Thanks Daniel.

I will try the first approach. My time dependent Function class returns an 
update and not a new value. Actually, I am trying to solve a free surface 
flow problem with moving mesh(for very small displacements). I am 
implementing the flow and mesh movement in a decoupled way. So at the end 
of every time step I get the flow solution(velocity and pressure). So I 
advect(displace) the free surface vertices as (U_{t_n} + 
U_{t_{n+1}})*time_step/2. This is the incremental displacement which I want 
to add to previous displacements. I use this free surface boundary 
displacements to solve for the interior vertices displacements using a 
simple 'laplacian'(which is linear and thus laplacian_system_matrix is 
assembled only once). And finally apply these displacements to the entire 
(initial)mesh. 
Of course all this can be done using just incremental displacements instead 
of cumulative displacement(as I am moving the mesh anyway at every time 
step), I just want to try with cumulative.

I will revert for any further clarifications. 

Thanks,
Bhanu.

On Monday, December 4, 2017 at 4:54:11 PM UTC+5:30, Daniel Arndt wrote:
>
> Bhanu,
>
> [...]
>>       VectorTools::interpolate_boundary_values(move_dof_handler, 106, 
>> move_boundary_values_function, move_boundary_values);
>>       MatrixTools::apply_boundary_values(move_boundary_values, 
>> move_system_matrix, move_solution, move_system_rhs);
>>
>> instead of 'constraints'. 
>> Now, I have to add the current time step dirichlet values to the 
>> 'previous cumulative dirichlet values at this boundary' in my 
>> 'move_boundary_values_function' object of type  'template <int dim> class 
>> MoveBoundaryValues106 : public Function<dim>'. How can I accomplish this in 
>> my member function
>>
>>   template <int dim>
>>   void  MoveBoundaryValues106<dim>::vector_value(const Point<dim> &p, 
>> Vector<double> &values) const
>>   {
>>     // std::vector<Tensor<1,dim>> 
>> previouscumulative(n_boundary_dofs_of_type_106);
>>       const double time = this->get_time();
>>       previuouscumulative += get_function_values();
>>
>>       values[0] = previouscumulative[];
>>       values[1] = previouscumulative[];
>>       values[2] = previouscumulative[];
>>       values[3] = previouscumulative[]; 
>>   }
>>
> So you have a time-dependent Function class that only returns an update 
> instead of the new value?
> In this case, I would still call 
>
>    VectorTools::interpolate_boundary_values(move_dof_handler, 106, 
> move_boundary_values_function, move_boundary_values_update);
>
> and add to the previous vector
>
> for (auto& it=move_boundary_values.begin(); 
> it!=move_boundary_values.end(); ++it)
>   it->second += move_boundary_values_update[it->first];
>
> Since move_boundary_values are also just the boundary values for your 
> previous solution, you could also compute move_boundary_values on the fly
> by extracting the boundary DoFs using DoFTools::extract_boundary_dofs 
> <https://www.dealii.org/8.5.1/doxygen/deal.II/namespaceDoFTools.html#ad3067f335a97de429176178689222f3a>
>  
> and accessing the respective values in the solution vector, i.e.
>
> for (const IndexSet::ElementIterator& it=boundary_dofs.begin(); 
> it!=boundary_dofs.end(); ++it)
>   move_boundary_values[*it] = solution(*it) + 
> move_boundary_values_update[*it];
>
> This is also the approach you would need to use if you want to refine your 
> mesh between time steps.
>
> All of this would of course be much simpler if your Function class would 
> simply return the actual values and not just an update.
>
> Best,
> Daniel

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