From: Martin Kronbichler Date: Fri, 23 Aug 2013 22:38:34 +0000 (+0000) Subject: Add function VectorTools::compute_normal_flux_constraints X-Git-Tag: v8.1.0~972 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=475ee66baae86fc65ebeeee7eeac85df0367de83;p=dealii.git Add function VectorTools::compute_normal_flux_constraints git-svn-id: https://svn.dealii.org/trunk@30466 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h index 95099c18b9..9dba3186c6 100644 --- a/deal.II/doc/news/changes.h +++ b/deal.II/doc/news/changes.h @@ -68,6 +68,13 @@ inconvenience this causes.

Specific improvements

    +
  1. + New: The method VectorTools::compute_normal_flux_constraints can be used to + force a vector finite element function to be normal to the boundary. +
    + (Martin Kronbichler, 2013/08/23) +
    2. +
  2. Improved: MappingQ now uses the points of the Gauss-Lobatto quadrature formula as support points instead of equispaced ones. This allows its use diff --git a/deal.II/include/deal.II/numerics/vector_tools.h b/deal.II/include/deal.II/numerics/vector_tools.h index 1121e1ff66..f83d28fc42 100644 --- a/deal.II/include/deal.II/numerics/vector_tools.h +++ b/deal.II/include/deal.II/numerics/vector_tools.h @@ -1404,300 +1404,167 @@ namespace VectorTools /** - * 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 - * dim 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 - * [first_vector_component,first_vector_component+dim) - * come from the same base finite - * element. For example, in the - * Stokes example above, it would - * not make sense to use a - * FESystem@(FE_Q@(2), - * 1, FE_Q@(1), dim) - * (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 dim 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 + * [first_vector_component,first_vector_component+dim) come + * from the same base finite element. For example, in the Stokes example + * above, it would not make sense to use a + * FESystem@(FE_Q@(2), 1, FE_Q@(1), dim) + * (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 . * * *

    Computing constraints in 2d

    * - * Computing these constraints requires - * some smarts. The main question - * revolves around the question what the - * normal vector is. Consider the - * following situation: - *

    - * @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:

    @image html no_normal_flux_1.png *

    * - * 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. all 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 each of these normal - * vectors but only for the - * average 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. all 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 each of these normal + * vectors but only for the average 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: * *

    * @image html no_normal_flux_2.png *

    * - * 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 different 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 different 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: * *

    * @image html no_normal_flux_3.png *

    * - * 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. * * *

    Computing constraints in 3d

    * - * 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: * *

    * @image html no_normal_flux_4.png *

    * - * 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. * * *

    Results

    * - * 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: * *

    @@ -1705,16 +1572,10 @@ namespace VectorTools * @image html no_normal_flux_6.png *

