<h3>Specific improvements</h3>
<ol>
+ <li>
+ New: The method VectorTools::compute_normal_flux_constraints can be used to
+ force a vector finite element function to be normal to the boundary.
+ <br>
+ (Martin Kronbichler, 2013/08/23)
+ </li>
+
<li>
Improved: MappingQ now uses the points of the Gauss-Lobatto quadrature
formula as support points instead of equispaced ones. This allows its use
/**
- * Compute the constraints that
- * correspond to boundary conditions of
- * the form $\vec n \cdot \vec u=0$,
- * i.e. no normal flux if $\vec u$ is a
- * vector-valued quantity. These
- * conditions have exactly the form
- * handled by the ConstraintMatrix class,
- * so instead of creating a map between
- * boundary degrees of freedom and
- * corresponding value, we here create a
- * list of constraints that are written
- * into a ConstraintMatrix. This object
- * may already have some content, for
- * example from hanging node constraints,
- * that remains untouched. These
- * constraints have to be applied to the
- * linear system like any other such
- * constraints, i.e. you have to condense
- * the linear system with the constraints
- * before solving, and you have to
- * distribute the solution vector
- * afterwards.
- *
- * The use of this function is
- * explained in more detail in
- * step-31. It
- * doesn't make much sense in 1d,
- * so the function throws an
- * exception in that case.
- *
- * The second argument of this
- * function denotes the first
- * vector component in the finite
- * element that corresponds to
- * the vector function that you
- * want to constrain. For
- * example, if we were solving a
- * Stokes equation in 2d and the
- * finite element had components
- * $(u,v,p)$, then @p
- * first_vector_component would
- * be zero. On the other hand, if
- * we solved the Maxwell
- * equations in 3d and the finite
- * element has components
- * $(E_x,E_y,E_z,B_x,B_y,B_z)$
- * and we want the boundary
- * condition $\vec n\cdot \vec
- * B=0$, then @p
- * first_vector_component would
- * be 3. Vectors are implicitly
- * assumed to have exactly
- * <code>dim</code> components
- * that are ordered in the same
- * way as we usually order the
- * coordinate directions,
- * i.e. $x$-, $y$-, and finally
- * $z$-component. The function
- * assumes, but can't check, that
- * the vector components in the
- * range
- * <code>[first_vector_component,first_vector_component+dim)</code>
- * come from the same base finite
- * element. For example, in the
- * Stokes example above, it would
- * not make sense to use a
- * <code>FESystem@<dim@>(FE_Q@<dim@>(2),
- * 1, FE_Q@<dim@>(1), dim)</code>
- * (note that the first velocity
- * vector component is a $Q_2$
- * element, whereas all the other
- * ones are $Q_1$ elements) as
- * there would be points on the
- * boundary where the
- * $x$-velocity is defined but no
- * corresponding $y$- or
- * $z$-velocities.
- *
- * The third argument denotes the set of
- * boundary indicators on which the
- * boundary condition is to be
- * enforced. Note that, as explained
- * below, this is one of the few
- * functions where it makes a difference
- * where we call the function multiple
- * times with only one boundary
- * indicator, or whether we call the
- * function onces with the whole set of
- * boundary indicators at once.
- *
- * The mapping argument is used to
- * compute the boundary points where the function
- * needs to request the normal vector $\vec n$
- * from the boundary description.
- *
- * @note When combining adaptively
- * refined meshes with hanging node
- * constraints and boundary conditions
- * like from the current function within
- * one ConstraintMatrix object, the
- * hanging node constraints should always
- * be set first, and then the boundary
- * conditions since boundary conditions
- * are not set in the second operation on
- * degrees of freedom that are already
- * constrained. This makes sure that the
- * discretization remains conforming as
- * is needed. See the discussion on
- * conflicting constraints in the module
- * on @ref constraints .
+ * Compute the constraints that correspond to boundary conditions of the
+ * form $\vec n \cdot \vec u=0$, i.e. no normal flux if $\vec u$ is a
+ * vector-valued quantity. These conditions have exactly the form handled by
+ * the ConstraintMatrix class, so instead of creating a map between boundary
+ * degrees of freedom and corresponding value, we here create a list of
+ * constraints that are written into a ConstraintMatrix. This object may
+ * already have some content, for example from hanging node constraints,
+ * that remains untouched. These constraints have to be applied to the
+ * linear system like any other such constraints, i.e. you have to condense
+ * the linear system with the constraints before solving, and you have to
+ * distribute the solution vector afterwards.
+ *
+ * The use of this function is explained in more detail in step-31. It
+ * doesn't make much sense in 1d, so the function throws an exception in
+ * that case.
+ *
+ * The second argument of this function denotes the first vector component
+ * in the finite element that corresponds to the vector function that you
+ * want to constrain. For example, if we were solving a Stokes equation in
+ * 2d and the finite element had components $(u,v,p)$, then @p
+ * first_vector_component would be zero. On the other hand, if we solved the
+ * Maxwell equations in 3d and the finite element has components
+ * $(E_x,E_y,E_z,B_x,B_y,B_z)$ and we want the boundary condition $\vec
+ * n\cdot \vec B=0$, then @p first_vector_component would be 3. Vectors are
+ * implicitly assumed to have exactly <code>dim</code> components that are
+ * ordered in the same way as we usually order the coordinate directions,
+ * i.e. $x$-, $y$-, and finally $z$-component. The function assumes, but
+ * can't check, that the vector components in the range
+ * <code>[first_vector_component,first_vector_component+dim)</code> come
+ * from the same base finite element. For example, in the Stokes example
+ * above, it would not make sense to use a
+ * <code>FESystem@<dim@>(FE_Q@<dim@>(2), 1, FE_Q@<dim@>(1), dim)</code>
+ * (note that the first velocity vector component is a $Q_2$ element,
+ * whereas all the other ones are $Q_1$ elements) as there would be points
+ * on the boundary where the $x$-velocity is defined but no corresponding
+ * $y$- or $z$-velocities.
+ *
+ * The third argument denotes the set of boundary indicators on which the
+ * boundary condition is to be enforced. Note that, as explained below, this
+ * is one of the few functions where it makes a difference where we call the
+ * function multiple times with only one boundary indicator, or whether we
+ * call the function onces with the whole set of boundary indicators at
+ * once.
+ *
+ * The mapping argument is used to compute the boundary points where the
+ * function needs to request the normal vector $\vec n$ from the boundary
+ * description.
+ *
+ * @note When combining adaptively refined meshes with hanging node
+ * constraints and boundary conditions like from the current function within
+ * one ConstraintMatrix object, the hanging node constraints should always
+ * be set first, and then the boundary conditions since boundary conditions
+ * are not set in the second operation on degrees of freedom that are
+ * already constrained. This makes sure that the discretization remains
+ * conforming as is needed. See the discussion on conflicting constraints in
+ * the module on @ref constraints .
*
*
* <h4>Computing constraints in 2d</h4>
*
- * Computing these constraints requires
- * some smarts. The main question
- * revolves around the question what the
- * normal vector is. Consider the
- * following situation:
- * <p ALIGN="center">
- * @image html no_normal_flux_1.png
+ * Computing these constraints requires some smarts. The main question
+ * revolves around the question what the normal vector is. Consider the
+ * following situation: <p ALIGN="center"> @image html no_normal_flux_1.png
* </p>
*
- * Here, we have two cells that use a
- * bilinear mapping
- * (i.e. MappingQ1). Consequently, for
- * each of the cells, the normal vector
- * is perpendicular to the straight
- * edge. If the two edges at the top and
- * right are meant to approximate a
- * curved boundary (as indicated by the
- * dashed line), then neither of the two
- * computed normal vectors are equal to
- * the exact normal vector (though they
- * approximate it as the mesh is refined
- * further). What is worse, if we
- * constrain $\vec n \cdot \vec u=0$ at
- * the common vertex with the normal
- * vector from both cells, then we
- * constrain the vector $\vec u$ with
- * respect to two linearly independent
- * vectors; consequently, the constraint
- * would be $\vec u=0$ at this point
- * (i.e. <i>all</i> components of the
- * vector), which is not what we wanted.
- *
- * To deal with this situation, the
- * algorithm works in the following way:
- * at each point where we want to
- * constrain $\vec u$, we first collect
- * all normal vectors that adjacent cells
- * might compute at this point. We then
- * do not constrain $\vec n \cdot \vec
- * u=0$ for <i>each</i> of these normal
- * vectors but only for the
- * <i>average</i> of the normal
- * vectors. In the example above, we
- * therefore record only a single
- * constraint $\vec n \cdot \vec {\bar
- * u}=0$, where $\vec {\bar u}$ is the
- * average of the two indicated normal
- * vectors.
- *
- * Unfortunately, this is not quite
- * enough. Consider the situation here:
+ * Here, we have two cells that use a bilinear mapping
+ * (i.e. MappingQ1). Consequently, for each of the cells, the normal vector
+ * is perpendicular to the straight edge. If the two edges at the top and
+ * right are meant to approximate a curved boundary (as indicated by the
+ * dashed line), then neither of the two computed normal vectors are equal
+ * to the exact normal vector (though they approximate it as the mesh is
+ * refined further). What is worse, if we constrain $\vec n \cdot \vec u=0$
+ * at the common vertex with the normal vector from both cells, then we
+ * constrain the vector $\vec u$ with respect to two linearly independent
+ * vectors; consequently, the constraint would be $\vec u=0$ at this point
+ * (i.e. <i>all</i> components of the vector), which is not what we wanted.
+ *
+ * To deal with this situation, the algorithm works in the following way: at
+ * each point where we want to constrain $\vec u$, we first collect all
+ * normal vectors that adjacent cells might compute at this point. We then
+ * do not constrain $\vec n \cdot \vec u=0$ for <i>each</i> of these normal
+ * vectors but only for the <i>average</i> of the normal vectors. In the
+ * example above, we therefore record only a single constraint $\vec n \cdot
+ * \vec {\bar u}=0$, where $\vec {\bar u}$ is the average of the two
+ * indicated normal vectors.
+ *
+ * Unfortunately, this is not quite enough. Consider the situation here:
*
* <p ALIGN="center">
* @image html no_normal_flux_2.png
* </p>
*
- * If again the top and right edges
- * approximate a curved boundary, and the
- * left boundary a separate boundary (for
- * example straight) so that the exact
- * boundary has indeed a corner at the
- * top left vertex, then the above
- * construction would not work: here, we
- * indeed want the constraint that $\vec
- * u$ at this point (because the normal
- * velocities with respect to both the
- * left normal as well as the top normal
- * vector should be zero), not that the
- * velocity in the direction of the
- * average normal vector is zero.
- *
- * Consequently, we use the following
- * heuristic to determine whether all
- * normal vectors computed at one point
- * are to be averaged: if two normal
- * vectors for the same point are
- * computed on <i>different</i> cells,
- * then they are to be averaged. This
- * covers the first example above. If
- * they are computed from the same cell,
- * then the fact that they are different
- * is considered indication that they
- * come from different parts of the
- * boundary that might be joined by a
- * real corner, and must not be averaged.
- *
- * There is one problem with this
- * scheme. If, for example, the same
- * domain we have considered above, is
- * discretized with the following mesh,
- * then we get into trouble:
+ * If again the top and right edges approximate a curved boundary, and the
+ * left boundary a separate boundary (for example straight) so that the
+ * exact boundary has indeed a corner at the top left vertex, then the above
+ * construction would not work: here, we indeed want the constraint that
+ * $\vec u$ at this point (because the normal velocities with respect to
+ * both the left normal as well as the top normal vector should be zero),
+ * not that the velocity in the direction of the average normal vector is
+ * zero.
+ *
+ * Consequently, we use the following heuristic to determine whether all
+ * normal vectors computed at one point are to be averaged: if two normal
+ * vectors for the same point are computed on <i>different</i> cells, then
+ * they are to be averaged. This covers the first example above. If they are
+ * computed from the same cell, then the fact that they are different is
+ * considered indication that they come from different parts of the boundary
+ * that might be joined by a real corner, and must not be averaged.
+ *
+ * There is one problem with this scheme. If, for example, the same domain
+ * we have considered above, is discretized with the following mesh, then we
+ * get into trouble:
*
* <p ALIGN="center">
* @image html no_normal_flux_3.png
* </p>
*
- * Here, the algorithm assumes that the
- * boundary does not have a corner at the
- * point where faces $F1$ and $F2$ join
- * because at that point there are two
- * different normal vectors computed from
- * different cells. If you intend for
- * there to be a corner of the exact
- * boundary at this point, the only way
- * to deal with this is to assign the two
- * parts of the boundary different
- * boundary indicators and call this
- * function twice, once for each boundary
- * indicators; doing so will yield only
- * one normal vector at this point per
- * invocation (because we consider only
- * one boundary part at a time), with the
- * result that the normal vectors will
- * not be averaged.
+ * Here, the algorithm assumes that the boundary does not have a corner at
+ * the point where faces $F1$ and $F2$ join because at that point there are
+ * two different normal vectors computed from different cells. If you intend
+ * for there to be a corner of the exact boundary at this point, the only
+ * way to deal with this is to assign the two parts of the boundary
+ * different boundary indicators and call this function twice, once for each
+ * boundary indicators; doing so will yield only one normal vector at this
+ * point per invocation (because we consider only one boundary part at a
+ * time), with the result that the normal vectors will not be averaged.
*
*
* <h4>Computing constraints in 3d</h4>
*
- * The situation is more
- * complicated in 3d. Consider
- * the following case where we
- * want to compute the
- * constraints at the marked
- * vertex:
+ * The situation is more complicated in 3d. Consider the following case
+ * where we want to compute the constraints at the marked vertex:
*
* <p ALIGN="center">
* @image html no_normal_flux_4.png
* </p>
*
- * Here, we get four different
- * normal vectors, one from each
- * of the four faces that meet at
- * the vertex. Even though they
- * may form a complete set of
- * vectors, it is not our intent
- * to constrain all components of
- * the vector field at this
- * point. Rather, we would like
- * to still allow tangential
- * flow, where the term
- * "tangential" has to be
- * suitably defined.
