If my understanding of how dofs are numbered is correct. Essentially what I
want to do is
std::vector<bool> boundary_dofs (dof_handler.n_dofs(), false);
DoFTools::extract_boundary_dofs (dof_handler, ComponentMask(),
boundary_dofs);
constraints.clear();
for (unsigned int i = dofs_per_block[0] + dofs_per_block[1]; i <
dof_handler.n_dofs(); ++i)
{
if(boundary_dofs[i] == true)
{
constraints.add_line (i);
\\ find 'corresponding_U_dof' of 'W_dof' with index 'i' according
to above said criterion
constraints.add_entry (i, corresponding_U_dof, 1);
}
}
constraints.close ();
So I want a way to find 'corresponding_U_dof' from 'W_dof' with index 'i'.
Or please suggest any other way to achieve this.
Thanks,
Bhanu Teja.
On Friday, April 20, 2018 at 12:45:51 PM UTC+5:30, Bhanu Teja wrote:
>
> Thanks Prof Bangerth,
> I overlooked it. I had Q2 for U and Q1 for W in mind when I was building
> the code and writing the query. With this combination I guess the criterion
> satisfies as 'Q1, dim' has dofs present on geometric vertices and same
> with' Q2, dim' (along with mid points of edges and some in the interior
> depending on the dimension). I am planning to use this combination for some
> time. I will sure read the paper. In this case can you suggest how to build
> the constraints? Or should I necessarily use 'FE_Q_Hierarchical'? Can you
> direct me to any tutorial or any reading material in which
> 'FE_Q_Hierarchical' is used.
>
> Thanks,
> Bhanu Teja.
>
> On Friday, April 20, 2018 at 3:40:01 AM UTC+5:30, Wolfgang Bangerth wrote:
>>
>>
>> Bhanu,
>>
>> > In my application, the FESystem is 'fe(FE_Q<dim>(degree+1), dim,
>> > FE_Q<dim>(degree), 1, FE_Q<dim>(degree), dim)'. As you can see there
>> are
>> > three unknown solution variables(lets call them U, p and W), in which
>> > the first and last are vector valued with 'dim' components and the
>> first
>> > one is one degree higher than the last. The boundary
>> > condition/constraint I have is 'W = U' in every component at a
>> > particular boundary with boundary_id. (U dof is present at every W dof
>> > as U is one degree higher than W, but not the other way).
>>
>> This is not actually true, and it's going to make the algorithm you are
>> seeking substantially more complicated. Think about a Q3 element for U
>> and a Q2 element for W: U has nodes at 1/3 and 2/3 along each edge, but
>> W has nodes only at the midpoint of each edge.
>>
>> So the algorithm you're seeking cannot be as simple as set some degrees
>> of freedom equal to others, and the rest to zero. Rather, the problem
>> you want to solve is in essence what one does in hp finite element
>> methods where you have a Q3 and a Q2 element coming together at one
>> edge. You may want to read the paper I wrote with Oliver Kayser-Herold
>> many years ago about this.
>>
>> An alternative could be to use FE_Q_Hierarchical instead. That one,
>> truly, satisfies the property you describe and would make construction
>> of these constraints easier.
>>
>> Best
>> W.
>>
>> --
>> ------------------------------------------------------------------------
>> Wolfgang Bangerth email: [email protected]
>> www: http://www.math.colostate.edu/~bangerth/
>>
>
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