    * - * 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 * @@ -1728,6 +1589,22 @@ namespace VectorTools ConstraintMatrix &constraints, const Mapping &mapping = StaticMappingQ1::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 class DH, int spacedim> + void + compute_normal_flux_constraints (const DH &dof_handler, + const unsigned int first_vector_component, + const std::set &boundary_ids, + ConstraintMatrix &constraints, + const Mapping &mapping = StaticMappingQ1::mapping); + //@} /** diff --git a/deal.II/include/deal.II/numerics/vector_tools.templates.h b/deal.II/include/deal.II/numerics/vector_tools.templates.h index 32bd467905..99cb82e21b 100644 --- a/deal.II/include/deal.II/numerics/vector_tools.templates.h +++ b/deal.II/include/deal.II/numerics/vector_tools.templates.h @@ -60,6 +60,7 @@ #include #include +#include #include #include #include @@ -3183,19 +3184,10 @@ namespace VectorTools } } - // 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); @@ -3225,12 +3217,8 @@ namespace VectorTools } } - // 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) { @@ -3335,32 +3323,18 @@ namespace VectorTools ConstraintMatrix &constraints, const Mapping &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 degree * (degree + - // 1) 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 + // degree * (degree + 1) to obtain the values for the + // corresponding degrees of freedom. const unsigned int superdegree = dof_handler.get_fe ().degree; const QGauss reference_face_quadrature (2 * superdegree); const unsigned int dofs_per_face = dof_handler.get_fe ().dofs_per_face; @@ -3603,19 +3577,12 @@ namespace VectorTools for (unsigned int face = 0; face < GeometryInfo::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*> (&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*> (&cell->get_fe ()) == 0) { typedef FiniteElement FEL; @@ -3689,19 +3656,12 @@ namespace VectorTools for (unsigned int face = 0; face < GeometryInfo::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*> (&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*> (&cell->get_fe ()) == 0) { typedef FiniteElement FEL; @@ -3731,11 +3691,8 @@ namespace VectorTools 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, @@ -3772,10 +3729,8 @@ namespace VectorTools 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 void compute_face_projection_div_conforming (const cell_iterator &cell, @@ -3786,13 +3741,9 @@ namespace VectorTools const std::vector > &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 > &normals = fe_values.get_normal_vectors (); @@ -3802,9 +3753,7 @@ namespace VectorTools values (fe_values.n_quadrature_points, Vector (2)); Vector 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 > & quadrature_points = fe_values.get_quadrature_points (); @@ -3834,10 +3783,8 @@ namespace VectorTools 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]))) { @@ -3848,9 +3795,7 @@ namespace VectorTools } } - // dummy implementation of above - // function for all other - // dimensions + // dummy implementation of above function for all other dimensions template void compute_face_projection_div_conforming (const cell_iterator &, @@ -3864,10 +3809,8 @@ namespace VectorTools 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 void compute_face_projection_div_conforming (const cell_iterator &cell, @@ -3879,13 +3822,9 @@ namespace VectorTools std::vector &dof_values, std::vector &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 > &normals = fe_values.get_normal_vectors (); @@ -4711,6 +4650,153 @@ namespace VectorTools + namespace + { + template + struct PointComparator + { + bool operator ()(const std_cxx1x::array &p1, + const std_cxx1x::array &p2) + { + for (unsigned int d=0; d class DH, int spacedim> + void + compute_normal_flux_constraints (const DH&dof_handler, + const unsigned int first_vector_component, + const std::set &boundary_ids, + ConstraintMatrix &constraints, + const Mapping &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, PointComparator > vector_dofs; + std::vector face_dofs; + + std::vector > cell_vector_dofs; + for (typename DH::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::faces_per_cell; + ++face_no) + if (boundary_ids.find(cell->face(face_no)->boundary_indicator()) + != boundary_ids.end()) + { + const FiniteElement &fe = cell->get_fe(); + typename DH::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= 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,PointComparator >:: + 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 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 normal; + unsigned constrained_index = -1; + for (unsigned int d=0; d >* 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; csize(); ++c) + { + int index = -1; + for (unsigned int d=0; d 1e-13) + constraints.add_entry(new_index, (*it)[constrained_index], + -normal[d]); + } + } + } + } + } + + + namespace internal { template diff --git