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