- *
- * In a case like this, the
- * algorithm proceeds as follows:
- * for each cell that has
- * computed two tangential
- * vectors at this point, we
- * compute the unconstrained
- * direction as the outer product
- * of the two tangential vectors
- * (if necessary multiplied by
- * minus one). We then average
- * these tangential
- * vectors. Finally, we compute
- * constraints for the two
- * directions perpendicular to
- * this averaged tangential
- * direction.
- *
- * There are cases where one cell
- * contributes two tangential
- * directions and another one
- * only one; for example, this
- * would happen if both top and
- * front faces of the left cell
- * belong to the boundary
- * selected whereas only the top
- * face of the right cell belongs
- * to it. This case is not
- * currently implemented.
+ * Here, we get four different normal vectors, one from each of the four
+ * faces that meet at the vertex. Even though they may form a complete set
+ * of vectors, it is not our intent to constrain all components of the
+ * vector field at this point. Rather, we would like to still allow
+ * tangential flow, where the term "tangential" has to be suitably defined.
+ *
+ * In a case like this, the algorithm proceeds as follows: for each cell
+ * that has computed two tangential vectors at this point, we compute the
+ * unconstrained direction as the outer product of the two tangential
+ * vectors (if necessary multiplied by minus one). We then average these
+ * tangential vectors. Finally, we compute constraints for the two
+ * directions perpendicular to this averaged tangential direction.
+ *
+ * There are cases where one cell contributes two tangential directions and
+ * another one only one; for example, this would happen if both top and
+ * front faces of the left cell belong to the boundary selected whereas only
+ * the top face of the right cell belongs to it. This case is not currently
+ * implemented.
*
*
* <h4>Results</h4>
*
- * Because it makes for good
- * pictures, here are two images
- * of vector fields on a circle
- * and on a sphere to which the
- * constraints computed by this
+ * Because it makes for good pictures, here are two images of vector fields
+ * on a circle and on a sphere to which the constraints computed by this
* function have been applied:
*
* <p ALIGN="center">
* @image html no_normal_flux_6.png
* </p>
*
- * The vectors fields are not
- * physically reasonable but the
- * tangentiality constraint is
- * clearly enforced. The fact
- * that the vector fields are
- * zero at some points on the
- * boundary is an artifact of the
- * way it is created, it is not
- * constrained to be zero at
- * these points.
+ * The vectors fields are not physically reasonable but the tangentiality
+ * constraint is clearly enforced. The fact that the vector fields are zero
+ * at some points on the boundary is an artifact of the way it is created,
+ * it is not constrained to be zero at these points.
*
* @ingroup constraints
*
ConstraintMatrix &constraints,
const Mapping<dim, spacedim> &mapping = StaticMappingQ1<dim>::mapping);
+ /**
+ * Compute the constraints that correspond to boundary conditions of the
+ * form $\vec n \times \vec u=0$, i.e. flow normal to the boundary if $\vec
+ * u$ is a vector-valued quantity. This function constrains exactly those
+ * vector-valued components that are left unconstrained by
+ * compute_no_normal_flux_constraints, and leaves the one component
+ * unconstrained that is constrained by compute_no_normal_flux_constraints.
+ */
+ template <int dim, template <int, int> class DH, int spacedim>
+ void
+ compute_normal_flux_constraints (const DH<dim,spacedim> &dof_handler,
+ const unsigned int first_vector_component,
+ const std::set<types::boundary_id> &boundary_ids,
+ ConstraintMatrix &constraints,
+ const Mapping<dim, spacedim> &mapping = StaticMappingQ1<dim>::mapping);
+
//@}
/**
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/base/std_cxx1x/array.h>
#include <numeric>
#include <algorithm>
#include <vector>
}
}
- // Create the system
- // matrix by
- // multiplying the
- // assembling matrix
- // with its transposed
- // and the right
- // hand side vector
- // by mutliplying
- // the assembling
- // matrix with the
- // assembling vector.
- // Invert the system
- // matrix.
+ // Create the system matrix by multiplying the assembling matrix
+ // with its transposed and the right hand side vector by mutliplying
+ // the assembling matrix with the assembling vector. Invert the
+ // system matrix.
assembling_matrix.mTmult (cell_matrix, assembling_matrix);
cell_matrix_inv.invert (cell_matrix);
assembling_matrix.vmult (cell_rhs, assembling_vector);
}
}
- // Now we do the
- // same as above
- // with the vertical
- // shape functions
- // instead of the
- // horizontal ones.
+ // Now we do the same as above with the vertical shape functions
+ // instead of the horizontal ones.
for (unsigned int q_point = 0;
q_point < fe_values.n_quadrature_points; ++q_point)
{
ConstraintMatrix &constraints,
const Mapping<dim> &mapping)
{
- // Projection-based interpolation
- // is performed in two (in 2D)
- // respectively three (in 3D)
- // steps. First the tangential
- // component of the function is
- // interpolated on each edge. This
- // gives the values for the degrees
- // of freedom corresponding to the
- // edge shape functions. Now we are
- // done for 2D, but in 3D we possibly
- // have also degrees of freedom, which
- // are located in the interior of
- // the faces. Therefore we compute
- // the residual of the function
- // describing the boundary values
- // and the interpolated part, which
- // we have computed in the last
- // step. On the faces there are
- // two kinds of shape functions,
- // the horizontal and the vertical
- // ones. Thus we have to solve two
- // linear systems of equations of
- // size <tt>degree * (degree +
- // 1)<tt> to obtain the values for
- // the corresponding degrees of
- // freedom.
+ // Projection-based interpolation is performed in two (in 2D) respectively
+ // three (in 3D) steps. First the tangential component of the function is
+ // interpolated on each edge. This gives the values for the degrees of
+ // freedom corresponding to the edge shape functions. Now we are done for
+ // 2D, but in 3D we possibly have also degrees of freedom, which are
+ // located in the interior of the faces. Therefore we compute the residual
+ // of the function describing the boundary values and the interpolated
+ // part, which we have computed in the last step. On the faces there are
+ // two kinds of shape functions, the horizontal and the vertical
+ // ones. Thus we have to solve two linear systems of equations of size
+ // <tt>degree * (degree + 1)<tt> to obtain the values for the
+ // corresponding degrees of freedom.
const unsigned int superdegree = dof_handler.get_fe ().degree;
const QGauss<dim - 1> reference_face_quadrature (2 * superdegree);
const unsigned int dofs_per_face = dof_handler.get_fe ().dofs_per_face;
for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell; ++face)
if (cell->face (face)->boundary_indicator () == boundary_component)
{
- // if the FE is a
- // FE_Nothing object
- // there is no work to
- // do
+ // if the FE is a FE_Nothing object there is no work to do
if (dynamic_cast<const FE_Nothing<dim>*> (&cell->get_fe ()) != 0)
return;
- // This is only
- // implemented, if the
- // FE is a Nedelec
- // element. If the FE is
- // a FESystem we cannot
- // check this.
+ // This is only implemented, if the FE is a Nedelec
+ // element. If the FE is a FESystem we cannot check this.
if (dynamic_cast<const FESystem<dim>*> (&cell->get_fe ()) == 0)
{
typedef FiniteElement<dim> FEL;
for (unsigned int face = 0; face < GeometryInfo<dim>::faces_per_cell; ++face)
if (cell->face (face)->boundary_indicator () == boundary_component)
{
- // if the FE is a
- // FE_Nothing object
- // there is no work to
- // do
+ // if the FE is a FE_Nothing object there is no work to do
if (dynamic_cast<const FE_Nothing<dim>*> (&cell->get_fe ()) != 0)
return;
- // This is only
- // implemented, if the
- // FE is a Nedelec
- // element. If the FE is
- // a FESystem we cannot
- // check this.
+ // This is only implemented, if the FE is a Nedelec
+ // element. If the FE is a FESystem we cannot check this.
if (dynamic_cast<const FESystem<dim>*> (&cell->get_fe ()) == 0)
{
typedef FiniteElement<dim> FEL;
first_vector_component,
dof_values, dofs_processed);
- // If there are higher
- // order shape
- // functions, there is
- // still some work
- // left.
+ // If there are higher order shape functions, there is still
+ // some work left.
if (degree > 0)
internals
::compute_face_projection_curl_conforming (cell, face, fe_face_values,
namespace internals
{
- // This function computes the
- // projection of the boundary
- // function on the boundary
- // in 2d.
+ // This function computes the projection of the boundary function on the
+ // boundary in 2d.
template <typename cell_iterator>
void
compute_face_projection_div_conforming (const cell_iterator &cell,
const std::vector<DerivativeForm<1,2,2> > &jacobians,
ConstraintMatrix &constraints)
{
- // Compute the intergral over
- // the product of the normal
- // components of the boundary
- // function times the normal
- // components of the shape
- // functions supported on the
- // boundary.
+ // Compute the intergral over the product of the normal components of
+ // the boundary function times the normal components of the shape
+ // functions supported on the boundary.
const FEValuesExtractors::Vector vec (first_vector_component);
const FiniteElement<2> &fe = cell->get_fe ();
const std::vector<Point<2> > &normals = fe_values.get_normal_vectors ();
values (fe_values.n_quadrature_points, Vector<double> (2));
Vector<double> dof_values (fe.dofs_per_face);
- // Get the values of the
- // boundary function at the
- // quadrature points.
+ // Get the values of the boundary function at the quadrature points.
{
const std::vector<Point<2> > &
quadrature_points = fe_values.get_quadrature_points ();
cell->face (face)->get_dof_indices (face_dof_indices, cell->active_fe_index ());
- // Copy the computed values
- // in the ConstraintMatrix only,
- // if the degree of freedom is
- // not already constrained.
+ // Copy the computed values in the ConstraintMatrix only, if the degree
+ // of freedom is not already constrained.
for (unsigned int i = 0; i < fe.dofs_per_face; ++i)
if (!(constraints.is_constrained (face_dof_indices[i])))
{
}
}
- // dummy implementation of above
- // function for all other
- // dimensions
+ // dummy implementation of above function for all other dimensions
template<int dim, typename cell_iterator>
void
compute_face_projection_div_conforming (const cell_iterator &,
Assert (false, ExcNotImplemented ());
}
- // This function computes the
- // projection of the boundary
- // function on the boundary
- // in 3d.
+ // This function computes the projection of the boundary function on the
+ // boundary in 3d.
template<typename cell_iterator>
void
compute_face_projection_div_conforming (const cell_iterator &cell,
std::vector<double> &dof_values,
std::vector<types::global_dof_index> &projected_dofs)
{
- // Compute the intergral over
- // the product of the normal
- // components of the boundary
- // function times the normal
- // components of the shape
- // functions supported on the
- // boundary.
+ // Compute the intergral over the product of the normal components of
+ // the boundary function times the normal components of the shape
+ // functions supported on the boundary.
const FEValuesExtractors::Vector vec (first_vector_component);
const FiniteElement<3> &fe = cell->get_fe ();
const std::vector<Point<3> > &normals = fe_values.get_normal_vectors ();
+ namespace
+ {
+ template <int dim>
+ struct PointComparator
+ {
+ bool operator ()(const std_cxx1x::array<types::global_dof_index,dim> &p1,
+ const std_cxx1x::array<types::global_dof_index,dim> &p2)
+ {
+ for (unsigned int d=0; d<dim; ++d)
+ if (p1[d] < p2[d])
+ return true;
+ return false;
+ }
+ };
+ }
+
+
+
+ template <int dim, template <int, int> class DH, int spacedim>
+ void
+ compute_normal_flux_constraints (const DH<dim,spacedim>&dof_handler,
+ const unsigned int first_vector_component,
+ const std::set<types::boundary_id> &boundary_ids,
+ ConstraintMatrix &constraints,
+ const Mapping<dim, spacedim> &mapping)
+ {
+ ConstraintMatrix no_normal_flux_constraints(constraints.get_local_lines());
+ compute_no_normal_flux_constraints (dof_handler,
+ first_vector_component,
+ boundary_ids,
+ no_normal_flux_constraints,
+ mapping);
+
+ // Extract a list that collects all vector components that belong to the
+ // same node (scalar basis function). When creating that list, we use an
+ // array of dim components that stores the global degree of freedom.
+ std::set<std_cxx1x::array<types::global_dof_index,dim>, PointComparator<dim> > vector_dofs;
+ std::vector<types::global_dof_index> face_dofs;
+
+ std::vector<std_cxx1x::array<types::global_dof_index,dim> > cell_vector_dofs;
+ for (typename DH<dim,spacedim>::active_cell_iterator cell =
+ dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
+ if (!cell->is_artificial())
+ for (unsigned int face_no=0; face_no < GeometryInfo<dim>::faces_per_cell;
+ ++face_no)
+ if (boundary_ids.find(cell->face(face_no)->boundary_indicator())
+ != boundary_ids.end())
+ {
+ const FiniteElement<dim> &fe = cell->get_fe();
+ typename DH<dim,spacedim>::face_iterator face=cell->face(face_no);
+
+ // get the indices of the dofs on this cell...