a/tests/deal.II/normal_flux_01.cc b/tests/deal.II/normal_flux_01.cc new file mode 100644 index 0000000000..b0ec01d7f8 --- /dev/null +++ b/tests/deal.II/normal_flux_01.cc @@ -0,0 +1,94 @@ +// --------------------------------------------------------------------- +// $Id$ +// +// 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 +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + + +template +void test (const Triangulation &tr, + const FiniteElement &fe) +{ + DoFHandler dof(tr); + dof.distribute_dofs(fe); + + for (unsigned int i=0; i::faces_per_cell; ++i) + { + deallog << "FE=" << fe.get_name() + << ", case=" << i + << std::endl; + + std::set 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 +void test_hyper_cube() +{ + Triangulation tr; + GridGenerator::hyper_cube(tr); + + for (unsigned int i=0; i::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 fe (FE_Q(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>(); +} diff --git a/tests/deal.II/normal_flux_01/cmp/generic b/tests/deal.II/normal_flux_01/cmp/generic new file mode 100644 index 0000000000..4e4bf7d8d4 --- /dev/null +++ b/tests/deal.II/normal_flux_01/cmp/generic @@ -0,0 +1,9560 @@ + +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 + 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=5 + 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 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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 diff --git a/tests/deal.II/normal_flux_02.cc b/tests/deal.II/normal_flux_02.cc new file mode 100644 index 0000000000..adb5611821 --- /dev/null +++ b/tests/deal.II/normal_flux_02.cc @@ -0,0 +1,98 @@ +// --------------------------------------------------------------------- +// $Id$ +// +// 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 +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + + + +template +void test (const Triangulation &tr, + const FiniteElement &fe) +{ + DoFHandler dof(tr); + dof.distribute_dofs(fe); + + for (unsigned int i=0; i::faces_per_cell; ++i) + { + deallog << "FE=" << fe.get_name() + << ", case=" << i + << std::endl; + + std::set 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 +void test_hyper_cube() +{ + Triangulation tr; + GridGenerator::hyper_cube(tr); + + for (unsigned int i=0; i::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 fe (FE_Q(degree+1), 1, + FE_Q(degree), dim, + FE_Q(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>(); +} diff --git a/tests/deal.II/normal_flux_02/cmp/generic b/tests/deal.II/normal_flux_02/cmp/generic new file mode 100644 index 0000000000..ae1f7e5045 --- /dev/null +++ b/tests/deal.II/normal_flux_02/cmp/generic @@ -0,0 +1,9560 @@ + +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 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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 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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 + 26 = 0 + 28 = 0 + 32 = 0 + 33 = 0 + 79 = 0 + 80 = 0 + 81 = 0 + 84 = 0 + 85 = 0 + 89 = 0 + 91 = 0 + 127 = 0 + 128 = 0 + 129 = 0 + 132 = 0 + 133 = 0 + 138 = 0 + 139 = 0 + 175 = 0 + 176 = 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 + 333 = 0 + 334 = 0 + 337 = 0 + 338 = 0 + 342 = 0 + 344 = 0 + 385 = 0 + 386 = 0 + 387 = 0 + 390 = 0 + 391 = 0 + 392 = 0 + 396 = 0 + 397 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1213 = 0 + 1216 = 0 + 1217 = 0 + 1241 = 0 + 1242 = 0 + 1243 = 0 + 1246 = 0 + 1247 = 0 + 1271 = 0 + 1272 = 0 + 1290 = 0 + 1292 = 0 + 1320 = 0 + 1321 = 0 + 1322 = 0 + 1326 = 0 + 1327 = 0 + 1370 = 0 + 1371 = 0 + 1388 = 0 + 1389 = 0 + 1390 = 0 + 1393 = 0 + 1394 = 0 + 1423 = 0 + 1424 = 0 + 1425 = 0 + 1448 = 0 + 1449 = 0 + 1467 = 0 + 1468 = 0 + 1469 = 0 + 1487 = 0 + 1488 = 0 + 1535 = 0 + 1536 = 0 + 1537 = 0 + 1540 = 0 + 1542 = 0 + 1565 = 0 + 1567 = 0 + 1584 = 0 + 1585 = 0 + 1586 = 0 + 1589 = 0 + 1590 = 0 + 1614 = 0 + 1615 = 0 + 1638 = 0 + 1639 = 0 + 1640 = 0 + 1663 = 0 + 1664 = 0 + 1665 = 0 + 1702 = 0 + 1703 = 0 + 1720 = 0 + 1722 = 0 + 1739 = 0 + 1740 = 0 + 1741 = 0 + 1758 = 0 + 1759 = 0 + 1777 = 0 + 1778 = 0 + 1779 = 0 + 1796 = 0 + 1797 = 0 + 1798 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=0 + 2 = 0 + 3 = 0 + 12 = 0 + 13 = 0 + 22 = 0 + 23 = 0 + 32 = 0 + 33 = 0 + 43 = 0 + 44 = 0 + 71 = 0 + 72 = 0 + 99 = 0 + 100 = 0 + 113 = 0 + 114 = 0 + 361 = 0 + 362 = 0 + 371 = 0 + 372 = 0 + 382 = 0 + 383 = 0 + 403 = 0 + 404 = 0 + 424 = 0 + 425 = 0 + 619 = 0 + 620 = 0 + 629 = 0 + 630 = 0 + 640 = 0 + 641 = 0 + 668 = 0 + 669 = 0 + 682 = 0 + 683 = 0 + 877 = 0 + 878 = 0 + 888 = 0 + 889 = 0 + 909 = 0 + 910 = 0 + 1951 = 0 + 1952 = 0 + 1961 = 0 + 1962 = 0 + 1972 = 0 + 1973 = 0 + 1993 = 0 + 1994 = 0 + 2014 = 0 + 2015 = 0 + 2209 = 0 + 2210 = 0 + 2219 = 0 + 2220 = 0 + 2230 = 0 + 2231 = 0 + 2251 = 0 + 2252 = 0 + 2272 = 0 + 2273 = 0 + 2467 = 0 + 2468 = 0 + 2478 = 0 + 2479 = 0 + 2499 = 0 + 2500 = 0 + 2653 = 0 + 2654 = 0 + 2664 = 0 + 2665 = 0 + 2685 = 