Iterating over a grid

A fundamental task in many finite element-type discretizations is iterating over the elements of a grid, for example in order to numerically compute integrals on it. All DUNE grids provide a unified interface for this and related operations.

First, we set up a simple structured grid. Here we use the Dune::YaspGrid class in four dimensions in order to demonstrate that even dimension larger than three can be used.

  const int dim = 4;
  using Grid = Dune::YaspGrid<dim>;
  Dune::FieldVector<double,dim> len; for (auto& l : len) l=1.0;
  std::array<int,dim> cells; for (auto& c : cells) c=4;
  Grid grid(len,cells);

Grids in Dune are hierachical, i.e. they are organized into levels (originating from refinement) and entities that are not further refined. Each of these subsets is accessible via Dune::GridView and iteration over is possible only over grid views. So we extract the Dune::LeafGridView:

  auto gv = grid.leafGridView();

Now we can iterate over all the entities of a certain codimension in a grid view using a range-based for loop:

  const int codim = 2;
  for (const auto& e : entities(gv,Dune::Codim<codim>{}))
    if (!e.type().isCube()) std::cout << "not a cube" << std::endl;

As an example we extract the type of an element and test for it to be a cube.

Instead of specifying the codimension explicitly you can also use the following predefined names in the range-based for loop:

  for ([[maybe_unused]] const auto& e : elements(gv)); // codim=0
  for ([[maybe_unused]] const auto& e : vertices(gv)); // codim=dim
  for ([[maybe_unused]] const auto& e : edges(gv));    // codim=dim-1
  for ([[maybe_unused]] const auto& e : facets(gv));   // codim=1

Finally, from entities of codimension 0 (aka elements) you can access all subentities of all codimensions using the following code:

  const int mycodim = 2;
  for (const auto& e : elements(gv))
    for (unsigned int i=0; i<e.subEntities(mycodim); ++i)
      [[maybe_unused]] auto v = e.template subEntity<codim>(i);

Full example code: recipe-iterate-over-grid.cc