+ face_dofs.resize (fe.dofs_per_face);
+ face->get_dof_indices (face_dofs, cell->active_fe_index());
+
+ unsigned int n_scalar_indices = 0;
+ cell_vector_dofs.resize(fe.dofs_per_face);
+ for (unsigned int i=0; i<fe.dofs_per_face; ++i)
+ if (fe.face_system_to_component_index(i).first >= first_vector_component &&
+ fe.face_system_to_component_index(i).first < first_vector_component + dim)
+ {
+ n_scalar_indices =
+ std::max(n_scalar_indices,
+ fe.face_system_to_component_index(i).second);
+ cell_vector_dofs[fe.face_system_to_component_index(i).second]
+ [fe.face_system_to_component_index(i).first-first_vector_component]
+ = face_dofs[i];
+ }
+
+ // now we identified the vector indices on the cell, so next
+ // insert them into the set (it would be expensive to directly
+ // insert incomplete points into the set)
+ for (unsigned int i=0; i<n_scalar_indices; ++i)
+ vector_dofs.insert(cell_vector_dofs[i]);
+ }
+
+ // iterate over the list of all vector components we found and see if we
+ // can find constrained ones
+ for (typename std::set<std_cxx1x::array<unsigned int,dim>,PointComparator<dim> >::
+ const_iterator it=vector_dofs.begin(); it!=vector_dofs.end(); ++it)
+ {
+ unsigned int n_constraints = 0;
+ bool is_constrained[dim];
+ for (unsigned int d=0; d<dim; ++d)
+ if (no_normal_flux_constraints.is_constrained((*it)[d]))
+ {
+ is_constrained[d] = true;
+ ++n_constraints;
+ }
+ else
+ is_constrained[d] = false;
+ if (n_constraints > 0 && n_constraints < dim)
+ {
+ // if more than one no-flux constraint is present, no normal flux
+ // can be set on the boundary
+ if (n_constraints > 1)
+ {
+ for (unsigned int d=0; d<dim; ++d)
+ constraints.add_line((*it)[d]);
+ continue;
+ }
+
+ // ok, this is a no-flux constraint, so get the index of the dof
+ // that is currently constrained and make it unconstrained. The
+ // constraint indices will get the normal that contain the other
+ // indices.
+ Tensor<1,dim> normal;
+ unsigned constrained_index = -1;
+ for (unsigned int d=0; d<dim; ++d)
+ if (is_constrained[d])
+ {
+ constrained_index = d;
+ normal[d] = 1.;
+ }
+ const std::vector<std::pair<unsigned int, double> >* constrained
+ = no_normal_flux_constraints.get_constraint_entries((*it)[constrained_index]);
+ // find components to which this index is constrained to
+ Assert(constrained != 0, ExcInternalError());
+ Assert(constrained->size() < dim, ExcInternalError());
+ for (unsigned int c=0; c<constrained->size(); ++c)
+ {
+ int index = -1;
+ for (unsigned int d=0; d<dim; ++d)
+ if ((*constrained)[c].first == (*it)[d])
+ index = d;
+ Assert (index != -1, ExcInternalError());
+ normal[index] = (*constrained)[c].second;
+ }
+ for (unsigned int d=0; d<dim; ++d)
+ {
+ if (is_constrained[d])
+ continue;
+ const unsigned int new_index = (*it)[d];
+ if (!constraints.is_constrained(new_index))
+ {
+ constraints.add_line(new_index);
+ if (std::abs(normal[d]) > 1e-13)
+ constraints.add_entry(new_index, (*it)[constrained_index],
+ -normal[d]);
+ }
+ }
+ }
+ }
+ }
+
+
+
namespace internal
{
template <int dim, int spacedim>
--- /dev/null
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2007 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+
+// check the creation of normal flux boundary conditions for a finite
+// element that consists of only a single set of vector components
+// (i.e. it has dim components). Similar as the no-flux test in no_flux_01.cc
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_q1.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+ const FiniteElement<dim> &fe)
+{
+ DoFHandler<dim> dof(tr);
+ dof.distribute_dofs(fe);
+
+ for (unsigned int i=0; i<GeometryInfo<dim>::faces_per_cell; ++i)
+ {
+ deallog << "FE=" << fe.get_name()
+ << ", case=" << i
+ << std::endl;
+
+ std::set<types::boundary_id> boundary_ids;
+ for (unsigned int j=0; j<=i; ++j)
+ boundary_ids.insert (j);
+
+ ConstraintMatrix cm;
+ VectorTools::compute_normal_flux_constraints (dof, 0, boundary_ids, cm);
+
+ cm.print (deallog.get_file_stream ());
+ }
+}
+
+
+template<int dim>
+void test_hyper_cube()
+{
+ Triangulation<dim> tr;
+ GridGenerator::hyper_cube(tr);
+
+ for (unsigned int i=0; i<GeometryInfo<dim>::faces_per_cell; ++i)
+ tr.begin_active()->face(i)->set_boundary_indicator (i);
+
+ tr.refine_global(2);
+
+ for (unsigned int degree=1; degree<4; ++degree)
+ {
+ FESystem<dim> fe (FE_Q<dim>(degree), dim);
+ test(tr, fe);
+ }
+}
+
+
+int main()
+{
+ std::ofstream logfile ("normal_flux_01/output");
+ deallog << std::setprecision (2);
+ deallog << std::fixed;
+ deallog.attach(logfile);
+ deallog.depth_console (0);
+ deallog.threshold_double(1.e-12);
+
+ test_hyper_cube<2>();
+ test_hyper_cube<3>();
+}
--- /dev/null
+
+DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=0
+ 1 = 0
+ 5 = 0
+ 13 = 0
+ 31 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=1
+ 1 = 0
+ 5 = 0
+ 13 = 0
+ 23 = 0
+ 25 = 0
+ 29 = 0
+ 31 = 0
+ 45 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=2
+ 2 = 0
+ 5 = 0
+ 8 = 0
+ 13 = 0
+ 18 = 0
+ 25 = 0
+ 29 = 0
+ 31 = 0
+ 45 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=3
+ 2 = 0
+ 5 = 0
+ 8 = 0
+ 13 = 0
+ 18 = 0
+ 25 = 0
+ 29 = 0
+ 31 = 0
+ 38 = 0
+ 40 = 0
+ 45 = 0
+ 46 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=0
+ 1 = 0
+ 5 = 0
+ 31 = 0
+ 91 = 0
+ 111 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=1
+ 1 = 0
+ 5 = 0
+ 31 = 0
+ 63 = 0
+ 65 = 0
+ 83 = 0
+ 91 = 0
+ 111 = 0
+ 139 = 0
+ 155 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=2
+ 2 = 0
+ 5 = 0
+ 18 = 0
+ 31 = 0
+ 50 = 0
+ 65 = 0
+ 83 = 0
+ 91 = 0
+ 111 = 0
+ 139 = 0
+ 155 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=3
+ 2 = 0
+ 5 = 0
+ 18 = 0
+ 31 = 0
+ 50 = 0
+ 65 = 0
+ 83 = 0
+ 91 = 0
+ 112 = 0
+ 122 = 0
+ 139 = 0
+ 146 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=0
+ 1 = 0
+ 5 = 0
+ 10 = 0
+ 57 = 0
+ 62 = 0
+ 183 = 0
+ 188 = 0
+ 225 = 0
+ 230 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=1
+ 1 = 0
+ 5 = 0
+ 10 = 0
+ 57 = 0
+ 62 = 0
+ 123 = 0
+ 125 = 0
+ 128 = 0
+ 165 = 0
+ 168 = 0
+ 183 = 0
+ 188 = 0
+ 225 = 0
+ 230 = 0
+ 285 = 0
+ 288 = 0
+ 321 = 0
+ 324 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=2
+ 2 = 0
+ 5 = 0
+ 10 = 0
+ 16 = 0
+ 32 = 0
+ 40 = 0
+ 57 = 0
+ 62 = 0
+ 98 = 0
+ 106 = 0
+ 125 = 0
+ 128 = 0
+ 130 = 0
+ 165 = 0
+ 168 = 0
+ 183 = 0
+ 188 = 0
+ 225 = 0
+ 230 = 0
+ 285 = 0
+ 288 = 0
+ 321 = 0
+ 324 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=3
+ 2 = 0
+ 5 = 0
+ 10 = 0
+ 16 = 0
+ 32 = 0
+ 40 = 0
+ 57 = 0
+ 62 = 0
+ 98 = 0
+ 106 = 0
+ 125 = 0
+ 128 = 0
+ 130 = 0
+ 165 = 0
+ 168 = 0
+ 183 = 0
+ 188 = 0
+ 226 = 0
+ 230 = 0
+ 236 = 0
+ 248 = 0
+ 254 = 0
+ 285 = 0
+ 288 = 0
+ 302 = 0
+ 308 = 0
+ 324 = 0
+ 326 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=0
+ 1 = 0
+ 2 = 0
+ 7 = 0
+ 8 = 0
+ 13 = 0
+ 14 = 0
+ 19 = 0
+ 20 = 0
+ 37 = 0
+ 38 = 0
+ 43 = 0
+ 44 = 0
+ 55 = 0
+ 56 = 0
+ 61 = 0
+ 62 = 0
+ 73 = 0
+ 74 = 0
+ 136 = 0
+ 137 = 0
+ 142 = 0
+ 143 = 0
+ 154 = 0
+ 155 = 0
+ 160 = 0
+ 161 = 0
+ 172 = 0
+ 173 = 0
+ 181 = 0
+ 182 = 0
+ 226 = 0
+ 227 = 0
+ 232 = 0
+ 233 = 0
+ 244 = 0
+ 245 = 0
+ 253 = 0
+ 254 = 0
+ 259 = 0
+ 260 = 0
+ 271 = 0
+ 272 = 0
+ 316 = 0
+ 317 = 0
+ 325 = 0
+ 326 = 0
+ 334 = 0
+ 335 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=1
+ 1 = 0
+ 2 = 0
+ 7 = 0
+ 8 = 0
+ 13 = 0
+ 14 = 0
+ 19 = 0
+ 20 = 0
+ 37 = 0
+ 38 = 0
+ 43 = 0
+ 44 = 0
+ 55 = 0
+ 56 = 0
+ 61 = 0
+ 62 = 0
+ 73 = 0
+ 74 = 0
+ 94 = 0
+ 95 = 0
+ 97 = 0
+ 98 = 0
+ 100 = 0
+ 101 = 0
+ 103 = 0
+ 104 = 0
+ 112 = 0
+ 113 = 0
+ 115 = 0
+ 116 = 0
+ 124 = 0
+ 125 = 0
+ 127 = 0
+ 128 = 0
+ 133 = 0
+ 134 = 0
+ 136 = 0
+ 137 = 0
+ 142 = 0
+ 143 = 0
+ 154 = 0
+ 155 = 0
+ 160 = 0
+ 161 = 0
+ 172 = 0
+ 173 = 0
+ 181 = 0
+ 182 = 0
+ 196 = 0
+ 197 = 0
+ 199 = 0
+ 200 = 0
+ 208 = 0
+ 209 = 0
+ 211 = 0
+ 212 = 0
+ 217 = 0
+ 218 = 0
+ 223 = 0
+ 224 = 0
+ 226 = 0
+ 227 = 0
+ 232 = 0
+ 233 = 0
+ 244 = 0
+ 245 = 0
+ 253 = 0
+ 254 = 0
+ 259 = 0
+ 260 = 0
+ 271 = 0
+ 272 = 0
+ 286 = 0
+ 287 = 0
+ 289 = 0
+ 290 = 0
+ 295 = 0
+ 296 = 0
+ 304 = 0
+ 305 = 0
+ 307 = 0
+ 308 = 0
+ 313 = 0
+ 314 = 0
+ 316 = 0
+ 317 = 0
+ 325 = 0
+ 326 = 0
+ 334 = 0
+ 335 = 0
+ 355 = 0
+ 356 = 0
+ 361 = 0
+ 362 = 0
+ 367 = 0
+ 368 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=2
+ 0 = 0
+ 1 = 0
+ 2 = 0
+ 3 = 0
+ 5 = 0
+ 7 = 0
+ 8 = 0
+ 12 = 0
+ 13 = 0
+ 14 = 0
+ 15 = 0
+ 17 = 0
+ 19 = 0
+ 20 = 0
+ 24 = 0
+ 26 = 0
+ 30 = 0
+ 32 = 0
+ 37 = 0
+ 38 = 0
+ 43 = 0
+ 44 = 0
+ 54 = 0
+ 55 = 0
+ 56 = 0
+ 57 = 0
+ 59 = 0
+ 61 = 0
+ 62 = 0
+ 66 = 0
+ 68 = 0
+ 73 = 0
+ 74 = 0
+ 81 = 0
+ 83 = 0
+ 87 = 0
+ 89 = 0
+ 93 = 0
+ 94 = 0
+ 95 = 0
+ 97 = 0
+ 98 = 0
+ 99 = 0
+ 100 = 0
+ 101 = 0
+ 103 = 0
+ 104 = 0
+ 112 = 0
+ 113 = 0
+ 115 = 0
+ 116 = 0
+ 117 = 0
+ 119 = 0
+ 123 = 0
+ 124 = 0
+ 125 = 0
+ 127 = 0
+ 128 = 0
+ 133 = 0
+ 134 = 0
+ 136 = 0
+ 137 = 0
+ 142 = 0
+ 143 = 0
+ 154 = 0
+ 155 = 0
+ 160 = 0
+ 161 = 0
+ 172 = 0
+ 173 = 0
+ 181 = 0
+ 182 = 0
+ 196 = 0
+ 197 = 0
+ 199 = 0
+ 200 = 0
+ 208 = 0
+ 209 = 0
+ 211 = 0
+ 212 = 0
+ 217 = 0
+ 218 = 0
+ 223 = 0
+ 224 = 0
+ 225 = 0