0 + 2686 = 0 + 3583 = 0 + 3584 = 0 + 3593 = 0 + 3594 = 0 + 3604 = 0 + 3605 = 0 + 3632 = 0 + 3633 = 0 + 3646 = 0 + 3647 = 0 + 3841 = 0 + 3842 = 0 + 3852 = 0 + 3853 = 0 + 3873 = 0 + 3874 = 0 + 4027 = 0 + 4028 = 0 + 4037 = 0 + 4038 = 0 + 4048 = 0 + 4049 = 0 + 4076 = 0 + 4077 = 0 + 4090 = 0 + 4091 = 0 + 4285 = 0 + 4286 = 0 + 4296 = 0 + 4297 = 0 + 4317 = 0 + 4318 = 0 + 5215 = 0 + 5216 = 0 + 5226 = 0 + 5227 = 0 + 5247 = 0 + 5248 = 0 + 5401 = 0 + 5402 = 0 + 5412 = 0 + 5413 = 0 + 5433 = 0 + 5434 = 0 + 5587 = 0 + 5588 = 0 + 5598 = 0 + 5599 = 0 + 5619 = 0 + 5620 = 0 + 5773 = 0 + 5774 = 0 + 5784 = 0 + 5785 = 0 + 5805 = 0 + 5806 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=1 + 2 = 0 + 3 = 0 + 12 = 0 + 13 = 0 + 22 = 0 + 23 = 0 + 32 = 0 + 33 = 0 + 43 = 0 + 44 = 0 + 71 = 0 + 72 = 0 + 99 = 0 + 100 = 0 + 113 = 0 + 114 = 0 + 361 = 0 + 362 = 0 + 371 = 0 + 372 = 0 + 382 = 0 + 383 = 0 + 403 = 0 + 404 = 0 + 424 = 0 + 425 = 0 + 619 = 0 + 620 = 0 + 629 = 0 + 630 = 0 + 640 = 0 + 641 = 0 + 668 = 0 + 669 = 0 + 682 = 0 + 683 = 0 + 877 = 0 + 878 = 0 + 888 = 0 + 889 = 0 + 909 = 0 + 910 = 0 + 1213 = 0 + 1214 = 0 + 1218 = 0 + 1219 = 0 + 1223 = 0 + 1224 = 0 + 1228 = 0 + 1229 = 0 + 1234 = 0 + 1235 = 0 + 1255 = 0 + 1256 = 0 + 1276 = 0 + 1277 = 0 + 1283 = 0 + 1284 = 0 + 1471 = 0 + 1472 = 0 + 1476 = 0 + 1477 = 0 + 1482 = 0 + 1483 = 0 + 1496 = 0 + 1497 = 0 + 1510 = 0 + 1511 = 0 + 1687 = 0 + 1688 = 0 + 1692 = 0 + 1693 = 0 + 1698 = 0 + 1699 = 0 + 1719 = 0 + 1720 = 0 + 1726 = 0 + 1727 = 0 + 1873 = 0 + 1874 = 0 + 1879 = 0 + 1880 = 0 + 1893 = 0 + 1894 = 0 + 1951 = 0 + 1952 = 0 + 1961 = 0 + 1962 = 0 + 1972 = 0 + 1973 = 0 + 1993 = 0 + 1994 = 0 + 2014 = 0 + 2015 = 0 + 2209 = 0 + 2210 = 0 + 2219 = 0 + 2220 = 0 + 2230 = 0 + 2231 = 0 + 2251 = 0 + 2252 = 0 + 2272 = 0 + 2273 = 0 + 2467 = 0 + 2468 = 0 + 2478 = 0 + 2479 = 0 + 2499 = 0 + 2500 = 0 + 2653 = 0 + 2654 = 0 + 2664 = 0 + 2665 = 0 + 2685 = 0 + 2686 = 0 + 2947 = 0 + 2948 = 0 + 2952 = 0 + 2953 = 0 + 2958 = 0 + 2959 = 0 + 2972 = 0 + 2973 = 0 + 2986 = 0 + 2987 = 0 + 3163 = 0 + 3164 = 0 + 3168 = 0 + 3169 = 0 + 3174 = 0 + 3175 = 0 + 3188 = 0 + 3189 = 0 + 3202 = 0 + 3203 = 0 + 3349 = 0 + 3350 = 0 + 3355 = 0 + 3356 = 0 + 3369 = 0 + 3370 = 0 + 3505 = 0 + 3506 = 0 + 3511 = 0 + 3512 = 0 + 3525 = 0 + 3526 = 0 + 3583 = 0 + 3584 = 0 + 3593 = 0 + 3594 = 0 + 3604 = 0 + 3605 = 0 + 3632 = 0 + 3633 = 0 + 3646 = 0 + 3647 = 0 + 3841 = 0 + 3842 = 0 + 3852 = 0 + 3853 = 0 + 3873 = 0 + 3874 = 0 + 4027 = 0 + 4028 = 0 + 4037 = 0 + 4038 = 0 + 4048 = 0 + 4049 = 0 + 4076 = 0 + 4077 = 0 + 4090 = 0 + 4091 = 0 + 4285 = 0 + 4286 = 0 + 4296 = 0 + 4297 = 0 + 4317 = 0 + 4318 = 0 + 4579 = 0 + 4580 = 0 + 4584 = 0 + 4585 = 0 + 4590 = 0 + 4591 = 0 + 4611 = 0 + 4612 = 0 + 4618 = 0 + 4619 = 0 + 4765 = 0 + 4766 = 0 + 4771 = 0 + 4772 = 0 + 4785 = 0 + 4786 = 0 + 4951 = 0 + 4952 = 0 + 4956 = 0 + 4957 = 0 + 4962 = 0 + 4963 = 0 + 4983 = 0 + 4984 = 0 + 4990 = 0 + 4991 = 0 + 5137 = 0 + 5138 = 0 + 5143 = 0 + 5144 = 0 + 5157 = 0 + 5158 = 0 + 5215 = 0 + 5216 = 0 + 5226 = 0 + 5227 = 0 + 5247 = 0 + 5248 = 0 + 5401 = 0 + 5402 = 0 + 5412 = 0 + 5413 = 0 + 5433 = 0 + 5434 = 0 + 5587 = 0 + 5588 = 0 + 5598 = 0 + 5599 = 0 + 5619 = 0 + 5620 = 0 + 5773 = 0 + 5774 = 0 + 5784 = 0 + 5785 = 0 + 5805 = 0 + 5806 = 0 + 6037 = 0 + 6038 = 0 + 6043 = 0 + 6044 = 0 + 6057 = 0 + 6058 = 0 + 6193 = 0 + 6194 = 0 + 6199 = 0 + 6200 = 0 + 6213 = 0 + 6214 = 0 + 6349 = 0 + 6350 = 0 + 6355 = 0 + 6356 = 0 + 6369 = 0 + 6370 = 0 + 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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 diff --git a/tests/deal.II/normal_flux_03.cc b/tests/deal.II/normal_flux_03.cc new file mode 100644 index 0000000000..db6adaa995 --- /dev/null +++ b/tests/deal.II/normal_flux_03.cc @@ -0,0 +1,88 @@ +// --------------------------------------------------------------------- +// $Id$ +// +// 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 +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + + +template +void test (const Triangulation &tr, + const FiniteElement &fe) +{ + DoFHandler dof(tr); + dof.distribute_dofs(fe); + + deallog << "FE=" << fe.get_name() + << std::endl; + + std::set 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 +void test_hyper_sphere() +{ + Triangulation tr; + GridGenerator::hyper_ball(tr); + + static const HyperBallBoundary boundary; + tr.set_boundary (0, boundary); + + tr.refine_global(2); + + for (unsigned int degree=1; degree<4; ++degree) + { + FESystem fe (FE_Q(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>(); +} diff --git a/tests/deal.II/normal_flux_03/cmp/generic b/tests/deal.II/normal_flux_03/cmp/generic new file mode 100644 index 0000000000..355823b0e8 --- /dev/null +++ b/tests/deal.II/normal_flux_03/cmp/generic @@ -0,0 +1,2384 @@ + +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 + 1425 1426: -0.427330 + 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 + 2188 2189: 1.00000 + 2190 2192: 0.449490 + 2191 2192: 1.00000 + 2193 