Transforming a cartesian mesh

Using GeometryGrid, one can transform an existing mesh into a different shape. This is particularly useful for modelling complex geometries based on efficient structured grids like YaspGrid.

A grid transformation is a user-defined function which gives the transformation of a point x in the base cartesian grid to a final geometry:

\( y = F(x) : \Omega -> \hat \Omega. \)

First, let's set up a rectangular grid:

  const unsigned int dim = 2;
  Dune::FieldVector<double,dim> L = {4.0,2.0};
  std::array<int,dim> N ={64,32};
 
  typedef Dune::YaspGrid<dim> SquareGrid;
  SquareGrid sgrid(L,N);

Then, lets define a function that maps the grid to a new geometry:

template <int dim>
class GridTransformation
: public Dune :: AnalyticalCoordFunction< double, dim, dim, GridTransformation <dim> >{
    typedef GridTransformation This;
    typedef Dune :: AnalyticalCoordFunction< double, dim, dim, This > Base;
 
    public:
    typedef typename Base :: DomainVector DomainVector;
    typedef typename Base :: RangeVector RangeVector;
 
    GridTransformation(){}
 
    void evaluate(const DomainVector &x, RangeVector &y) const{
        y = x;
        if(x[0] < 0.8)
            y[1] = (1.0 + 5.0/4.0 * (sin(M_PI/18.0) - 1.0) * x[0]) * (x[1] - 1.0);
        else
            y[1] = sin((x[0] - 0.6)/3.6 * M_PI) * (x[1] - 1.0);
        if(x[0] > 3.8)
            y[0] += 0.5*(x[0] - 3.8) * (1.0 - pow(x[1] - 1.0, 2.0));
    }
};

Finally, lets map our initial grid using the GridTransformation we defined:

  typedef GridTransformation<dim> GridTransformation;
  GridTransformation gTrafo;
 
  typedef typename Dune::GeometryGrid<SquareGrid,GridTransformation> Grid;
  Grid grid(sgrid,gTrafo);

Full example code: recipe-geometry-grid.cc