+ 226 = 0
+ 227 = 0
+ 228 = 0
+ 230 = 0
+ 232 = 0
+ 233 = 0
+ 237 = 0
+ 239 = 0
+ 244 = 0
+ 245 = 0
+ 252 = 0
+ 253 = 0
+ 254 = 0
+ 255 = 0
+ 257 = 0
+ 259 = 0
+ 260 = 0
+ 264 = 0
+ 266 = 0
+ 271 = 0
+ 272 = 0
+ 279 = 0
+ 281 = 0
+ 285 = 0
+ 286 = 0
+ 287 = 0
+ 289 = 0
+ 290 = 0
+ 295 = 0
+ 296 = 0
+ 297 = 0
+ 299 = 0
+ 303 = 0
+ 304 = 0
+ 305 = 0
+ 307 = 0
+ 308 = 0
+ 313 = 0
+ 314 = 0
+ 316 = 0
+ 317 = 0
+ 325 = 0
+ 326 = 0
+ 334 = 0
+ 335 = 0
+ 355 = 0
+ 356 = 0
+ 361 = 0
+ 362 = 0
+ 367 = 0
+ 368 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=3
+ 0 = 0
+ 1 = 0
+ 2 = 0
+ 3 = 0
+ 5 = 0
+ 7 = 0
+ 8 = 0
+ 12 = 0
+ 13 = 0
+ 14 = 0
+ 15 = 0
+ 17 = 0
+ 19 = 0
+ 20 = 0
+ 24 = 0
+ 26 = 0
+ 30 = 0
+ 32 = 0
+ 37 = 0
+ 38 = 0
+ 43 = 0
+ 44 = 0
+ 54 = 0
+ 55 = 0
+ 56 = 0
+ 57 = 0
+ 59 = 0
+ 61 = 0
+ 62 = 0
+ 66 = 0
+ 68 = 0
+ 73 = 0
+ 74 = 0
+ 81 = 0
+ 83 = 0
+ 87 = 0
+ 89 = 0
+ 93 = 0
+ 94 = 0
+ 95 = 0
+ 97 = 0
+ 98 = 0
+ 99 = 0
+ 100 = 0
+ 101 = 0
+ 103 = 0
+ 104 = 0
+ 112 = 0
+ 113 = 0
+ 115 = 0
+ 116 = 0
+ 117 = 0
+ 119 = 0
+ 123 = 0
+ 124 = 0
+ 125 = 0
+ 127 = 0
+ 128 = 0
+ 133 = 0
+ 134 = 0
+ 136 = 0
+ 137 = 0
+ 142 = 0
+ 143 = 0
+ 153 = 0
+ 154 = 0
+ 155 = 0
+ 156 = 0
+ 158 = 0
+ 159 = 0
+ 160 = 0
+ 161 = 0
+ 162 = 0
+ 164 = 0
+ 165 = 0
+ 167 = 0
+ 168 = 0
+ 170 = 0
+ 172 = 0
+ 173 = 0
+ 180 = 0
+ 181 = 0
+ 182 = 0
+ 183 = 0
+ 185 = 0
+ 186 = 0
+ 188 = 0
+ 196 = 0
+ 197 = 0
+ 199 = 0
+ 200 = 0
+ 201 = 0
+ 203 = 0
+ 204 = 0
+ 206 = 0
+ 207 = 0
+ 208 = 0
+ 209 = 0
+ 210 = 0
+ 211 = 0
+ 212 = 0
+ 217 = 0
+ 218 = 0
+ 219 = 0
+ 221 = 0
+ 222 = 0
+ 223 = 0
+ 224 = 0
+ 225 = 0
+ 226 = 0
+ 227 = 0
+ 228 = 0
+ 230 = 0
+ 232 = 0
+ 233 = 0
+ 237 = 0
+ 239 = 0
+ 244 = 0
+ 245 = 0
+ 252 = 0
+ 253 = 0
+ 254 = 0
+ 255 = 0
+ 257 = 0
+ 259 = 0
+ 260 = 0
+ 264 = 0
+ 266 = 0
+ 271 = 0
+ 272 = 0
+ 279 = 0
+ 281 = 0
+ 285 = 0
+ 286 = 0
+ 287 = 0
+ 289 = 0
+ 290 = 0
+ 295 = 0
+ 296 = 0
+ 297 = 0
+ 299 = 0
+ 303 = 0
+ 304 = 0
+ 305 = 0
+ 307 = 0
+ 308 = 0
+ 313 = 0
+ 314 = 0
+ 316 = 0
+ 317 = 0
+ 324 = 0
+ 325 = 0
+ 326 = 0
+ 327 = 0
+ 329 = 0
+ 330 = 0
+ 332 = 0
+ 334 = 0
+ 335 = 0
+ 342 = 0
+ 343 = 0
+ 344 = 0
+ 345 = 0
+ 347 = 0
+ 348 = 0
+ 350 = 0
+ 355 = 0
+ 356 = 0
+ 357 = 0
+ 359 = 0
+ 360 = 0
+ 361 = 0
+ 362 = 0
+ 367 = 0
+ 368 = 0
+ 369 = 0
+ 371 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=4
+ 3 = 0
+ 4 = 0
+ 5 = 0
+ 6 = 0
+ 7 = 0
+ 8 = 0
+ 9 = 0
+ 10 = 0
+ 12 = 0
+ 13 = 0
+ 14 = 0
+ 15 = 0
+ 17 = 0
+ 19 = 0
+ 20 = 0
+ 24 = 0
+ 25 = 0
+ 26 = 0
+ 27 = 0
+ 28 = 0
+ 30 = 0
+ 32 = 0
+ 36 = 0
+ 37 = 0
+ 38 = 0
+ 39 = 0
+ 40 = 0
+ 43 = 0
+ 44 = 0
+ 48 = 0
+ 49 = 0
+ 54 = 0
+ 55 = 0
+ 56 = 0
+ 57 = 0
+ 59 = 0
+ 61 = 0
+ 62 = 0
+ 66 = 0
+ 68 = 0
+ 73 = 0
+ 74 = 0
+ 81 = 0
+ 82 = 0
+ 83 = 0
+ 84 = 0
+ 85 = 0
+ 87 = 0
+ 89 = 0
+ 96 = 0
+ 97 = 0
+ 98 = 0
+ 99 = 0
+ 100 = 0
+ 101 = 0
+ 103 = 0
+ 104 = 0
+ 105 = 0
+ 106 = 0
+ 111 = 0
+ 112 = 0
+ 113 = 0
+ 115 = 0
+ 116 = 0
+ 117 = 0
+ 119 = 0
+ 123 = 0
+ 124 = 0
+ 125 = 0
+ 127 = 0
+ 128 = 0
+ 133 = 0
+ 134 = 0
+ 135 = 0
+ 136 = 0
+ 137 = 0
+ 138 = 0
+ 139 = 0
+ 142 = 0
+ 143 = 0
+ 147 = 0
+ 148 = 0
+ 156 = 0
+ 157 = 0
+ 158 = 0
+ 159 = 0
+ 160 = 0
+ 161 = 0
+ 162 = 0
+ 164 = 0
+ 165 = 0
+ 166 = 0
+ 167 = 0
+ 168 = 0
+ 170 = 0
+ 172 = 0
+ 173 = 0
+ 180 = 0
+ 181 = 0
+ 182 = 0
+ 183 = 0
+ 185 = 0
+ 186 = 0
+ 188 = 0
+ 189 = 0
+ 190 = 0
+ 195 = 0
+ 196 = 0
+ 197 = 0
+ 199 = 0
+ 200 = 0
+ 201 = 0
+ 202 = 0
+ 203 = 0
+ 204 = 0
+ 206 = 0
+ 210 = 0
+ 211 = 0
+ 212 = 0
+ 217 = 0
+ 218 = 0
+ 219 = 0
+ 221 = 0
+ 222 = 0
+ 223 = 0
+ 224 = 0
+ 225 = 0
+ 226 = 0
+ 227 = 0
+ 228 = 0
+ 230 = 0
+ 232 = 0
+ 233 = 0
+ 237 = 0
+ 239 = 0
+ 244 = 0
+ 245 = 0
+ 252 = 0
+ 253 = 0
+ 254 = 0
+ 255 = 0
+ 257 = 0
+ 259 = 0
+ 260 = 0
+ 264 = 0
+ 266 = 0
+ 271 = 0
+ 272 = 0
+ 279 = 0
+ 281 = 0
+ 285 = 0
+ 286 = 0
+ 287 = 0
+ 289 = 0
+ 290 = 0
+ 295 = 0
+ 296 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=5
+ 3 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=0
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=1
+ 1 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=2
+ 0 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=3
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=4
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=5
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=1
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=2
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=3
+ 0 = 0
+ 1 = 0
+ 2 = 0
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+ 6553 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=4
+ 3 = 0
+ 4 = 0
+ 5 = 0
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+ 6553 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3], case=5
+ 3 = 0
+ 4 = 0
+ 5 = 0
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+ 354 = 0
+ 356 = 0
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+ 357 = 0
+ 360 = 0
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+ 5395 = 0
+ 5399 = 0
+ 5400 = 0
+ 5402 = 0
+ 5404 = 0
+ 5401 = 0
+ 5403 = 0
+ 5405 = 0
+ 5406 = 0
+ 5410 = 0
+ 5407 = 0
+ 5411 = 0
+ 5416 = 0
+ 5420 = 0
+ 5417 = 0
+ 5421 = 0
+ 5418 = 0
+ 5422 = 0
+ 5436 = 0
+ 5444 = 0
+ 5437 = 0
+ 5445 = 0
+ 5438 = 0
+ 5446 = 0
+ 5484 = 0
+ 5486 = 0
+ 5493 = 0
+ 5497 = 0
+ 5494 = 0
+ 5498 = 0
+ 5499 = 0
+ 5503 = 0
+ 5500 = 0
+ 5504 = 0
+ 5517 = 0
+ 5525 = 0
+ 5518 = 0
+ 5526 = 0
+ 5519 = 0
+ 5527 = 0
+ 5565 = 0
+ 5566 = 0
+ 5567 = 0
+ 5568 = 0
+ 5569 = 0
+ 5571 = 0
+ 5573 = 0
+ 5575 = 0
+ 5572 = 0
+ 5574 = 0
+ 5576 = 0
+ 5577 = 0
+ 5579 = 0
+ 5578 = 0
+ 5580 = 0
+ 5583 = 0
+ 5585 = 0
+ 5584 = 0
+ 5586 = 0
+ 5591 = 0
+ 5593 = 0
+ 5592 = 0
+ 5594 = 0
+ 5605 = 0
+ 5609 = 0
+ 5606 = 0
+ 5610 = 0
+ 5607 = 0
+ 5611 = 0
+ 5637 = 0
+ 5641 = 0
+ 5638 = 0
+ 5642 = 0
+ 5639 = 0
+ 5643 = 0
+ 5673 = 0
+ 5674 = 0
+ 5676 = 0
+ 5678 = 0
+ 5677 = 0
+ 5679 = 0
+ 5682 = 0
+ 5684 = 0
+ 5683 = 0
+ 5685 = 0
+ 5718 = 0
+ 5722 = 0
+ 5719 = 0
+ 5723 = 0
+ 5720 = 0
+ 5724 = 0
+ 5757 = 0
+ 5758 = 0
+ 5759 = 0
+ 5760 = 0
+ 5762 = 0
+ 5764 = 0
+ 5761 = 0
+ 5763 = 0
+ 5765 = 0
+ 5766 = 0
+ 5768 = 0
+ 5767 = 0
+ 5769 = 0
+ 5772 = 0
+ 5774 = 0
+ 5776 = 0
+ 5773 = 0
+ 5775 = 0
+ 5777 = 0
+ 5778 = 0
+ 5780 = 0
+ 5782 = 0
+ 5779 = 0
+ 5781 = 0
+ 5783 = 0
+ 5784 = 0
+ 5788 = 0
+ 5785 = 0
+ 5789 = 0
+ 5794 = 0
+ 5798 = 0
+ 5795 = 0
+ 5799 = 0
+ 5796 = 0
+ 5800 = 0
+ 5814 = 0
+ 5822 = 0
+ 5815 = 0
+ 5823 = 0
+ 5816 = 0
+ 5824 = 0
+ 5826 = 0
+ 5830 = 0
+ 5827 = 0
+ 5831 = 0
+ 5828 = 0
+ 5832 = 0
+ 5862 = 0
+ 5863 = 0
+ 5864 = 0
+ 5865 = 0
+ 5867 = 0
+ 5866 = 0
+ 5868 = 0
+ 5871 = 0
+ 5873 = 0
+ 5875 = 0
+ 5872 = 0
+ 5874 = 0
+ 5876 = 0
+ 5877 = 0
+ 5881 = 0
+ 5878 = 0
+ 5882 = 0
+ 5895 = 0
+ 5903 = 0
+ 5896 = 0
+ 5904 = 0
+ 5897 = 0
+ 5905 = 0
+ 5907 = 0
+ 5911 = 0
+ 5908 = 0
+ 5912 = 0
+ 5909 = 0
+ 5913 = 0
+ 6025 = 0
+ 6026 = 0
+ 6029 = 0
+ 6031 = 0
+ 6030 = 0
+ 6032 = 0
+ 6041 = 0
+ 6043 = 0
+ 6042 = 0
+ 6044 = 0
+ 6049 = 0
+ 6053 = 0
+ 6050 = 0
+ 6054 = 0
+ 6051 = 0
+ 6055 = 0
+ 6105 = 0
+ 6107 = 0
+ 6114 = 0
+ 6118 = 0
+ 6115 = 0
+ 6119 = 0
+ 6120 = 0
+ 6124 = 0
+ 6121 = 0
+ 6125 = 0
+ 6138 = 0
+ 6146 = 0
+ 6139 = 0
+ 6147 = 0
+ 6140 = 0
+ 6148 = 0
+ 6186 = 0
+ 6187 = 0
+ 6188 = 0
+ 6191 = 0
+ 6193 = 0
+ 6192 = 0
+ 6194 = 0
+ 6195 = 0
+ 6199 = 0
+ 6196 = 0
+ 6200 = 0
+ 6201 = 0
+ 6203 = 0
+ 6205 = 0
+ 6202 = 0
+ 6204 = 0
+ 6206 = 0
+ 6211 = 0
+ 6215 = 0
+ 6212 = 0
+ 6216 = 0
+ 6213 = 0
+ 6217 = 0
+ 6219 = 0
+ 6227 = 0
+ 6220 = 0
+ 6228 = 0
+ 6221 = 0
+ 6229 = 0
+ 6267 = 0
+ 6268 = 0
+ 6270 = 0
+ 6272 = 0
+ 6271 = 0
+ 6273 = 0
+ 6276 = 0
+ 6278 = 0
+ 6277 = 0
+ 6279 = 0
+ 6312 = 0
+ 6316 = 0
+ 6313 = 0
+ 6317 = 0
+ 6314 = 0
+ 6318 = 0
+ 6348 = 0
+ 6349 = 0
+ 6350 = 0
+ 6351 = 0
+ 6353 = 0
+ 6355 = 0
+ 6352 = 0
+ 6354 = 0
+ 6356 = 0
+ 6357 = 0
+ 6359 = 0
+ 6358 = 0
+ 6360 = 0
+ 6365 = 0
+ 6367 = 0
+ 6366 = 0
+ 6368 = 0
+ 6373 = 0
+ 6377 = 0
+ 6374 = 0
+ 6378 = 0
+ 6375 = 0
+ 6379 = 0
+ 6393 = 0
+ 6397 = 0
+ 6394 = 0
+ 6398 = 0
+ 6395 = 0
+ 6399 = 0
+ 6429 = 0
+ 6430 = 0
+ 6431 = 0
+ 6432 = 0
+ 6434 = 0
+ 6433 = 0
+ 6435 = 0
+ 6438 = 0
+ 6440 = 0
+ 6442 = 0
+ 6439 = 0
+ 6441 = 0
+ 6443 = 0
+ 6444 = 0
+ 6448 = 0
+ 6445 = 0
+ 6449 = 0
+ 6462 = 0
+ 6470 = 0
+ 6463 = 0
+ 6471 = 0
+ 6464 = 0
+ 6472 = 0
+ 6474 = 0
+ 6478 = 0
+ 6475 = 0
+ 6479 = 0
+ 6476 = 0
+ 6480 = 0
+ 6513 = 0
+ 6515 = 0
+ 6517 = 0
+ 6514 = 0
+ 6516 = 0
+ 6518 = 0
+ 6519 = 0
+ 6521 = 0
+ 6523 = 0
+ 6520 = 0
+ 6522 = 0
+ 6524 = 0
+ 6525 = 0
+ 6527 = 0
+ 6529 = 0
+ 6526 = 0
+ 6528 = 0
+ 6530 = 0
+ 6535 = 0
+ 6539 = 0
+ 6536 = 0
+ 6540 = 0
+ 6537 = 0
+ 6541 = 0
+ 6543 = 0
+ 6551 = 0
+ 6544 = 0
+ 6552 = 0
+ 6545 = 0
+ 6553 = 0
+ 6555 = 0
+ 6559 = 0
+ 6556 = 0
+ 6560 = 0
+ 6557 = 0
+ 6561 = 0
--- /dev/null
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2007 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// check the creation of normal flux boundary conditions for a finite
+// element that consists of more than dim components and where
+// therefore we have to pick the vector components from somewhere in
+// the middle (opposite constraints as no_flux_02.cc does).
