Degrees of Freedom

The distribution and numbering of degrees of freedom (dofs) are handled by the DofHandler. The DofHandler will be used to query information about the dofs. For example we can obtain the dofs for a particular cell, which we need when assembling the system.

The DofHandler is based on the grid. Here we create a simple grid with Triangle cells, and then create a DofHandler based on the grid

grid = generate_grid(Triangle, (20, 20))
dh = DofHandler(grid)

DofHandler{2, Grid{2, Triangle, Float64}}
  Fields:
  Not closed!

Fields

Before we can distribute the dofs we need to specify fields. A field is simply the unknown function(s) we are solving for. To add a field we need a name (a Symbol) and the the interpolation describing the shape functions for the field. Here we add a scalar field :p, interpolated using linear (degree 1) shape functions on a triangle, and a vector field :u, also interpolated with linear shape functions on a triangle, but raised to the power 2 to indicate that it is a vector field with 2 components (for a 2D problem).

add!(dh, :p, Lagrange{RefTriangle, 1}())
add!(dh, :u, Lagrange{RefTriangle, 1}()^2)

DofHandler{2, Grid{2, Triangle, Float64}}
  Fields:
    :p, Lagrange{RefTriangle, 1}()
    :u, Lagrange{RefTriangle, 1}()^2
  Not closed!  Not closed!

Finally, when we have added all the fields, we have to close! the DofHandler. When the DofHandler is closed it will traverse the grid and distribute all the dofs for the fields we added.

close!(dh)

DofHandler{2, Grid{2, Triangle, Float64}}
  Fields:
    :p, Lagrange{RefTriangle, 1}()
    :u, Lagrange{RefTriangle, 1}()^2
  Dofs per cell: 9
  Total dofs: 1323

Ordering of Dofs