Differential Operators

Constant differential operators

There exist two ways to apply a differential operator to a variable.

  1. First, one can use a local stiffness matrix as follows:

         Local_stiffness_matrix<double> loc_m(grid); 
         ....
         f = loc_m(u);
  1. Second, one can use a stencil matrix as follows:

         Sten_matrix<double, Stencil_variable> stencil(grid); 
         ....
         f = stencil(u);

Example:

Let u,v be a variable of type Variable<double> and let

Local_stiffness_matrix<double> Laplace(grid);

   Laplace.Calculate(grad(v_())*grad(w_()));
   f = Laplace(u);

Furthermore, let be the nodal basis function with respect to the grid point . Then, the following equation holds:



Differential operator with variable coefficient (not implemented up to now)

To the differential operator of a local stiffness matrix corresponds a differential operator with a variable coefficient. This variable coefficient might be defined by a Variable or a Variable_cell . Let op be a differential operator and a such a variable. Then,

op.var(a)

is a differential operator with variable coefficient.

Handbook

Last modified: Mon Feb 7 16:19:57 MET 2000