+
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_q1.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+
+
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+ const FiniteElement<dim> &fe)
+{
+ DoFHandler<dim> dof(tr);
+ dof.distribute_dofs(fe);
+
+ for (unsigned int i=0; i<GeometryInfo<dim>::faces_per_cell; ++i)
+ {
+ deallog << "FE=" << fe.get_name()
+ << ", case=" << i
+ << std::endl;
+
+ std::set<types::boundary_id> boundary_ids;
+ for (unsigned int j=0; j<=i; ++j)
+ boundary_ids.insert (j);
+
+ ConstraintMatrix cm;
+ VectorTools::compute_normal_flux_constraints (dof, 1, boundary_ids, cm);
+
+ cm.print (deallog.get_file_stream ());
+ }
+}
+
+
+template<int dim>
+void test_hyper_cube()
+{
+ Triangulation<dim> tr;
+ GridGenerator::hyper_cube(tr);
+
+ for (unsigned int i=0; i<GeometryInfo<dim>::faces_per_cell; ++i)
+ tr.begin_active()->face(i)->set_boundary_indicator (i);
+
+ tr.refine_global(2);
+
+ for (unsigned int degree=1; degree<4; ++degree)
+ {
+ FESystem<dim> fe (FE_Q<dim>(degree+1), 1,
+ FE_Q<dim>(degree), dim,
+ FE_Q<dim>(degree+1), 1);
+ test(tr, fe);
+ }
+}
+
+
+int main()
+{
+ std::ofstream logfile ("normal_flux_02/output");
+ deallog << std::setprecision (2);
+ deallog << std::fixed;
+ deallog.attach(logfile);
+ deallog.depth_console (0);
+ deallog.threshold_double(1.e-12);
+
+ test_hyper_cube<2>();
+ test_hyper_cube<3>();
+}
--- /dev/null
+
+DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=0
+ 2 = 0
+ 10 = 0
+ 44 = 0
+ 122 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=1
+ 2 = 0
+ 10 = 0
+ 44 = 0
+ 86 = 0
+ 90 = 0
+ 112 = 0
+ 122 = 0
+ 184 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=2
+ 5 = 0
+ 10 = 0
+ 27 = 0
+ 44 = 0
+ 69 = 0
+ 90 = 0
+ 112 = 0
+ 122 = 0
+ 184 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=3
+ 5 = 0
+ 10 = 0
+ 27 = 0
+ 44 = 0
+ 69 = 0
+ 90 = 0
+ 112 = 0
+ 122 = 0
+ 151 = 0
+ 163 = 0
+ 184 = 0
+ 193 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=0
+ 2 = 0
+ 10 = 0
+ 88 = 0
+ 274 = 0
+ 336 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=1
+ 2 = 0
+ 10 = 0
+ 88 = 0
+ 186 = 0
+ 190 = 0
+ 248 = 0
+ 274 = 0
+ 336 = 0
+ 424 = 0
+ 476 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=2
+ 5 = 0
+ 10 = 0
+ 51 = 0
+ 88 = 0
+ 149 = 0
+ 190 = 0
+ 248 = 0
+ 274 = 0
+ 336 = 0
+ 424 = 0
+ 476 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=3
+ 5 = 0
+ 10 = 0
+ 51 = 0
+ 88 = 0
+ 149 = 0
+ 190 = 0
+ 248 = 0
+ 274 = 0
+ 339 = 0
+ 371 = 0
+ 424 = 0
+ 449 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=0
+ 2 = 0
+ 10 = 0
+ 21 = 0
+ 148 = 0
+ 159 = 0
+ 490 = 0
+ 501 = 0
+ 604 = 0
+ 615 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=1
+ 2 = 0
+ 10 = 0
+ 21 = 0
+ 148 = 0
+ 159 = 0
+ 326 = 0
+ 330 = 0
+ 337 = 0
+ 440 = 0
+ 447 = 0
+ 490 = 0
+ 501 = 0
+ 604 = 0
+ 615 = 0
+ 768 = 0
+ 775 = 0
+ 868 = 0
+ 875 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=2
+ 5 = 0
+ 10 = 0
+ 21 = 0
+ 39 = 0
+ 83 = 0
+ 103 = 0
+ 148 = 0
+ 159 = 0
+ 261 = 0
+ 281 = 0
+ 330 = 0
+ 337 = 0
+ 345 = 0
+ 440 = 0
+ 447 = 0
+ 490 = 0
+ 501 = 0
+ 604 = 0
+ 615 = 0
+ 768 = 0
+ 775 = 0
+ 868 = 0
+ 875 = 0
+DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=3
+ 5 = 0
+ 10 = 0
+ 21 = 0
+ 39 = 0
+ 83 = 0
+ 103 = 0
+ 148 = 0
+ 159 = 0
+ 261 = 0
+ 281 = 0
+ 330 = 0
+ 337 = 0
+ 345 = 0
+ 440 = 0
+ 447 = 0
+ 490 = 0
+ 501 = 0
+ 607 = 0
+ 615 = 0
+ 633 = 0
+ 667 = 0
+ 683 = 0
+ 768 = 0
+ 775 = 0
+ 817 = 0
+ 833 = 0
+ 875 = 0
+ 883 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=0
+ 2 = 0
+ 3 = 0
+ 12 = 0
+ 13 = 0
+ 22 = 0
+ 23 = 0
+ 32 = 0
+ 33 = 0
+ 128 = 0
+ 129 = 0
+ 138 = 0
+ 139 = 0
+ 206 = 0
+ 207 = 0
+ 216 = 0
+ 217 = 0
+ 284 = 0
+ 285 = 0
+ 587 = 0
+ 588 = 0
+ 597 = 0
+ 598 = 0
+ 665 = 0
+ 666 = 0
+ 675 = 0
+ 676 = 0
+ 743 = 0
+ 744 = 0
+ 792 = 0
+ 793 = 0
+ 1037 = 0
+ 1038 = 0
+ 1047 = 0
+ 1048 = 0
+ 1115 = 0
+ 1116 = 0
+ 1164 = 0
+ 1165 = 0
+ 1174 = 0
+ 1175 = 0
+ 1242 = 0
+ 1243 = 0
+ 1487 = 0
+ 1488 = 0
+ 1536 = 0
+ 1537 = 0
+ 1585 = 0
+ 1586 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=1
+ 2 = 0
+ 3 = 0
+ 12 = 0
+ 13 = 0
+ 22 = 0
+ 23 = 0
+ 32 = 0
+ 33 = 0
+ 128 = 0
+ 129 = 0
+ 138 = 0
+ 139 = 0
+ 206 = 0
+ 207 = 0
+ 216 = 0
+ 217 = 0
+ 284 = 0
+ 285 = 0
+ 381 = 0
+ 382 = 0
+ 386 = 0
+ 387 = 0
+ 391 = 0
+ 392 = 0
+ 396 = 0
+ 397 = 0
+ 459 = 0
+ 460 = 0
+ 464 = 0
+ 465 = 0
+ 519 = 0
+ 520 = 0
+ 524 = 0
+ 525 = 0
+ 568 = 0
+ 569 = 0
+ 587 = 0
+ 588 = 0
+ 597 = 0
+ 598 = 0
+ 665 = 0
+ 666 = 0
+ 675 = 0
+ 676 = 0
+ 743 = 0
+ 744 = 0
+ 792 = 0
+ 793 = 0
+ 871 = 0
+ 872 = 0
+ 876 = 0
+ 877 = 0
+ 931 = 0
+ 932 = 0
+ 936 = 0
+ 937 = 0
+ 980 = 0
+ 981 = 0
+ 1018 = 0
+ 1019 = 0
+ 1037 = 0
+ 1038 = 0
+ 1047 = 0
+ 1048 = 0
+ 1115 = 0
+ 1116 = 0
+ 1164 = 0
+ 1165 = 0
+ 1174 = 0
+ 1175 = 0
+ 1242 = 0
+ 1243 = 0
+ 1321 = 0
+ 1322 = 0
+ 1326 = 0
+ 1327 = 0
+ 1370 = 0
+ 1371 = 0
+ 1419 = 0
+ 1420 = 0
+ 1424 = 0
+ 1425 = 0
+ 1468 = 0
+ 1469 = 0
+ 1487 = 0
+ 1488 = 0
+ 1536 = 0
+ 1537 = 0
+ 1585 = 0
+ 1586 = 0
+ 1702 = 0
+ 1703 = 0
+ 1740 = 0
+ 1741 = 0
+ 1778 = 0
+ 1779 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=2
+ 1 = 0
+ 2 = 0
+ 3 = 0
+ 6 = 0
+ 8 = 0
+ 12 = 0
+ 13 = 0
+ 21 = 0
+ 22 = 0
+ 23 = 0
+ 26 = 0
+ 28 = 0
+ 32 = 0
+ 33 = 0
+ 79 = 0
+ 81 = 0
+ 89 = 0
+ 91 = 0
+ 128 = 0
+ 129 = 0
+ 138 = 0
+ 139 = 0
+ 205 = 0
+ 206 = 0
+ 207 = 0
+ 210 = 0
+ 212 = 0
+ 216 = 0
+ 217 = 0
+ 253 = 0
+ 255 = 0
+ 284 = 0
+ 285 = 0
+ 332 = 0
+ 334 = 0
+ 342 = 0
+ 344 = 0
+ 380 = 0
+ 381 = 0
+ 382 = 0
+ 386 = 0
+ 387 = 0
+ 390 = 0
+ 391 = 0
+ 392 = 0
+ 396 = 0
+ 397 = 0
+ 459 = 0
+ 460 = 0
+ 464 = 0
+ 465 = 0
+ 488 = 0
+ 490 = 0
+ 518 = 0
+ 519 = 0
+ 520 = 0
+ 524 = 0
+ 525 = 0
+ 568 = 0
+ 569 = 0
+ 587 = 0
+ 588 = 0
+ 597 = 0
+ 598 = 0
+ 665 = 0
+ 666 = 0
+ 675 = 0
+ 676 = 0
+ 743 = 0
+ 744 = 0
+ 792 = 0
+ 793 = 0
+ 871 = 0
+ 872 = 0
+ 876 = 0
+ 877 = 0
+ 931 = 0
+ 932 = 0
+ 936 = 0
+ 937 = 0
+ 980 = 0
+ 981 = 0
+ 1018 = 0
+ 1019 = 0
+ 1036 = 0
+ 1037 = 0
+ 1038 = 0
+ 1041 = 0
+ 1043 = 0
+ 1047 = 0
+ 1048 = 0
+ 1084 = 0
+ 1086 = 0
+ 1115 = 0
+ 1116 = 0
+ 1163 = 0
+ 1164 = 0
+ 1165 = 0
+ 1168 = 0
+ 1170 = 0
+ 1174 = 0
+ 1175 = 0
+ 1211 = 0
+ 1213 = 0
+ 1242 = 0
+ 1243 = 0
+ 1290 = 0
+ 1292 = 0
+ 1320 = 0
+ 1321 = 0
+ 1322 = 0
+ 1326 = 0
+ 1327 = 0
+ 1370 = 0
+ 1371 = 0
+ 1388 = 0
+ 1390 = 0
+ 1418 = 0
+ 1419 = 0
+ 1420 = 0
+ 1424 = 0
+ 1425 = 0
+ 1468 = 0
+ 1469 = 0
+ 1487 = 0
+ 1488 = 0
+ 1536 = 0
+ 1537 = 0
+ 1585 = 0
+ 1586 = 0
+ 1702 = 0
+ 1703 = 0
+ 1740 = 0
+ 1741 = 0
+ 1778 = 0
+ 1779 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=3
+ 1 = 0
+ 2 = 0
+ 3 = 0
+ 6 = 0
+ 8 = 0
+ 12 = 0
+ 13 = 0
+ 21 = 0
+ 22 = 0
+ 23 = 0
+ 26 = 0
+ 28 = 0
+ 32 = 0
+ 33 = 0
+ 79 = 0
+ 81 = 0
+ 89 = 0
+ 91 = 0
+ 128 = 0
+ 129 = 0
+ 138 = 0
+ 139 = 0
+ 205 = 0
+ 206 = 0
+ 207 = 0
+ 210 = 0
+ 212 = 0
+ 216 = 0
+ 217 = 0
+ 253 = 0
+ 255 = 0
+ 284 = 0
+ 285 = 0
+ 332 = 0
+ 334 = 0
+ 342 = 0
+ 344 = 0
+ 380 = 0
+ 381 = 0
+ 382 = 0
+ 386 = 0
+ 387 = 0
+ 390 = 0
+ 391 = 0
+ 392 = 0
+ 396 = 0
+ 397 = 0
+ 459 = 0
+ 460 = 0
+ 464 = 0
+ 465 = 0
+ 488 = 0
+ 490 = 0
+ 518 = 0
+ 519 = 0
+ 520 = 0
+ 524 = 0
+ 525 = 0
+ 568 = 0
+ 569 = 0
+ 587 = 0
+ 588 = 0
+ 597 = 0
+ 598 = 0
+ 664 = 0
+ 665 = 0
+ 666 = 0
+ 669 = 0
+ 671 = 0
+ 674 = 0
+ 675 = 0
+ 676 = 0
+ 679 = 0
+ 681 = 0
+ 712 = 0
+ 714 = 0
+ 717 = 0
+ 719 = 0
+ 743 = 0
+ 744 = 0
+ 791 = 0
+ 792 = 0
+ 793 = 0
+ 796 = 0
+ 798 = 0
+ 821 = 0
+ 823 = 0
+ 871 = 0
+ 872 = 0
+ 876 = 0
+ 877 = 0
+ 900 = 0
+ 902 = 0
+ 905 = 0
+ 907 = 0
+ 930 = 0
+ 931 = 0
+ 932 = 0
+ 935 = 0
+ 936 = 0
+ 937 = 0
+ 980 = 0
+ 981 = 0
+ 998 = 0
+ 1000 = 0
+ 1017 = 0
+ 1018 = 0
+ 1019 = 0
+ 1036 = 0
+ 1037 = 0
+ 1038 = 0
+ 1041 = 0
+ 1043 = 0
+ 1047 = 0
+ 1048 = 0
+ 1084 = 0
+ 1086 = 0
+ 1115 = 0
+ 1116 = 0
+ 1163 = 0
+ 1164 = 0
+ 1165 = 0
+ 1168 = 0
+ 1170 = 0
+ 1174 = 0
+ 1175 = 0
+ 1211 = 0
+ 1213 = 0
+ 1242 = 0
+ 1243 = 0
+ 1290 = 0
+ 1292 = 0
+ 1320 = 0
+ 1321 = 0
+ 1322 = 0
+ 1326 = 0
+ 1327 = 0
+ 1370 = 0
+ 1371 = 0
+ 1388 = 0
+ 1390 = 0
+ 1418 = 0
+ 1419 = 0
+ 1420 = 0
+ 1424 = 0
+ 1425 = 0
+ 1468 = 0
+ 1469 = 0
+ 1487 = 0
+ 1488 = 0
+ 1535 = 0
+ 1536 = 0
+ 1537 = 0
+ 1540 = 0
+ 1542 = 0
+ 1565 = 0
+ 1567 = 0
+ 1585 = 0
+ 1586 = 0
+ 1633 = 0
+ 1634 = 0
+ 1635 = 0
+ 1638 = 0
+ 1640 = 0
+ 1663 = 0
+ 1665 = 0
+ 1702 = 0
+ 1703 = 0
+ 1720 = 0
+ 1722 = 0
+ 1739 = 0
+ 1740 = 0
+ 1741 = 0
+ 1778 = 0
+ 1779 = 0
+ 1796 = 0
+ 1798 = 0
+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=4
+ 6 = 0
+ 7 = 0
+ 8 = 0
+ 11 = 0
+ 12 = 0
+ 13 = 0
+ 16 = 0
+ 17 = 0
+ 21 = 0
+ 22 = 0
+ 23 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=5
+ 6 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=0
+ 2 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=1
+ 2 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=2
