Constant differential operators
There exist two ways to apply a differential operator to a variable.
First, one can use a local stiffness matrix as follows:
Local_stiffness_matrix<double> loc_m(grid); .... f = loc_m(u);
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.
HandbookLast modified: Mon Feb 7 16:19:57 MET 2000