How to find the cell index by using global dof index

[Lance Zhang]

Hello team,

may I know how to find the cell index with the information of its global Dofs index?

I have the global dofs index ,I would like to find which cell this global dof belongs to.

Thanks in advance!

Best regards

Lance

[Daniel Arndt]

Lance,

Have a look at GridTools::vertex_to_cell_map(https://www.dealii.org/current/doxygen/deal.II/namespaceGridTools.html#a9b7e2ca8ecd26a472e5225ba91a58acb).

Best,

Daniel

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[Lance Zhang]

Hello Daniel,

thanks for your message.

I know how to find the cell index.

Could I ask one more question?

The question is about the grid.

In code I used the function below to create the grid.

 template <int dim>

  Point<dim> grid_y_transform (const Point<dim> &pt_in)

  {

    const double &x = pt_in[0];

    const double &y = pt_in[1];

    Point<dim> pt_out = pt_in;

    return pt_out;

  }

  template <int dim,typename NumberType>

  void Solid<dim,NumberType>::make_grid()

  {

    // Divide the beam, but only along the x- and y-coordinate directions

    std::vector< unsigned int > repetitions(dim, parameters.elements_per_edge);

    // Only allow one element through the thickness

    // (modelling a plane strain condition)

    if (dim == 3){

     repetitions[dim-1] = 8;

    

    //repetitions[0] = 0;

    //repetitions[1] = 2;

    //repetitions[2] = 2;

    }

    repetitions[1] = 8;

    repetitions[2] = 8;

        const Point<dim> top_right =Point<dim>(0.0, 0.0, -10); 

        const Point<dim> bottom_left =Point<dim>(40,20, 10);

        GridGenerator::subdivided_hyper_rectangle(triangulation,

                                              repetitions,

                                              bottom_left,

                                              top_right);

    // Since we wish to apply a Neumann BC to the right-hand surface, we

    // must find the cell faces in this part of the domain and mark them with

    // a distinct boundary ID number. The faces we are looking for are on the

    // +x surface and will get boundary ID 11.

    // Dirichlet boundaries exist on the left-hand face of the beam (this fixed

    // boundary will get ID 1) and on the +Z and -Z faces (which correspond to

    // ID 2 and we will use to impose the plane strain condition)

    const double tol_boundary = 1e-6;

    typename Triangulation<dim>::active_cell_iterator cell =

      triangulation.begin_active(), endc = triangulation.end();

for (; cell != endc; ++cell)

      for (unsigned int face = 0;

           face < GeometryInfo<dim>::faces_per_cell; ++face)

        if (cell->face(face)->at_boundary() == true)

          {

            if (std::abs(cell->face(face)->center()[0] - 0.0) < tol_boundary)

              cell->face(face)->set_boundary_id(1); // -X faces

            else if (std::abs(cell->face(face)->center()[0] - 40.0) < tol_boundary)

              cell->face(face)->set_boundary_id(11); // +X faces

            else if (dim == 3 && std::abs(std::abs(cell->face(face)->center()[2]) - 10) < tol_boundary)

              cell->face(face)->set_boundary_id(2); // +Z and -Z faces

          }

    // Transform the hyper-rectangle into the beam shape

    GridTools::transform(&grid_y_transform<dim>, triangulation);

    GridTools::scale(parameters.scale, triangulation);

    vol_reference = GridTools::volume(triangulation);

    vol_current = vol_reference;

    std::cout << "Grid:\n\t Reference volume: " << vol_reference << std::endl;

  }

My question is whether I can use NURBS to create the same grids and how I could create the grids with the NURBS.

Thanks in advance!

Best regards

Lance

Daniel Arndt <d.arnd...@gmail.com> 于 2023年12月4日周一 16:08写道：

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[Wolfgang Bangerth]

On 12/6/23 15:06, Lance Zhang wrote:
> My question is whether I can use NURBS to create the same grids and how I
> could create the grids with the NURBS.

Can you explain what you mean by this? NURBS are basis functions, a mesh is a
subdivision of a domain into cells. These are not the same thing, so it is not
clear to me what exactly it is you want to do.

Best
WB

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