Dear Prof. Bangerth,
Thank you for the guidance and correction.
I got the point now that for Neuman conditions I shall iterate for face
cells along desired edge for imposing condition like in the previous case
of step-8. I also went through the step-7, thank you for the guidance it
made me understand more about the face_cell_values for making rhs. As far
as I have understood the step-7 is iterating through each cell and
implementing simply the Neuman condition at the face cells:
for (; cell!=endc; ++cell)
{
cell_matrix = 0;
cell_rhs = 0;
fe_values.reinit
<https://www.dealii.org/current/doxygen/deal.II/classFEValues.html#aec8f5b8b3e4c5dcf35dfd029a1ecbbd0>
(cell);
right_hand_side.value_list (fe_values.get_quadrature_points
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#a5f8732ebe2d3c6746f6de26a79cb1e45>
(),
rhs_values);
for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
for (unsigned int i=0; i<dofs_per_cell; ++i)
{
for (unsigned int j=0; j<dofs_per_cell; ++j)
cell_matrix(i,j) += ((fe_values.shape_grad
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ac4cee7628c2903a89c5c399fddeb00a5>(i,q_point)
*
fe_values.shape_grad
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ac4cee7628c2903a89c5c399fddeb00a5>
(j,q_point)
+
fe_values.shape_value
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#abe4de48ff59778bb82a0ec13037804aa>(i,q_point)
*
fe_values.shape_value
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#abe4de48ff59778bb82a0ec13037804aa>(j,q_point))
*
fe_values.JxW
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ad097580a2f71878695096cc73b271b9d>
(q_point));
cell_rhs(i) += (fe_values.shape_value
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#abe4de48ff59778bb82a0ec13037804aa>(i,q_point)
*
rhs_values [q_point] *
fe_values.JxW
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ad097580a2f71878695096cc73b271b9d>
(q_point));
}
for (unsigned int face_number=0;
face_number<GeometryInfo<dim>::faces_per_cell; ++face_number)
if (cell->face(face_number)->at_boundary()
&&
(cell->face(face_number)->boundary_id() == 1))
{
fe_face_values.reinit
<https://www.dealii.org/current/doxygen/deal.II/classFEFaceValues.html#af6e079ca7429d54433343d50bd334c3c>
(cell, face_number);
for (unsigned int q_point=0; q_point<n_face_q_points; ++q_point)
{
const double neumann_value
= (exact_solution.gradient (fe_face_values.quadrature_point
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ab1aa3aa2940125b47df95ff82ad733b9>(q_point))
*
fe_face_values.normal_vector
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#a130eea0fa89263d93b20521addc830c7>
(q_point));
for (unsigned int i=0; i<dofs_per_cell; ++i)
cell_rhs(i) += (neumann_value *
fe_face_values.shape_value
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#abe4de48ff59778bb82a0ec13037804aa>(i,q_point)
*
fe_face_values.JxW
<https://www.dealii.org/current/doxygen/deal.II/classFEValuesBase.html#ad097580a2f71878695096cc73b271b9d>
(q_point));
}
}
cell->get_dof_indices (local_dof_indices);
for (unsigned int i=0; i<dofs_per_cell; ++i)
{
for (unsigned int j=0; j<dofs_per_cell; ++j)
system_matrix.add (local_dof_indices[i],
local_dof_indices[j],
cell_matrix(i,j));
system_rhs(local_dof_indices[i]) += cell_rhs(i);
}
}
*But the step-26 which I am now concerned about is directly forming rhs
somehow using the function:*
RightHandSide<dim> rhs_function;
rhs_function.set_time(time);
VectorTools::create_right_hand_side(dof_handler,
QGauss<dim>(fe.degree+1),
rhs_function,
tmp);
So how can I possibly implement heat flux on cell faces in this example
case step-26 ? If I can, then I guess my problem is solved to learn
implementing Neuman BC for Heat equation in deal.ii. Thank you very much in
advance?
On Wednesday, April 10, 2019 at 5:56:46 AM UTC+2, Wolfgang Bangerth wrote:
>
> On 4/9/19 10:01 AM, Muhammad Mashhood wrote:
> > I want to apply the heat flux BC on one of the edge instead i.e. *dU(t,
> x,
> > y=1)/dy* at top. For this so far I could only find a method to make a
> heat
> > source using the already present function as follows:
>
> I don't know how you use the class you implement, but I would try to avoid
> all
> confusion by naming the class RightHandSide: This is the name we generally
> use
> for forcing terms of the differential equation, and not for the right hand
> side of boundary conditions.
>
> Just like for your previous question, it is not correct to "convert" the
> right
> hand side of a boundary condition into a right hand side of the equation.
> This
> is mathematically not correct and will not lead to the correct solution.
>
> Have you looked at step-7? This program deals with Neumann boundary
> conditions
> and may have exactly what you are looking for.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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