Integration over the boundary

Let us consider a bilinear form which integrates over the boundary.

The local stiffness mnatrix corresponding to such a bilinear form is constructed by the member function

   Local_stiffness_matrix<double> local_stiff_bo(grid);
   local_stiff_m.Calculate_boundary(expression_bilinear_form);

where expression_bilinear_form is an expression describing the integrand in the bilinear form using the notation in Colsamm.

To explain this in more detail, let u,f be a variables and let

   Local_stiffness_matrix<double> helm_boundary(grid);
   helm_boundary.Calculate_boundary(v_()*w_());
   f = helm_boundary(u);

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

Example: The measure of the surface of the discretization domain is:

Local_stiffness_matrix<double> helm_boundary(grid);

  helm_boundary.Calculate_boundary(v_()*w_());
  Variable<double> one;
  Variable<double> u;

  one = 1.0;
  u = 0.0;
  u =  helm_boundary(one);
  cout << " surface: " << product(u,one) << endl;
     

Last modified: Fri Feb 11 09:18:59 MET 2000