+ 1 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=3
+ 1 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=4
+ 6 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=5
+ 6 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=0
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=1
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=2
+ 1 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=3
+ 1 = 0
+ 2 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=4
+ 6 = 0
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+ 142 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(4)-FE_Q<3>(3)^3-FE_Q<3>(4)], case=5
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+ 9939 = 0
+ 9938 = 0
+ 9940 = 0
+ 9969 = 0
+ 9973 = 0
+ 9970 = 0
+ 9974 = 0
+ 9971 = 0
+ 9975 = 0
+ 10025 = 0
+ 10033 = 0
+ 10026 = 0
+ 10034 = 0
+ 10027 = 0
+ 10035 = 0
+ 10085 = 0
+ 10089 = 0
+ 10086 = 0
+ 10090 = 0
+ 10087 = 0
+ 10091 = 0
+ 10185 = 0
+ 10186 = 0
+ 10187 = 0
+ 10190 = 0
+ 10191 = 0
+ 10197 = 0
+ 10199 = 0
+ 10198 = 0
+ 10200 = 0
+ 10209 = 0
+ 10211 = 0
+ 10213 = 0
+ 10210 = 0
+ 10212 = 0
+ 10214 = 0
+ 10221 = 0
+ 10223 = 0
+ 10222 = 0
+ 10224 = 0
+ 10233 = 0
+ 10237 = 0
+ 10234 = 0
+ 10238 = 0
+ 10293 = 0
+ 10301 = 0
+ 10294 = 0
+ 10302 = 0
+ 10295 = 0
+ 10303 = 0
+ 10353 = 0
+ 10357 = 0
+ 10354 = 0
+ 10358 = 0
+ 10355 = 0
+ 10359 = 0
+ 10453 = 0
+ 10454 = 0
+ 10455 = 0
+ 10458 = 0
+ 10459 = 0
+ 10465 = 0
+ 10467 = 0
+ 10469 = 0
+ 10466 = 0
+ 10468 = 0
+ 10470 = 0
+ 10477 = 0
+ 10479 = 0
+ 10478 = 0
+ 10480 = 0
+ 10489 = 0
+ 10491 = 0
+ 10490 = 0
+ 10492 = 0
+ 10503 = 0
+ 10505 = 0
+ 10504 = 0
+ 10506 = 0
+ 10535 = 0
+ 10539 = 0
+ 10536 = 0
+ 10540 = 0
+ 10537 = 0
+ 10541 = 0
+ 10621 = 0
+ 10625 = 0
+ 10622 = 0
+ 10626 = 0
+ 10623 = 0
+ 10627 = 0
+ 10721 = 0
+ 10722 = 0
+ 10728 = 0
+ 10730 = 0
+ 10729 = 0
+ 10731 = 0
+ 10740 = 0
+ 10742 = 0
+ 10741 = 0
+ 10743 = 0
+ 10830 = 0
+ 10834 = 0
+ 10831 = 0
+ 10835 = 0
+ 10832 = 0
+ 10836 = 0
+ 10930 = 0
+ 10932 = 0
+ 10954 = 0
+ 10958 = 0
+ 10955 = 0
+ 10959 = 0
+ 10978 = 0
+ 10982 = 0
+ 10979 = 0
+ 10983 = 0
+ 11038 = 0
+ 11046 = 0
+ 11039 = 0
+ 11047 = 0
+ 11040 = 0
+ 11048 = 0
+ 11198 = 0
+ 11199 = 0
+ 11200 = 0
+ 11204 = 0
+ 11205 = 0
+ 11212 = 0
+ 11214 = 0
+ 11213 = 0
+ 11215 = 0
+ 11222 = 0
+ 11226 = 0
+ 11223 = 0
+ 11227 = 0
+ 11246 = 0
+ 11248 = 0
+ 11250 = 0
+ 11247 = 0
+ 11249 = 0
+ 11251 = 0
+ 11260 = 0
+ 11262 = 0
+ 11261 = 0
+ 11263 = 0
+ 11280 = 0
+ 11284 = 0
+ 11281 = 0
+ 11285 = 0
+ 11282 = 0
+ 11286 = 0
+ 11306 = 0
+ 11314 = 0
+ 11307 = 0
+ 11315 = 0
+ 11308 = 0
+ 11316 = 0
+ 11676 = 0
+ 11677 = 0
+ 11684 = 0
+ 11686 = 0
+ 11685 = 0
+ 11687 = 0
+ 11708 = 0
+ 11710 = 0
+ 11709 = 0
+ 11711 = 0
+ 11728 = 0
+ 11732 = 0
+ 11729 = 0
+ 11733 = 0
+ 11730 = 0
+ 11734 = 0
+ 11884 = 0
+ 11885 = 0
+ 11886 = 0
+ 11889 = 0
+ 11890 = 0
+ 11896 = 0
+ 11898 = 0
+ 11897 = 0
+ 11899 = 0
+ 11908 = 0
+ 11910 = 0
+ 11912 = 0
+ 11909 = 0
+ 11911 = 0
+ 11913 = 0
+ 11920 = 0
+ 11922 = 0
+ 11921 = 0
+ 11923 = 0
+ 11932 = 0
+ 11936 = 0
+ 11933 = 0
+ 11937 = 0
+ 11992 = 0
+ 12000 = 0
+ 11993 = 0
+ 12001 = 0
+ 11994 = 0
+ 12002 = 0
+ 12052 = 0
+ 12056 = 0
+ 12053 = 0
+ 12057 = 0
+ 12054 = 0
+ 12058 = 0
+ 12157 = 0
+ 12158 = 0
+ 12159 = 0
+ 12164 = 0
+ 12166 = 0
+ 12168 = 0
+ 12165 = 0
+ 12167 = 0
+ 12169 = 0
+ 12176 = 0
+ 12178 = 0
+ 12180 = 0
+ 12177 = 0
+ 12179 = 0
+ 12181 = 0
+ 12188 = 0
+ 12190 = 0
+ 12189 = 0
+ 12191 = 0
+ 12200 = 0
+ 12202 = 0
+ 12204 = 0
+ 12201 = 0
+ 12203 = 0
+ 12205 = 0
+ 12214 = 0
+ 12216 = 0
+ 12215 = 0
+ 12217 = 0
+ 12234 = 0
+ 12238 = 0
+ 12235 = 0
+ 12239 = 0
+ 12236 = 0
+ 12240 = 0
+ 12260 = 0
+ 12268 = 0
+ 12261 = 0
+ 12269 = 0
+ 12262 = 0
+ 12270 = 0
+ 12320 = 0
+ 12324 = 0
+ 12321 = 0
+ 12325 = 0
+ 12322 = 0
+ 12326 = 0
+ 12420 = 0
+ 12421 = 0
+ 12427 = 0
+ 12429 = 0
+ 12428 = 0
+ 12430 = 0
+ 12439 = 0
+ 12441 = 0
+ 12440 = 0
+ 12442 = 0
+ 12529 = 0
+ 12533 = 0
+ 12530 = 0
+ 12534 = 0
+ 12531 = 0
+ 12535 = 0
+ 12629 = 0
+ 12630 = 0
+ 12631 = 0
+ 12636 = 0
+ 12638 = 0
+ 12640 = 0
+ 12637 = 0
+ 12639 = 0
+ 12641 = 0
+ 12648 = 0
+ 12650 = 0
+ 12649 = 0
+ 12651 = 0
+ 12662 = 0
+ 12664 = 0
+ 12663 = 0
+ 12665 = 0
+ 12682 = 0
+ 12686 = 0
+ 12683 = 0
+ 12687 = 0
+ 12684 = 0
+ 12688 = 0
+ 12738 = 0
+ 12742 = 0
+ 12739 = 0
+ 12743 = 0
+ 12740 = 0
+ 12744 = 0
+ 12839 = 0
+ 12840 = 0
+ 12852 = 0
+ 12854 = 0
+ 12853 = 0
+ 12855 = 0
+ 12888 = 0
+ 12890 = 0
+ 12889 = 0
+ 12891 = 0
+ 12920 = 0
+ 12924 = 0
+ 12921 = 0
+ 12925 = 0
+ 12922 = 0
+ 12926 = 0
+ 13315 = 0
+ 13316 = 0
+ 13317 = 0
+ 13320 = 0
+ 13322 = 0
+ 13329 = 0
+ 13331 = 0
+ 13330 = 0
+ 13332 = 0
+ 13351 = 0
+ 13355 = 0
+ 13352 = 0
+ 13356 = 0
+ 13363 = 0
+ 13365 = 0
+ 13367 = 0
+ 13364 = 0
+ 13366 = 0
+ 13368 = 0
+ 13375 = 0
+ 13379 = 0
+ 13376 = 0
+ 13380 = 0
+ 13397 = 0
+ 13401 = 0
+ 13398 = 0
+ 13402 = 0
+ 13399 = 0
+ 13403 = 0
+ 13453 = 0
+ 13461 = 0
+ 13454 = 0
+ 13462 = 0
+ 13455 = 0
+ 13463 = 0
+ 13583 = 0
+ 13585 = 0
+ 13602 = 0
+ 13606 = 0
+ 13603 = 0
+ 13607 = 0
+ 13614 = 0
+ 13618 = 0
+ 13615 = 0
+ 13619 = 0
+ 13662 = 0
+ 13670 = 0
+ 13663 = 0
+ 13671 = 0
+ 13664 = 0
+ 13672 = 0
+ 13792 = 0
+ 13793 = 0
+ 13794 = 0
+ 13797 = 0
+ 13798 = 0
+ 13804 = 0
+ 13806 = 0
+ 13808 = 0
+ 13805 = 0
+ 13807 = 0
+ 13809 = 0
+ 13816 = 0
+ 13818 = 0
+ 13817 = 0
+ 13819 = 0
+ 13828 = 0
+ 13830 = 0
+ 13829 = 0
+ 13831 = 0
+ 13842 = 0
+ 13844 = 0
+ 13843 = 0
+ 13845 = 0
+ 13874 = 0
+ 13878 = 0
+ 13875 = 0
+ 13879 = 0
+ 13876 = 0
+ 13880 = 0
+ 13960 = 0
+ 13964 = 0
+ 13961 = 0
+ 13965 = 0
+ 13962 = 0
+ 13966 = 0
+ 14060 = 0
+ 14061 = 0
+ 14067 = 0
+ 14069 = 0
+ 14068 = 0
+ 14070 = 0
+ 14079 = 0
+ 14081 = 0
+ 14080 = 0
+ 14082 = 0
+ 14169 = 0
+ 14173 = 0
+ 14170 = 0
+ 14174 = 0
+ 14171 = 0
+ 14175 = 0
+ 14274 = 0
+ 14275 = 0
+ 14276 = 0
+ 14281 = 0
+ 14283 = 0
+ 14285 = 0
+ 14282 = 0
+ 14284 = 0
+ 14286 = 0
+ 14293 = 0
+ 14295 = 0
+ 14294 = 0
+ 14296 = 0
+ 14305 = 0
+ 14307 = 0
+ 14309 = 0
+ 14306 = 0
+ 14308 = 0
+ 14310 = 0
+ 14317 = 0
+ 14319 = 0
+ 14321 = 0
+ 14318 = 0
+ 14320 = 0
+ 14322 = 0
+ 14329 = 0
+ 14333 = 0
+ 14330 = 0
+ 14334 = 0
+ 14351 = 0
+ 14355 = 0
+ 14352 = 0
+ 14356 = 0
+ 14353 = 0
+ 14357 = 0
+ 14407 = 0
+ 14415 = 0
+ 14408 = 0
+ 14416 = 0
+ 14409 = 0
+ 14417 = 0
+ 14437 = 0
+ 14441 = 0
+ 14438 = 0
+ 14442 = 0
+ 14439 = 0
+ 14443 = 0
+ 14537 = 0
+ 14538 = 0
+ 14539 = 0
+ 14544 = 0
+ 14546 = 0
+ 14545 = 0
+ 14547 = 0
+ 14556 = 0
+ 14558 = 0
+ 14560 = 0
+ 14557 = 0
+ 14559 = 0
+ 14561 = 0
+ 14568 = 0
+ 14572 = 0
+ 14569 = 0
+ 14573 = 0
+ 14616 = 0
+ 14624 = 0
+ 14617 = 0
+ 14625 = 0
+ 14618 = 0
+ 14626 = 0
+ 14646 = 0
+ 14650 = 0
+ 14647 = 0
+ 14651 = 0
+ 14648 = 0
+ 14652 = 0
+ 14956 = 0
+ 14957 = 0
+ 14964 = 0
+ 14966 = 0
+ 14965 = 0
+ 14967 = 0
+ 14988 = 0
+ 14990 = 0
+ 14989 = 0
+ 14991 = 0
+ 15008 = 0
+ 15012 = 0
+ 15009 = 0
+ 15013 = 0
+ 15010 = 0
+ 15014 = 0
+ 15164 = 0
+ 15166 = 0
+ 15183 = 0
+ 15187 = 0
+ 15184 = 0
+ 15188 = 0
+ 15195 = 0
+ 15199 = 0
+ 15196 = 0
+ 15200 = 0
+ 15243 = 0
+ 15251 = 0
+ 15244 = 0
+ 15252 = 0
+ 15245 = 0
+ 15253 = 0
+ 15373 = 0
+ 15374 = 0
+ 15375 = 0
+ 15382 = 0
+ 15384 = 0
+ 15383 = 0
+ 15385 = 0
+ 15392 = 0
+ 15396 = 0
+ 15393 = 0
+ 15397 = 0
+ 15404 = 0
+ 15406 = 0
+ 15408 = 0
+ 15405 = 0
+ 15407 = 0
+ 15409 = 0
+ 15426 = 0
+ 15430 = 0
+ 15427 = 0
+ 15431 = 0
+ 15428 = 0
+ 15432 = 0
+ 15452 = 0
+ 15460 = 0
+ 15453 = 0
+ 15461 = 0
+ 15454 = 0
+ 15462 = 0
+ 15582 = 0
+ 15583 = 0
+ 15589 = 0
+ 15591 = 0
+ 15590 = 0
+ 15592 = 0
+ 15601 = 0
+ 15603 = 0
+ 15602 = 0
+ 15604 = 0
+ 15691 = 0
+ 15695 = 0
+ 15692 = 0
+ 15696 = 0
+ 15693 = 0
+ 15697 = 0
+ 15791 = 0
+ 15792 = 0
+ 15793 = 0
+ 15798 = 0
+ 15800 = 0
+ 15802 = 0
+ 15799 = 0
+ 15801 = 0
+ 15803 = 0
+ 15810 = 0
+ 15812 = 0
+ 15811 = 0
+ 15813 = 0
+ 15824 = 0
+ 15826 = 0
+ 15825 = 0
+ 15827 = 0
+ 15844 = 0
+ 15848 = 0
+ 15845 = 0
+ 15849 = 0
+ 15846 = 0
+ 15850 = 0
+ 15900 = 0
+ 15904 = 0
+ 15901 = 0
+ 15905 = 0
+ 15902 = 0
+ 15906 = 0
+ 16000 = 0
+ 16001 = 0
+ 16002 = 0
+ 16007 = 0
+ 16009 = 0
+ 16008 = 0
+ 16010 = 0
+ 16019 = 0
+ 16021 = 0
+ 16023 = 0
+ 16020 = 0
+ 16022 = 0
+ 16024 = 0
+ 16031 = 0
+ 16035 = 0
+ 16032 = 0
+ 16036 = 0
+ 16079 = 0
+ 16087 = 0
+ 16080 = 0
+ 16088 = 0
+ 16081 = 0
+ 16089 = 0
+ 16109 = 0
+ 16113 = 0
+ 16110 = 0
+ 16114 = 0
+ 16111 = 0
+ 16115 = 0
+ 16216 = 0
+ 16218 = 0
+ 16220 = 0
+ 16217 = 0
+ 16219 = 0
+ 16221 = 0
+ 16228 = 0
+ 16230 = 0
+ 16232 = 0
+ 16229 = 0
+ 16231 = 0
+ 16233 = 0
+ 16240 = 0
+ 16242 = 0
+ 16244 = 0
+ 16241 = 0
+ 16243 = 0
+ 16245 = 0
+ 16262 = 0
+ 16266 = 0
+ 16263 = 0
+ 16267 = 0
+ 16264 = 0
+ 16268 = 0
+ 16288 = 0
+ 16296 = 0
+ 16289 = 0
+ 16297 = 0
+ 16290 = 0
+ 16298 = 0
+ 16318 = 0
+ 16322 = 0
+ 16319 = 0
+ 16323 = 0
+ 16320 = 0
+ 16324 = 0
--- /dev/null
