Hello everyone,

I am using deal.ii to solve a 3D solid mechanics problem. My code uses 
PetSc and P4est.

The geometry is a cubical box [0 1] X [0 1] X [0 1] with a uniform 
rectilinear mesh in the domain.

I have obtained the scalar solution vector u in the domain.

I need to find the line integral of the solution along the boundary. For 
example: lets say
I want to integrate the solution variable
\int u dx on the line which is on +z face and goes from from (0,0,1) to 
(1,0,1).

Can someone please help to figure out how to do this? In the pseudo code, 
my doubt is how to initialize
the fe_face_values (line values?) object and the gauss quadrature formula 
for this?

integral = 0;

for (; cell != endc; ++cell)
        if (cell->is_locally_owned())
        {
          for (face = 0; face<GeometryInfo<dim::faces_per_cell;++face)
                if(cell->face(face)->boundary_id == my_boundary_id) // 
normal facing the -y direction: bottom face
                     for (line = 0; 
face<GeometryInfo<dim::lines_per_face;++line)
                           if (cell->face(face)->line(line)->center()(2) == 
1) // boundary line needed
                              for (q = 0; q < number_of_q_points; ++q)
                             integral += function_value_at_q * 
fe_face_values.JxW(q);
        }
integral = SUM of integral from all processes


Thanks.

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