms manually. That’s easy but tedious, see https://github.com/dealii/dealii/blob/master/tests/fe/fe_enriched_step-36b.cc#L455-L590

which implements PUM without FE_Enriched.

What is worse is managing FE_Collection and figuring out all the constraints to keep continuous FE space. 

On each element you would go  local_dof -> global_dof -> enrichment_function.

I guess it’s doable, but not trivial in implementation.

The second case you have a space spanned by { Ni(x), Ni(x) * [F(x) - F(xi)] } \equiv {Ni(x), Ni(x) * F(x) } is perfectly doable with FE_Enriched.

Regards,

Denis.

[Denis Davydov]

On 2 Nov 2017, at 20:45, Denis Davydov <davy...@gmail.com> wrote:

Hi Edith,

On 2 Nov 2017, at 20:08, Edith Sotelo <sotelo...@gmail.com> wrote:

Hey Denis,

I think I was not clear enough in describing what I want to do . I apologize, that’s my bad. I hope the next lines explain it better

I want to implement Ni*F(x-xi) or   Ni*[F(x)-F(xi)]  for the enrichment part

(below I assume you have the same FE for enriched and non-enriched parts).

If you have a FE space spanned by { Ni(x), Ni(x) * F(x-xi) } then it essentially means you have a different enrichment function for each DoF.

You might as well write it as  {Ni(x), Ni(x) * Fi (x) }   where Fi(x) := F(x-xi)

That won’t work with FE_Enriched because a single function F(x) is used to enrich all DoFs on the element.

There is no mechanism to selectively pick up a single DoF. You would have to do this manually.

If you need to enrich only a hand-full of all DoFs (say 10 out of 100000) each with a different function, 

then you can try to work out the chain-rule in your bilinear forms manually. That’s easy but tedious, see https://github.com/dealii/dealii/blob/master/tests/fe/fe_enriched_step-36b.cc#L455-L590

which implements PUM without FE_Enriched.

What is worse is managing FE_Collection and figuring out all the constraints to keep continuous FE space. 

p.s. constraints are actually simpler in this case. For scalar problem you only need two components in FE_System — one for enriched DoFs and one for standard.

[Edith Sotelo]

Hello Denis,

Coming back to this. I think it is still possible to use the FE-Enriched class..  My idea is to  access the “enrichments” class variable that contains the enrichments functions. However this variable is protected. 

Whatever solution I think of to  access this variable , it ends up modifying the class, which I think it is not the idea. (to make it public, to  declare a friend class/function) 

My final idea is to implement a get_point (Point<dim>  &) function in my enrichment function class and be able to apply it to the enrichments stored in the “enrichments” FE_Enriched class variable, something  similar to what you did in the “multiply_by_enrichment” FE_Enriched member function.

I will appreciate any suggestion regarding this and thank you for your help.

Edith

[Edith Sotelo]

Hello again,

My solution:  I just made a local copy of FE_Enriched.cc and .h and I am including in my main program the local the Enriched.h 

Still have to implement the rest, maybe more questions to come…

thank you for your help,

Edith

Edith