+// ---------------------------------------------------------------------
+// $Id$
+//
+// Copyright (C) 2007 - 2013 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// like normal_flux_01 but check on a hyper_sphere geometry
+
+#include "../tests.h"
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_q1.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <fstream>
+
+
+template<int dim>
+void test (const Triangulation<dim> &tr,
+ const FiniteElement<dim> &fe)
+{
+ DoFHandler<dim> dof(tr);
+ dof.distribute_dofs(fe);
+
+ deallog << "FE=" << fe.get_name()
+ << std::endl;
+
+ std::set<types::boundary_id> boundary_ids;
+ boundary_ids.insert (0);
+
+ ConstraintMatrix cm;
+ VectorTools::compute_normal_flux_constraints (dof, 0, boundary_ids, cm);
+
+ cm.print (deallog.get_file_stream ());
+}
+
+
+
+template<int dim>
+void test_hyper_sphere()
+{
+ Triangulation<dim> tr;
+ GridGenerator::hyper_ball(tr);
+
+ static const HyperBallBoundary<dim> boundary;
+ tr.set_boundary (0, boundary);
+
+ tr.refine_global(2);
+
+ for (unsigned int degree=1; degree<4; ++degree)
+ {
+ FESystem<dim> fe (FE_Q<dim>(degree), dim);
+ test(tr, fe);
+ }
+}
+
+
+int main()
+{
+ std::ofstream logfile ("normal_flux_03/output");
+ deallog << std::setprecision (2);
+
+ deallog.attach(logfile);
+ deallog.depth_console (0);
+ deallog.threshold_double(1.e-12);
+
+ test_hyper_sphere<2>();
+ test_hyper_sphere<3>();
+}
--- /dev/null
+
+DEAL::FE=FESystem<2>[FE_Q<2>(1)^2]
+ 0 1: 1.00000
+ 2 3: 0.414214
+ 8 = 0
+ 18 19: -0.414214
+ 22 23: -1.00000
+ 51 50: 0.414214
+ 57 = 0
+ 71 70: -0.414214
+ 76 77: -1.00000
+ 123 122: -0.414214
+ 127 = 0
+ 135 134: 0.414214
+ 154 155: -0.414214
+ 160 = 0
+ 170 171: 0.414214
+DEAL::FE=FESystem<2>[FE_Q<2>(2)^2]
+ 0 1: 1.00000
+ 2 3: 0.414214
+ 18 = 0
+ 50 51: -0.414214
+ 62 63: -1.00000
+ 163 162: 0.414214
+ 183 = 0
+ 235 234: -0.414214
+ 254 255: -1.00000
+ 435 434: -0.414214
+ 447 = 0
+ 475 474: 0.414214
+ 486 487: 1.00000
+ 562 563: -0.414214
+ 582 = 0
+ 626 627: 0.414214
+DEAL::FE=FESystem<2>[FE_Q<2>(3)^2]
+ 0 1: 1.00000
+ 2 3: 0.414214
+ 16 18: 0.768531
+ 32 = 0
+ 40 42: 0.268761
+ 98 99: -0.414214
+ 106 108: -0.130882
+ 122 123: -1.00000
+ 130 132: -0.576341
+ 339 338: 0.414214
+ 344 342: 0.768531
+ 381 = 0
+ 386 384: 0.268761
+ 495 494: -0.414214
+ 500 498: -0.130882
+ 536 537: -1.00000
+ 542 540: -0.576341
+ 939 938: -0.414214
+ 948 946: -0.768531
+ 963 = 0
+ 972 970: -0.268761
+ 1023 1022: 0.414214
+ 1032 1030: 0.130882
+ 1046 1047: 1.00000
+ 1056 1054: 0.576341
+ 1226 1227: -0.414214
+ 1230 1232: -0.768531
+ 1268 = 0
+ 1272 1274: -0.268761
+ 1370 1371: 0.414214
+ 1374 1376: 0.130882
+ 1412 1414: 0.576341
+DEAL::FE=FESystem<3>[FE_Q<3>(1)^3]
+ 375 377: 1.00000
+ 376 377: 1.00000
+ 378 380: 0.449490
+ 379 380: 1.00000
+ 381 383: 1.00000
+ 382 383: 0.449490
+ 384 386: 0.427330
+ 385 386: 0.427330
+ 399 = 0
+ 400 401: 1.00000
+ 402 = 0
+ 403 404: 0.414214
+ 411 413: 1.00000
+ 412 = 0
+ 414 416: 0.414214
+ 415 = 0
+ 423 = 0
+ 424 = 0
+ 456 458: -0.449490
+ 457 458: 1.00000
+ 459 461: -0.427330
+ 460 461: 0.427330
+ 468 470: -1.00000
+ 469 470: 1.00000
+ 471 473: -1.00000
+ 472 473: 0.449490
+ 480 482: -0.414214
+ 481 = 0
+ 486 488: -1.00000
+ 487 = 0
+ 510 512: 1.00000
+ 511 512: -0.449490
+ 513 515: 0.427330
+ 514 515: -0.427330
+ 522 = 0
+ 523 524: -0.414214
+ 528 530: 1.00000
+ 529 530: -1.00000
+ 531 533: 0.449490
+ 532 533: -1.00000
+ 540 = 0
+ 541 542: -1.00000
+ 564 566: -0.427330
+ 565 566: -0.427330
+ 570 572: -1.00000
+ 571 572: -0.449490
+ 576 578: -0.449490
+ 577 578: -1.00000
+ 582 584: -1.00000
+ 583 584: -1.00000
+ 675 676: -1.00000
+ 677 676: 0.449490
+ 679 678: -0.427330
+ 680 678: -0.427330
+ 688 = 0
+ 689 687: -0.414214
+ 702 703: -1.00000
+ 704 = 0
+ 706 705: -0.414214
+ 707 = 0
+ 715 = 0
+ 716 = 0
+ 730 729: 0.427330
+ 731 729: -0.427330
+ 735 736: 1.00000
+ 737 736: -0.449490
+ 748 747: 0.414214
+ 749 = 0
+ 753 754: 1.00000
+ 755 = 0
+ 795 796: -1.00000
+ 797 796: -0.449490
+ 799 798: -0.427330
+ 800 798: 0.427330
+ 808 = 0
+ 809 807: 0.414214
+ 822 824: 1.00000
+ 823 824: -1.00000
+ 825 827: 1.00000
+ 826 827: -0.449490
+ 834 836: 1.00000
+ 835 = 0
+ 850 849: 0.427330
+ 851 849: 0.427330
+ 855 856: 1.00000
+ 857 856: 0.449490
+ 867 869: 1.00000
+ 868 869: 0.449490
+ 915 917: -1.00000
+ 916 917: -1.00000
+ 918 920: -0.449490
+ 919 920: -1.00000
+ 927 929: -1.00000
+ 928 929: -0.449490
+ 930 932: -0.427330
+ 931 932: -0.427330
+ 939 = 0
+ 940 941: -1.00000
+ 945 = 0
+ 946 947: -0.414214
+ 969 971: -1.00000
+ 970 = 0
+ 972 974: -0.414214
+ 973 = 0
+ 981 = 0
+ 982 = 0
+ 996 998: 0.449490
+ 997 998: -1.00000
+ 1002 1004: 0.427330
+ 1003 1004: -0.427330
+ 1014 1016: 0.414214
+ 1015 = 0
+ 1059 1061: -1.00000
+ 1060 1061: 0.449490
+ 1062 1064: -0.427330
+ 1063 1064: 0.427330
+ 1071 = 0
+ 1072 1073: 0.414214
+ 1086 1088: -1.00000
+ 1087 1088: 1.00000
+ 1089 1091: -0.449490
+ 1090 1091: 1.00000
+ 1098 = 0
+ 1099 1100: 1.00000
+ 1113 1115: 0.427330
+ 1114 1115: 0.427330
+ 1122 1124: 0.449490
+ 1123 1124: 1.00000
+ 1155 1156: 1.00000
+ 1157 1156: 0.449490
+ 1162 1161: 0.427330
+ 1163 1161: 0.427330
+ 1174 = 0
+ 1175 1173: 0.414214
+ 1182 1183: 1.00000
+ 1184 = 0
+ 1189 1188: 0.414214
+ 1190 = 0
+ 1201 = 0
+ 1202 = 0
+ 1228 1227: -0.427330
+ 1229 1227: 0.427330
+ 1236 1237: -1.00000
+ 1238 1237: -0.449490
+ 1246 1245: -0.414214
+ 1247 = 0
+ 1254 1255: -1.00000
+ 1256 = 0
+ 1275 1276: 1.00000
+ 1277 1276: -0.449490
+ 1282 1281: 0.427330
+ 1283 1281: -0.427330
+ 1294 = 0
+ 1295 1293: -0.414214
+ 1312 1311: -0.427330
+ 1313 1311: -0.427330
+ 1320 1321: -1.00000
+ 1322 1321: 0.449490
+ 1335 1336: 0.427330
+ 1337 1336: 0.427330
+ 1341 = 0
+ 1343 1342: 0.414214
+ 1353 1354: 0.414214
+ 1355 = 0
+ 1359 = 0
+ 1361 = 0
+ 1371 1372: -0.427330
+ 1373 1372: 0.427330
+ 1380 1381: -0.414214
+ 1382 = 0
+ 1407 1408: 0.427330
+ 1409 1408: -0.427330
+ 1413 = 0
+ 1415 1414: -0.414214
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+ 1427 1426: -0.427330
+ 1443 1444: -0.427330
+ 1445 1444: -0.427330
+ 1452 = 0
+ 1454 1453: -0.414214
+ 1461 1462: -0.414214
+ 1463 = 0
+ 1470 = 0
+ 1472 = 0
+ 1491 1492: 0.427330
+ 1493 1492: -0.427330
+ 1500 1501: 0.414214
+ 1502 = 0
+ 1515 1516: -0.427330
+ 1517 1516: 0.427330
+ 1524 = 0
+ 1526 1525: 0.414214
+ 1539 1540: 0.427330
+ 1541 1540: 0.427330
+DEAL::FE=FESystem<3>[FE_Q<3>(2)^3]
+ 2187 2189: 1.00000
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+ 2218 2219: 1.00000
+ 2220 2222: 0.679605
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+ 2268 = 0
+ 2269 2270: 1.00000
+ 2271 = 0
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+ 2280 = 0
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+ 2322 2324: 1.00000
+ 2323 = 0
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+ 2341 = 0
+ 2376 = 0
+ 2377 = 0
+ 2382 = 0
+ 2383 2384: 0.198912
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+ 2386 = 0
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+ 2671 = 0
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+ 2680 = 0
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+ 2716 = 0
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+ 2916 = 0
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+ 2971 2972: -1.00000
+ 3006 = 0
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+ 4186 = 0
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+ 4201 = 0
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+ 4286 = 0
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+ 4336 = 0
+ 4337 = 0
+ 4345 4344: -0.198912
+ 4346 = 0
+ 4351 = 0
+ 4352 4350: -0.198912
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+ 4553 = 0
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+ 5050 = 0
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+ 5065 = 0
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+ 5199 5201: 1.00000
+ 5200 = 0
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+ 5215 = 0
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+ 5940 = 0
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+ 6138 = 0
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+ 6147 6149: -0.198912
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+ 6153 = 0
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+ 6370 = 0
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+ 6406 = 0
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+ 6873 = 0
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+ 6888 = 0
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+ 7023 = 0
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+ 7038 = 0
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+ 7678 = 0
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+ 7828 = 0
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+ 8189 = 0
