Dear community
in case of use, I attempted to write a small code that seems to solve the
issue of linking manifold cells to volume cells.
As first, two maps are defined:
*// maps*
*// the map surface_to_volumefaces_mapping contains the outcome of the
method extract_boundary_mesh and connects*
*// panels from the manifold triangulation to the faces on the boundary
of the volume triangulation.*
*// the map manifoldcells_to_volumecells_mapping pairs surface panels
from the manifold triangulation*
*// to the cells of the volume triangulation. It is used in the method
pair_the_triangulations().*
*//*
std::map<
*typename* parallel::shared::Triangulation<manifold_dim
,dim>::cell_iterator,
*typename* parallel::shared::Triangulation<dim>::face_iterator
>
surface_to_volumefaces_mapping;
std::map<
*typename* parallel::shared::Triangulation<manifold_dim
,dim>::cell_iterator,
*typename* parallel::shared::Triangulation<dim>::cell_iterator
>
manifoldcells_to_volumecells_mapping;
then the manifold grid is generated
*//*
*// Surface triangulation definition*
*//*
*this*->pcout << "\n Generation of surface discretization ... " << std
::flush;
surface_to_volumefaces_mapping = GridGenerator::extract_boundary_mesh (
*this*->triangulation, *this*->manifold_triangulation );
*this*->manifold_triangulation.set_all_manifold_ids(0);
*this*->manifold_dof_handler.distribute_dofs ( *this*->manifold_fe );
*this*->manifold_accumulated_solution.reinit (
*this*->manifold_dof_handler.n_dofs()
);
*this*->manifold_former_step_solution.reinit (
*this*->manifold_dof_handler.n_dofs()
);
*this*->manifold_initial_guess.reinit (
*this*->manifold_dof_handler.n_dofs()
);
*this*->pcout << " done \n" << std::flush;
*//*
*// Surface triangulation and volume triangulation pairing*
*//*
pair_the_triangulations();
In the method pair_the_triangulations() a manifold cell is linked to the
corresponding volume cell for parallel::shared::triangulations as follows.
pair_the_triangulations ( *bool* write_map_report )
*//*
*// this function associates each*
*// surface panel to the volume cell from which it emanates.*
*// the map manifoldcells_to_volumecells_mapping contains the pair
surface/volume panels*
*//*
{
*// unsigned face_counter = 0;*
*this*->pcout << "pairing the two triangulations ... " << std::flush;
*// loop through the volumetric triangulation*
*typename* parallel::shared::Triangulation<dim>::active_cell_iterator
cell = *this*->triangulation.begin_active (),
endc = *this*->triangulation.end();
*for* (; cell!=endc; ++cell)
*// We do not seek for locally_owned on the volumetric triangulation*
{
*// debug*
*// this->pcout << " new cell " << cell->id() << " " << std::flush;*
*// select a face at boundary*
*for* (*unsigned* *int* face_number=0;
face_number<GeometryInfo<dim>::faces_per_cell;
++face_number)
{
*const* *typename* parallel::shared::Triangulation<dim>::face_iterator
face = cell->face( face_number );
*if* ( face->at_boundary() )
{
*// scan the surface_to_volumefaces_mapping and*
*// associate maifold panels to volume panels*
*typename*
std::map< *typename* parallel::shared::Triangulation<manifold_dim
,dim>::cell_iterator,
*typename* parallel::shared::Triangulation<dim>::face_iterator >
::iterator
map_it = surface_to_volumefaces_mapping.begin(),
map_end = surface_to_volumefaces_mapping.end() ;
*for* (; map_it!=map_end; ++map_it)
*if* ( face == map_it->second )
{
*// debug*
*// this->pcout << cell->face_index(face_number) << ", " <<
std::flush;*
*// face_counter++;*
manifoldcells_to_volumecells_mapping[ map_it->first ] = cell ;
}
}
}
}
*// debug*
*// this->pcout << "\n I found " << face_counter << " faces. \n bye. \n
" << std::flush;*
*// map report*
*if* ( write_map_report )
{
*typename* std::map< *typename* parallel::shared::Triangulation<
manifold_dim,dim>::cell_iterator,
*typename* parallel::shared::Triangulation<dim>::cell_iterator >
::iterator
manifoldcells_to_volumecells_it =
manifoldcells_to_volumecells_mapping.begin()
,
manifoldcells_to_volumecells_end =
manifoldcells_to_volumecells_mapping.end()
;
*this*->pcout << "\n map report: " << std::flush;
*for* (;
manifoldcells_to_volumecells_it!=manifoldcells_to_volumecells_end;
++manifoldcells_to_volumecells_it)
*this*->pcout << "[ " << manifoldcells_to_volumecells_it->first->*id*()
<< ", " << manifoldcells_to_volumecells_it->second->*id*() << " ], " << std
::flush;
*this*->pcout << "\n done. \n" << std::flush;
}
*// debug*
*// std::exit( 0 );*
}
Comments and suggestions are very welcome.
Thank you in advance
Alberto
Il giorno sabato 7 settembre 2019 12:09:30 UTC+2, Alberto Salvadori ha
scritto:
>
> Dear community
>
> I apologize if the question was too generic. I attempt here to be more
> precise, asking for some suggestions.
>
> In solving a Laplace-Beltrami problem on an advecting surface one should
> identify the Gauss points on the manifold dim-1 cell and retrieve at such
> locations relevant information from the solution of the advection problem,
> using the dim dof_handler of the volume. I wonder how to connect a manifold
> dim-1 cell to the volumetric cell it was extracted from. The
> GridGenerator::extract_boundary_mesh method seem to provide some
> information, since "it returns A map that for each cell of the surface mesh
> (key) returns an iterator to the corresponding face of a cell of the volume
> mesh (value). " . I am not sure how I can use this map to link a manifold
> cell to the corresponding volume cell.
>
> Any help is very much appreciated. Thanks!
>
> Alberto
>
>
>
> Il giorno martedì 3 settembre 2019 18:36:59 UTC+2, Alberto Salvadori ha
> scritto:
>>
>> Dear community
>>
>> I am trying to find a good way to deal with the following problem.
>>
>> I am interested in a Laplace-Beltrami simulation (say with unknown scalar
>> field c) on a surface that advects (with displacement field u) enclosesing
>> a volume of say elastic material.
>> The two problems are per se uncoupled, but for the geometrical evolution.
>> In this regard, one may solve separately for displacements in the volume
>> and for c on the surface, once the latter is informed on the displacement
>> field (and related gradients) on the surface nodes (and Gauss points).
>> Extracting the surface mesh from the volume is quite simple. Which is
>> though the best way to extract (project) the displacement solution on the
>> boundary? Any suggestion/ hint?
>>
>> Many thanks,
>> Alberto
>>
>
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