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+ 8542 = 0
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+ 8557 = 0
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+ 8647 = 0
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+ 9114 9115: 0.437092
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+ 9135 = 0
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+ 9467 = 0
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+ 9909 = 0
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+ 10335 = 0
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+ 10751 = 0
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+ 10811 = 0
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+ 11007 = 0
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+ 11022 = 0
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+ 11097 = 0
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+DEAL::FE=FESystem<3>[FE_Q<3>(3)^3]
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+ 6783 = 0
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+ 6927 6929: 1.00000
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+ 6953 = 0
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+ 6954 = 0
+ 7023 7031: 0.774446
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+ 7071 = 0
+ 7072 = 0
+ 7077 = 0
+ 7079 7081: 0.268761
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+ 7080 7082: 0.130882
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+ 7085 = 0
+ 7084 7088: 0.130882
+ 7086 = 0
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+ 7909 = 0
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+ 7922 = 0
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+ 8030 = 0
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+ 8646 = 0
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+ 8898 = 0
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+ 8905 = 0
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+ 12820 = 0
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+ 13261 = 0
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+ 13286 = 0
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+ 13937 = 0
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+ 15628 = 0
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+ 19741 = 0
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+ 19850 = 0
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+ 21400 21408: -0.774446
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+ 21401 21409: -0.580402
+ 21405 21409: 0.138002
+ 21459 = 0
+ 21460 21461: 0.414214
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+ 21473 21475: 0.422732
+ 21472 21476: -0.135275
+ 21474 21476: 0.418366
+ 21483 = 0
+ 21485 21487: 0.130882
+ 21484 = 0
+ 21486 21488: 0.268761
+ 21507 21515: -0.271536
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+ 21841 21849: -0.789776
+ 21845 21849: 0.789776
+ 21842 21850: -0.596427
+ 21846 21850: 0.596427
+ 21900 = 0
+ 21901 21902: 1.00000
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+ 21914 21916: 1.00000
+ 21913 21917: -0.145063
+ 21915 21917: 1.00000
+ 21924 = 0
+ 21926 21928: 0.576341
+ 21925 = 0
+ 21927 21929: 0.768531
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+ 23972 23968: 0.604838
+ 23976 23968: 0.783313
+ 23973 23969: 0.783313
+ 23977 23969: 0.604838
+ 24160 = 0
+ 24161 24159: 0.414214
+ 24167 24165: 0.277533
+ 24169 24165: 0.422732
+ 24168 24166: 0.135275
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+ 24185 = 0
+ 24187 24183: 0.768531
+ 24186 = 0
+ 24188 24184: 0.576341
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+ 24348 24349: 1.00000
+ 24350 = 0
+ 24355 24354: 0.414214
+ 24356 = 0
+ 24362 24360: 0.768531
+ 24364 = 0
+ 24363 24361: 0.576341
+ 24365 = 0
+ 24384 24386: 1.00000
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+ 24414 24410: 0.771431
+ 24418 24410: 0.141216
+ 24601 = 0
+ 24602 = 0
+ 24608 24606: 0.268761
+ 24610 = 0
+ 24609 24607: 0.130882
+ 24611 = 0
+ 24626 = 0
+ 24628 24624: 0.268761
+ 24627 = 0
+ 24629 24625: 0.130882
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+ 25650 25646: -0.596427
+ 25654 25646: 0.596427
+ 25798 25797: -0.414214
+ 25799 = 0
+ 25805 25803: -0.130882
+ 25807 = 0
+ 25806 25804: -0.268761
+ 25808 = 0
+ 25823 25821: -0.422732
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+ 25839 25835: -0.132271
+ 25843 25835: 0.132271
+ 25986 25987: -1.00000
+ 25988 = 0
+ 25994 25992: -0.576341
+ 25996 = 0
+ 25995 25993: -0.768531
+ 25997 = 0
+ 26010 26012: -1.00000
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+ 26785 26777: -0.288063
+ 26968 = 0
+ 26969 26967: -0.414214
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+ 26993 = 0
+ 26995 26991: -0.130882
+ 26994 = 0
+ 26996 26992: -0.268761
+ 27007 27003: 0.271536
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+ 27186 27182: 0.789776
+ 27190 27182: -0.789776
+ 27326 = 0
+ 27328 27324: -0.576341
+ 27327 = 0
+ 27329 27325: -0.768531
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+ 29104 29108: 0.783313
+ 29112 29108: 0.604838
+ 29105 29109: 0.604838
+ 29113 29109: 0.783313
+ 29163 = 0
+ 29165 29164: 0.414214
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+ 29176 29178: 0.135275
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+ 29187 = 0
+ 29191 29189: 0.768531
+ 29188 = 0
+ 29192 29190: 0.576341
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+ 29433 29434: 0.414214
+ 29435 = 0
+ 29445 29447: 0.768531
+ 29449 = 0
+ 29446 29448: 0.576341
+ 29450 = 0
+ 29457 29459: 0.422732
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+ 29483 29487: 0.584650
+ 29491 29487: 0.282381
+ 29541 = 0
+ 29543 = 0
+ 29553 29555: 0.268761
+ 29557 = 0
+ 29554 29556: 0.130882
+ 29558 = 0
+ 29565 = 0
+ 29569 29567: 0.268761
+ 29566 = 0
+ 29570 29568: 0.130882
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+ 29941 29937: 0.789776
+ 30126 30127: -0.414214
+ 30128 = 0
+ 30138 30140: -0.130882
+ 30142 = 0
+ 30139 30141: -0.268761
+ 30143 = 0
+ 30150 30152: -0.422732
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+ 30184 30180: 0.274456
+ 30234 30236: -0.576341
+ 30238 = 0
+ 30235 30237: -0.768531
+ 30239 = 0
+ 30246 30250: -0.584650
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+ 31539 = 0
+ 31541 31540: -0.414214
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+ 31552 31554: 0.135275
+ 31556 31554: -0.418366
+ 31563 = 0
+ 31567 31565: -0.130882
+ 31564 = 0
+ 31568 31566: -0.268761
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+ 31842 31838: -0.789776
+ 31835 31839: 0.596427
+ 31843 31839: -0.596427
+ 31881 = 0
+ 31885 31883: -0.576341
+ 31882 = 0
+ 31886 31884: -0.768531
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+ 33449 33453: -0.783313
+ 33457 33453: -0.604838
+ 33600 = 0
+ 33602 33601: -0.414214
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+ 33607 33609: -0.135275
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+ 33624 = 0
+ 33628 33626: -0.768531
+ 33625 = 0
+ 33629 33627: -0.576341
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+ 33789 33790: -0.414214
+ 33791 = 0
+ 33795 33797: -0.768531
+ 33799 = 0
+ 33796 33798: -0.576341
+ 33800 = 0
+ 33813 33815: -0.422732
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+ 33835 33831: -0.141216
+ 33978 = 0
+ 33980 = 0
+ 33984 33986: -0.268761
+ 33988 = 0
+ 33985 33987: -0.130882
+ 33989 = 0
+ 34002 = 0
+ 34006 34004: -0.268761
+ 34003 = 0
+ 34007 34005: -0.130882
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+ 34917 34913: -0.789776
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+ 34918 34914: -0.596427
+ 35022 35023: 0.414214
+ 35024 = 0
+ 35028 35030: 0.130882
+ 35032 = 0
+ 35029 35031: 0.268761
+ 35033 = 0
+ 35046 35048: 0.422732
+ 35050 35048: -0.277533
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+ 35067 35063: -0.274456
+ 35060 35064: 0.132271
+ 35068 35064: -0.132271
+ 35211 35213: 0.576341
+ 35215 = 0
+ 35212 35214: 0.768531
+ 35216 = 0
+ 35223 35227: 0.584650
+ 35231 35227: -0.282381
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+ 35232 35228: -0.288063
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+ 35824 35828: -0.580402
+ 35832 35828: 0.138002
+ 35825 35829: -0.774446
+ 35833 35829: 0.288063
+ 35976 = 0
+ 35978 35977: 0.414214
+ 35982 35984: -0.277533
+ 35986 35984: 0.422732
+ 35983 35985: -0.135275
+ 35987 35985: 0.418366
+ 36000 = 0
+ 36004 36002: 0.130882
+ 36001 = 0
+ 36005 36003: 0.268761
+ 36012 36016: -0.271536
+ 36020 36016: 0.133733
+ 36013 36017: -0.132271
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+ 36186 36182: 0.596427
+ 36179 36183: -0.789776
+ 36187 36183: 0.789776
+ 36291 = 0
+ 36295 36293: 0.576341
+ 36292 = 0
+ 36296 36294: 0.768531
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