2195: 1.00000 + 2194 2195: 0.449490 + 2196 2198: 0.427330 + 2197 2198: 0.427330 + 2211 2213: 1.00000 + 2212 2213: 0.703508 + 2214 2216: 0.437092 + 2215 2216: 0.679605 + 2217 2219: 0.703508 + 2218 2219: 1.00000 + 2220 2222: 0.679605 + 2221 2222: 0.437092 + 2268 = 0 + 2269 2270: 1.00000 + 2271 = 0 + 2272 2273: 0.414214 + 2280 = 0 + 2281 2282: 0.668179 + 2283 2285: 0.219339 + 2284 2285: 1.00000 + 2286 2288: 0.205498 + 2287 2288: 0.420521 + 2322 2324: 1.00000 + 2323 = 0 + 2325 2327: 0.414214 + 2326 = 0 + 2334 2336: 1.00000 + 2335 2336: 0.219339 + 2337 2339: 0.420521 + 2338 2339: 0.205498 + 2340 2342: 0.668179 + 2341 = 0 + 2376 = 0 + 2377 = 0 + 2382 = 0 + 2383 2384: 0.198912 + 2385 2387: 0.198912 + 2386 = 0 + 2562 2564: -0.449490 + 2563 2564: 1.00000 + 2565 2567: -0.427330 + 2566 2567: 0.427330 + 2574 2576: -0.437092 + 2575 2576: 0.679605 + 2577 2579: -0.219339 + 2578 2579: 1.00000 + 2580 2582: -0.205498 + 2581 2582: 0.420521 + 2616 2618: -1.00000 + 2617 2618: 1.00000 + 2619 2621: -1.00000 + 2620 2621: 0.449490 + 2628 2630: -1.00000 + 2629 2630: 0.703508 + 2631 2633: -0.703508 + 2632 2633: 1.00000 + 2634 2636: -0.679605 + 2635 2636: 0.437092 + 2670 2672: -0.414214 + 2671 = 0 + 2676 2678: -0.420521 + 2677 2678: 0.205498 + 2679 2681: -0.198912 + 2680 = 0 + 2706 2708: -1.00000 + 2707 = 0 + 2712 2714: -1.00000 + 2713 2714: 0.219339 + 2715 2717: -0.668179 + 2716 = 0 + 2862 2864: 1.00000 + 2863 2864: -0.449490 + 2865 2867: 0.427330 + 2866 2867: -0.427330 + 2874 2876: 1.00000 + 2875 2876: -0.219339 + 2877 2879: 0.420521 + 2878 2879: -0.205498 + 2880 2882: 0.679605 + 2881 2882: -0.437092 + 2916 = 0 + 2917 2918: -0.414214 + 2922 = 0 + 2923 2924: -0.198912 + 2925 2927: 0.205498 + 2926 2927: -0.420521 + 2952 2954: 1.00000 + 2953 2954: -1.00000 + 2955 2957: 0.449490 + 2956 2957: -1.00000 + 2964 2966: 1.00000 + 2965 2966: -0.703508 + 2967 2969: 0.437092 + 2968 2969: -0.679605 + 2970 2972: 0.703508 + 2971 2972: -1.00000 + 3006 = 0 + 3007 3008: -1.00000 + 3012 = 0 + 3013 3014: -0.668179 + 3015 3017: 0.219339 + 3016 3017: -1.00000 + 3162 3164: -0.427330 + 3163 3164: -0.427330 + 3168 3170: -0.420521 + 3169 3170: -0.205498 + 3171 3173: -0.205498 + 3172 3173: -0.420521 + 3198 3200: -1.00000 + 3199 3200: -0.449490 + 3204 3206: -1.00000 + 3205 3206: -0.219339 + 3207 3209: -0.679605 + 3208 3209: -0.437092 + 3234 3236: -0.449490 + 3235 3236: -1.00000 + 3240 3242: -0.437092 + 3241 3242: -0.679605 + 3243 3245: -0.219339 + 3244 3245: -1.00000 + 3270 3272: -1.00000 + 3271 3272: -1.00000 + 3276 3278: -1.00000 + 3277 3278: -0.703508 + 3279 3281: -0.703508 + 3280 3281: -1.00000 + 4131 4132: -1.00000 + 4133 4132: 0.449490 + 4135 4134: -0.427330 + 4136 4134: -0.427330 + 4150 4149: -0.679605 + 4151 4149: -0.437092 + 4155 4156: -1.00000 + 4157 4156: 0.703508 + 4159 4158: -0.437092 + 4160 4158: -0.679605 + 4186 = 0 + 4187 4185: -0.414214 + 4195 4194: -0.205498 + 4196 4194: -0.420521 + 4201 = 0 + 4202 4200: -0.668179 + 4281 4282: -1.00000 + 4283 = 0 + 4285 4284: -0.414214 + 4286 = 0 + 4300 4299: -0.668179 + 4301 = 0 + 4305 4306: -1.00000 + 4307 4306: 0.219339 + 4309 4308: -0.420521 + 4310 4308: -0.205498 + 4336 = 0 + 4337 = 0 + 4345 4344: -0.198912 + 4346 = 0 + 4351 = 0 + 4352 4350: -0.198912 + 4432 4431: 0.427330 + 4433 4431: -0.427330 + 4441 4440: 0.205498 + 4442 4440: -0.420521 + 4447 4446: 0.437092 + 4448 4446: -0.679605 + 4467 4468: 1.00000 + 4469 4468: -0.449490 + 4477 4476: 0.679605 + 4478 4476: -0.437092 + 4482 4483: 1.00000 + 4484 4483: -0.703508 + 4552 4551: 0.414214 + 4553 = 0 + 4561 4560: 0.198912 + 4562 = 0 + 4567 4566: 0.420521 + 4568 4566: -0.205498 + 4587 4588: 1.00000 + 4589 = 0 + 4597 4596: 0.668179 + 4598 = 0 + 4602 4603: 1.00000 + 4604 4603: -0.219339 + 4995 4996: -1.00000 + 4997 4996: -0.449490 + 4999 4998: -0.427330 + 5000 4998: 0.427330 + 5014 5013: -0.679605 + 5015 5013: 0.437092 + 5019 5020: -1.00000 + 5021 5020: -0.219339 + 5023 5022: -0.420521 + 5024 5022: 0.205498 + 5050 = 0 + 5051 5049: 0.414214 + 5059 5058: -0.205498 + 5060 5058: 0.420521 + 5065 = 0 + 5066 5064: 0.198912 + 5145 5147: 1.00000 + 5146 5147: -1.00000 + 5148 5150: 1.00000 + 5149 5150: -0.449490 + 5163 5165: 1.00000 + 5164 5165: -0.703508 + 5169 5170: -1.00000 + 5171 5170: -0.703508 + 5173 5172: -0.437092 + 5174 5172: 0.679605 + 5199 5201: 1.00000 + 5200 = 0 + 5208 5210: 1.00000 + 5209 5210: -0.219339 + 5215 = 0 + 5216 5214: 0.668179 + 5296 5295: 0.427330 + 5297 5295: 0.427330 + 5305 5304: 0.205498 + 5306 5304: 0.420521 + 5311 5310: 0.420521 + 5312 5310: 0.205498 + 5331 5332: 1.00000 + 5333 5332: 0.449490 + 5341 5340: 0.679605 + 5342 5340: 0.437092 + 5346 5347: 1.00000 + 5348 5347: 0.219339 + 5415 5417: 1.00000 + 5416 5417: 0.449490 + 5424 5426: 1.00000 + 5425 5426: 0.219339 + 5431 5430: 0.437092 + 5432 5430: 0.679605 + 5451 5453: 1.00000 + 5452 5453: 1.00000 + 5460 5462: 1.00000 + 5461 5462: 0.703508 + 5466 5467: 1.00000 + 5468 5467: 0.703508 + 5859 5861: -1.00000 + 5860 5861: -1.00000 + 5862 5864: -0.449490 + 5863 5864: -1.00000 + 5871 5873: -1.00000 + 5872 5873: -0.449490 + 5874 5876: -0.427330 + 5875 5876: -0.427330 + 5889 5891: -0.703508 + 5890 5891: -1.00000 + 5901 5903: -0.679605 + 5902 5903: -0.437092 + 5907 5909: -1.00000 + 5908 5909: -0.703508 + 5910 5912: -0.437092 + 5911 5912: -0.679605 + 5940 = 0 + 5941 5942: -1.00000 + 5946 = 0 + 5947 5948: -0.414214 + 5955 5957: -0.219339 + 5956 5957: -1.00000 + 5964 5966: -0.205498 + 5965 5966: -0.420521 + 5970 = 0 + 5971 5972: -0.668179 + 6084 6086: -1.00000 + 6085 = 0 + 6087 6089: -0.414214 + 6088 = 0 + 6102 6104: -0.668179 + 6103 = 0 + 6108 6110: -1.00000 + 6109 6110: -0.219339 + 6111 6113: -0.420521 + 6112 6113: -0.205498 + 6138 = 0 + 6139 = 0 + 6147 6149: -0.198912 + 6148 = 0 + 6153 = 0 + 6154 6155: -0.198912 + 6234 6236: 0.449490 + 6235 6236: -1.00000 + 6240 6242: 0.427330 + 6241 6242: -0.427330 + 6249 6251: 0.219339 + 6250 6251: -1.00000 + 6258 6260: 0.205498 + 6259 6260: -0.420521 + 6264 6266: 0.437092 + 6265 6266: -0.679605 + 6288 6290: 0.703508 + 6289 6290: -1.00000 + 6294 6296: 0.679605 + 6295 6296: -0.437092 + 6369 6371: 0.414214 + 6370 = 0 + 6378 6380: 0.198912 + 6379 = 0 + 6384 6386: 0.420521 + 6385 6386: -0.205498 + 6405 6407: 0.668179 + 6406 = 0 + 6819 6821: -1.00000 + 6820 6821: 0.449490 + 6822 6824: -0.427330 + 6823 6824: 0.427330 + 6837 6839: -0.679605 + 6838 6839: 0.437092 + 6843 6845: -1.00000 + 6844 6845: 0.219339 + 6846 6848: -0.420521 + 6847 6848: 0.205498 + 6873 = 0 + 6874 6875: 0.414214 + 6882 6884: -0.205498 + 6883 6884: 0.420521 + 6888 = 0 + 6889 6890: 0.198912 + 6969 6971: -1.00000 + 6970 6971: 1.00000 + 6972 6974: -0.449490 + 6973 6974: 1.00000 + 6987 6989: -0.703508 + 6988 6989: 1.00000 + 6993 6995: -1.00000 + 6994 6995: 0.703508 + 6996 6998: -0.437092 + 6997 6998: 0.679605 + 7023 = 0 + 7024 7025: 1.00000 + 7032 7034: -0.219339 + 7033 7034: 1.00000 + 7038 = 0 + 7039 7040: 0.668179 + 7119 7121: 0.427330 + 7120 7121: 0.427330 + 7128 7130: 0.205498 + 7129 7130: 0.420521 + 7134 7136: 0.420521 + 7135 7136: 0.205498 + 7155 7157: 0.679605 + 7156 7157: 0.437092 + 7209 7211: 0.449490 + 7210 7211: 1.00000 + 7218 7220: 0.219339 + 7219 7220: 1.00000 + 7224 7226: 0.437092 + 7225 7226: 0.679605 + 7245 7247: 0.703508 + 7246 7247: 1.00000 + 7587 7588: 1.00000 + 7589 7588: 0.449490 + 7594 7593: 0.427330 + 7595 7593: 0.427330 + 7600 7599: 0.679605 + 7601 7599: 0.437092 + 7611 7612: 1.00000 + 7613 7612: 0.703508 + 7618 7617: 0.437092 + 7619 7617: 0.679605 + 7678 = 0 + 7679 7677: 0.414214 + 7684 7683: 0.205498 + 7685 7683: 0.420521 + 7693 = 0 + 7694 7692: 0.668179 + 7737 7738: 1.00000 + 7739 = 0 + 7744 7743: 0.414214 + 7745 = 0 + 7750 7749: 0.668179 + 7751 = 0 + 7761 7762: 1.00000 + 7763 7762: 0.219339 + 7768 7767: 0.420521 + 7769 7767: 0.205498 + 7828 = 0 + 7829 = 0 + 7834 7833: 0.198912 + 7835 = 0 + 7843 = 0 + 7844 7842: 0.198912 + 8068 8067: -0.427330 + 8069 8067: 0.427330 + 8074 8073: -0.205498 + 8075 8073: 0.420521 + 8083 8082: -0.437092 + 8084 8082: 0.679605 + 8127 8128: -1.00000 + 8129 8128: -0.449490 + 8134 8133: -0.679605 + 8135 8133: 0.437092 + 8142 8143: -1.00000 + 8144 8143: -0.703508 + 8188 8187: -0.414214 + 8189 = 0 + 8194 8193: -0.198912 + 8195 = 0 + 8203 8202: -0.420521 + 8204 8202: 0.205498 + 8247 8248: -1.00000 + 8249 = 0 + 8254 8253: -0.668179 + 8255 = 0 + 8262 8263: -1.00000 + 8264 8263: -0.219339 + 8451 8452: 1.00000 + 8453 8452: -0.449490 + 8458 8457: 0.427330 + 8459 8457: -0.427330 + 8464 8463: 0.679605 + 8465 8463: -0.437092 + 8475 8476: 1.00000 + 8477 8476: -0.219339 + 8482 8481: 0.420521 + 8483 8481: -0.205498 + 8542 = 0 + 8543 8541: -0.414214 + 8548 8547: 0.205498 + 8549 8547: -0.420521 + 8557 = 0 + 8558 8556: -0.198912 + 8601 8602: 1.00000 + 8603 8602: -0.703508 + 8608 8607: 0.437092 + 8609 8607: -0.679605 + 8647 = 0 + 8648 8646: -0.668179 + 8812 8811: -0.427330 + 8813 8811: -0.427330 + 8818 8817: -0.205498 + 8819 8817: -0.420521 + 8827 8826: -0.420521 + 8828 8826: -0.205498 + 8871 8872: -1.00000 + 8873 8872: 0.449490 + 8878 8877: -0.679605 + 8879 8877: -0.437092 + 8886 8887: -1.00000 + 8888 8887: 0.219339 + 8932 8931: -0.437092 + 8933 8931: -0.679605 + 8961 8962: -1.00000 + 8963 8962: 0.703508 + 9099 9100: 0.427330 + 9101 9100: 0.427330 + 9108 9109: 0.679605 + 9110 9109: 0.437092 + 9114 9115: 0.437092 + 9116 9115: 0.679605 + 9135 = 0 + 9137 9136: 0.414214 + 9144 9145: 0.205498 + 9146 9145: 0.420521 + 9150 = 0 + 9152 9151: 0.668179 + 9219 9220: 0.414214 + 9221 = 0 + 9228 9229: 0.668179 + 9230 = 0 + 9234 9235: 0.420521 + 9236 9235: 0.205498 + 9255 = 0 + 9257 = 0 + 9264 9265: 0.198912 + 9266 = 0 + 9270 = 0 + 9272 9271: 0.198912 + 9339 9340: -0.427330 + 9341 9340: 0.427330 + 9348 9349: -0.205498 + 9350 9349: 0.420521 + 9354 9355: -0.437092 + 9356 9355: 0.679605 + 9375 9376: -0.679605 + 9377 9376: 0.437092 + 9429 9430: -0.414214 + 9431 = 0 + 9438 9439: -0.198912 + 9440 = 0 + 9444 9445: -0.420521 + 9446 9445: 0.205498 + 9465 9466: -0.668179 + 9467 = 0 + 9771 9772: 0.427330 + 9773 9772: -0.427330 + 9780 9781: 0.679605 + 9782 9781: -0.437092 + 9786 9787: 0.420521 + 9788 9787: -0.205498 + 9807 = 0 + 9809 9808: -0.414214 + 9816 9817: 0.205498 + 9818 9817: -0.420521 + 9822 = 0 + 9824 9823: -0.198912 + 9891 9892: 0.437092 + 9893 9892: -0.679605 + 9909 = 0 + 9911 9910: -0.668179 + 9951 9952: -0.427330 + 9953 9952: -0.427330 + 9960 9961: -0.205498 + 9962 9961: -0.420521 + 9966 9967: -0.420521 + 9968 9967: -0.205498 + 9987 9988: -0.679605 + 9989 9988: -0.437092 + 10041 10042: -0.437092 + 10043 10042: -0.679605 + 10275 10276: -0.427330 + 10277 10276: -0.427330 + 10281 10282: -0.679605 + 10283 10282: -0.437092 + 10290 10291: -0.437092 + 10292 10291: -0.679605 + 10335 = 0 + 10337 10336: -0.414214 + 10341 10342: -0.205498 + 10343 10342: -0.420521 + 10350 = 0 + 10352 10351: -0.668179 + 10395 10396: -0.414214 + 10397 = 0 + 10401 10402: -0.668179 + 10403 = 0 + 10410 10411: -0.420521 + 10412 10411: -0.205498 + 10455 = 0 + 10457 = 0 + 10461 10462: -0.198912 + 10463 = 0 + 10470 = 0 + 10472 10471: -0.198912 + 10659 10660: 0.427330 + 10661 10660: -0.427330 + 10665 10666: 0.205498 + 10667 10666: -0.420521 + 10674 10675: 0.437092 + 10676 10675: -0.679605 + 10719 10720: 0.679605 + 10721 10720: -0.437092 + 10749 10750: 0.414214 + 10751 = 0 + 10755 10756: 0.198912 + 10757 = 0 + 10764 10765: 0.420521 + 10766 10765: -0.205498 + 10809 10810: 0.668179 + 10811 = 0 + 10947 10948: -0.427330 + 10949 10948: 0.427330 + 10953 10954: -0.679605 + 10955 10954: 0.437092 + 10962 10963: -0.420521 + 10964 10963: 0.205498 + 11007 = 0 + 11009 11008: 0.414214 + 11013 11014: -0.205498 + 11015 11014: 0.420521 + 11022 = 0 + 11024 11023: 0.198912 + 11067 11068: -0.437092 + 11069 11068: 0.679605 + 11097 = 0 + 11099 11098: 0.668179 + 11235 11236: 0.427330 + 11237 11236: 0.427330 + 11241 11242: 0.205498 + 11243 11242: 0.420521 + 11250 11251: 0.420521 + 11252 11251: 0.205498 + 11295 11296: 0.679605 + 11297 11296: 0.437092 + 11325 11326: 0.437092 + 11327 11326: 0.679605 +DEAL::FE=FESystem<3>[FE_Q<3>(3)^3] + 6591 6593: 1.00000 + 6592 6593: 1.00000 + 6594 6596: 0.449490 + 6595 6596: 1.00000 + 6597 6599: 1.00000 + 6598 6599: 0.449490 + 6600 6602: 0.427330 + 6601 6602: 0.427330 + 6615 6619: 1.00000 + 6617 6619: 0.797121 + 6616 6620: 1.00000 + 6618 6620: 0.614589 + 6621 6625: 0.440883 + 6623 6625: 0.777585 + 6622 6626: 0.433590 + 6624 6626: 0.589099 + 6627 6631: 0.797121 + 6629 6631: 1.00000 + 6628 6632: 0.614589 + 6630 6632: 1.00000 + 6633 6637: 0.777585 + 6635 6637: 0.440883 + 6634 6638: 0.589099 + 6636 6638: 0.433590 + 6735 6743: 0.789776 + 6739 6743: 0.789776 + 6736 6744: 0.604838 + 6740 6744: 0.783313 + 6737 6745: 0.783313 + 6741 6745: 0.604838 + 6783 = 0 + 6784 6785: 1.00000 + 6786 = 0 + 6787 6788: 0.414214 + 6795 = 0 + 6797 6799: 0.768531 + 6796 = 0 + 6798 6800: 0.576341 + 6801 6805: 0.294815 + 6803 6805: 1.00000 + 6802 6806: 0.145063 + 6804 6806: 1.00000 + 6807 6811: 0.277533 + 6809 6811: 0.422732 + 6808 6812: 0.135275 + 6810 6812: 0.418366 + 6879 6887: 0.288063 + 6883 6887: 0.774446 + 6880 6888: 0.141216 + 6884 6888: 0.771431 + 6881 6889: 0.282381 + 6885 6889: 0.584650 + 6927 6929: 1.00000 + 6928 = 0 + 6930 6932: 0.414214 + 6931 = 0 + 6939 6943: 1.00000 + 6941 6943: 0.294815 + 6940 6944: 1.00000 + 6942 6944: 0.145063 + 6945 6949: 0.422732 + 6947 6949: 0.277533 + 6946 6950: 0.418366 + 6948 6950: 0.135275 + 6951 6955: 0.768531 + 6953 = 0 + 6952 6956: 0.576341 + 6954 = 0 + 7023 7031: 0.774446 + 7027 7031: 0.288063 + 7024 7032: 0.584650 + 7028 7032: 0.282381 + 7025 7033: 0.771431 + 7029 7033: 0.141216 + 7071 = 0 + 7072 = 0 + 7077 = 0 + 7079 7081: 0.268761 + 7078 = 0 + 7080 7082: 0.130882 + 7083 7087: 0.268761 + 7085 = 0 + 7084 7088: 0.130882 + 7086 = 0 + 7131 7139: 0.274456 + 7135 7139: 0.274456 + 7132 7140: 0.133733 + 7136 7140: 0.271536 + 7133 7141: 0.271536 + 7137 7141: 0.133733 + 7620 7622: 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+ 7914 7918: -0.422732 + 7916 7918: 0.277533 + 7915 7919: -0.418366 + 7917 7919: 0.135275 + 7920 7924: -0.130882 + 7922 = 0 + 7921 7925: -0.268761 + 7923 = 0 + 7968 7976: -0.133733 + 7972 7976: 0.271536 + 7969 7977: -0.274456 + 7973 7977: 0.274456 + 7970 7978: -0.132271 + 7974 7978: 0.132271 + 8016 8018: -1.00000 + 8017 = 0 + 8022 8026: -1.00000 + 8024 8026: 0.294815 + 8023 8027: -1.00000 + 8025 8027: 0.145063 + 8028 8032: -0.576341 + 8030 = 0 + 8029 8033: -0.768531 + 8031 = 0 + 8076 8084: -0.584650 + 8080 8084: 0.282381 + 8077 8085: -0.774446 + 8081 8085: 0.288063 + 8078 8086: -0.580402 + 8082 8086: 0.138002 + 8502 8504: 1.00000 + 8503 8504: -0.449490 + 8505 8507: 0.427330 + 8506 8507: -0.427330 + 8514 8518: 1.00000 + 8516 8518: -0.145063 + 8515 8519: 1.00000 + 8517 8519: -0.294815 + 8520 8524: 0.418366 + 8522 8524: -0.135275 + 8521 8525: 0.422732 + 8523 8525: -0.277533 + 8526 8530: 0.777585 + 8528 8530: -0.440883 + 8527 8531: 0.589099 + 8529 8531: -0.433590 + 8598 8606: 0.771431 + 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-1.00000 + 18489 = 0 + 18490 18491: -0.414214 + 18501 18505: -0.294815 + 18503 18505: -1.00000 + 18502 18506: -0.145063 + 18504 18506: -1.00000 + 18519 18523: -0.277533 + 18521 18523: -0.422732 + 18520 18524: -0.135275 + 18522 18524: -0.418366 + 18531 = 0 + 18533 18535: -0.768531 + 18532 = 0 + 18534 18536: -0.576341 + 18555 18563: -0.288063 + 18559 18563: -0.774446 + 18556 18564: -0.282381 + 18560 18564: -0.584650 + 18557 18565: -0.141216 + 18561 18565: -0.771431 + 18879 18881: -1.00000 + 18880 = 0 + 18882 18884: -0.414214 + 18883 = 0 + 18903 18907: -0.768531 + 18905 = 0 + 18904 18908: -0.576341 + 18906 = 0 + 18915 18919: -1.00000 + 18917 18919: -0.294815 + 18916 18920: -1.00000 + 18918 18920: -0.145063 + 18921 18925: -0.422732 + 18923 18925: -0.277533 + 18922 18926: -0.418366 + 18924 18926: -0.135275 + 18963 18971: -0.774446 + 18967 18971: -0.288063 + 18964 18972: -0.771431 + 18968 18972: -0.141216 + 18965 18973: -0.584650 + 18969 18973: -0.282381 + 19023 = 0 + 19024 = 0 + 19035 19039: -0.268761 + 19037 = 0 + 19036 19040: -0.130882 + 19038 = 0 + 19047 = 0 + 19049 19051: -0.268761 + 19048 = 0 + 19050 19052: -0.130882 + 19071 19079: -0.274456 + 19075 19079: -0.274456 + 19072 19080: -0.271536 + 19076 19080: -0.133733 + 19073 19081: -0.133733 + 19077 19081: -0.271536 + 19320 19322: 0.449490 + 19321 19322: -1.00000 + 19326 19328: 0.427330 + 19327 19328: -0.427330 + 19338 19342: 0.145063 + 19340 19342: -1.00000 + 19339 19343: 0.294815 + 19341 19343: -1.00000 + 19356 19360: 0.135275 + 19358 19360: -0.418366 + 19357 19361: 0.277533 + 19359 19361: -0.422732 + 19368 19372: 0.440883 + 19370 19372: -0.777585 + 19369 19373: 0.433590 + 19371 19373: -0.589099 + 19392 19400: 0.141216 + 19396 19400: -0.771431 + 19393 19401: 0.138002 + 19397 19401: -0.580402 + 19394 19402: 0.288063 + 19398 19402: -0.774446 + 19464 19468: 0.614589 + 19466 19468: -1.00000 + 19465 19469: 0.797121 + 19467 19469: -1.00000 + 19476 19480: 0.589099 + 19478 19480: -0.433590 + 19477 19481: 0.777585 + 19479 19481: -0.440883 + 19488 19496: 0.604838 + 19492 19496: -0.783313 + 19489 19497: 0.596427 + 19493 19497: -0.596427 + 19490 19498: 0.789776 + 19494 19498: -0.789776 + 19740 19742: 0.414214 + 19741 = 0 + 19752 19756: 0.130882 + 19754 = 0 + 19753 19757: 0.268761 + 19755 = 0 + 19764 19768: 0.422732 + 19766 19768: -0.277533 + 19765 19769: 0.418366 + 19767 19769: -0.135275 + 19788 19796: 0.133733 + 19792 19796: -0.271536 + 19789 19797: 0.132271 + 19793 19797: -0.132271 + 19790 19798: 0.274456 + 19794 19798: -0.274456 + 19848 19852: 0.576341 + 19850 = 0 + 19849 19853: 0.768531 + 19851 = 0 + 19860 19868: 0.584650 + 19864 19868: -0.282381 + 19861 19869: 0.580402 + 19865 19869: -0.138002 + 19862 19870: 0.774446 + 19866 19870: -0.288063 + 21315 21317: -1.00000 + 21316 21317: 0.449490 + 21318 21320: -0.427330 + 21319 21320: 0.427330 + 21339 21343: -0.777585 + 21341 21343: 0.440883 + 21340 21344: -0.589099 + 21342 21344: 0.433590 + 21351 21355: -1.00000 + 21353 21355: 0.145063 + 21352 21356: 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21803: 0.777585 + 21840 21848: -0.783313 + 21844 21848: 0.604838 + 21841 21849: -0.789776 + 21845 21849: 0.789776 + 21842 21850: -0.596427 + 21846 21850: 0.596427 + 21900 = 0 + 21901 21902: 1.00000 + 21912 21916: -0.294815 + 21914 21916: 1.00000 + 21913 21917: -0.145063 + 21915 21917: 1.00000 + 21924 = 0 + 21926 21928: 0.576341 + 21925 = 0 + 21927 21929: 0.768531 + 21948 21956: -0.282381 + 21952 21956: 0.584650 + 21949 21957: -0.288063 + 21953 21957: 0.774446 + 21950 21958: -0.138002 + 21954 21958: 0.580402 + 22197 22199: 0.427330 + 22198 22199: 0.427330 + 22209 22213: 0.135275 + 22211 22213: 0.418366 + 22210 22214: 0.277533 + 22212 22214: 0.422732 + 22221 22225: 0.418366 + 22223 22225: 0.135275 + 22222 22226: 0.422732 + 22224 22226: 0.277533 + 22245 22253: 0.132271 + 22249 22253: 0.132271 + 22246 22254: 0.133733 + 22250 22254: 0.271536 + 22247 22255: 0.271536 + 22251 22255: 0.133733 + 22305 22309: 0.589099 + 22307 22309: 0.433590 + 22306 22310: 0.777585 + 22308 22310: 0.440883 + 22317 22325: 0.580402 + 22321 22325: 0.138002 + 22318 22326: 0.584650 + 22322 22326: 0.282381 + 22319 22327: 0.771431 + 22323 22327: 0.141216 + 22512 22514: 0.449490 + 22513 22514: 1.00000 + 22524 22528: 0.145063 + 22526 22528: 1.00000 + 22525 22529: 0.294815 + 22527 22529: 1.00000 + 22536 22540: 0.433590 + 22538 22540: 0.589099 + 22537 22541: 0.440883 + 22539 22541: 0.777585 + 22560 22568: 0.138002 + 22564 22568: 0.580402 + 22561 22569: 0.141216 + 22565 22569: 0.771431 + 22562 22570: 0.282381 + 22566 22570: 0.584650 + 22620 22624: 0.614589 + 22622 22624: 1.00000 + 22621 22625: 0.797121 + 22623 22625: 1.00000 + 22632 22640: 0.596427 + 22636 22640: 0.596427 + 22633 22641: 0.604838 + 22637 22641: 0.783313 + 22634 22642: 0.783313 + 22638 22642: 0.604838 + 23907 23908: 1.00000 + 23909 23908: 0.449490 + 23914 23913: 0.427330 + 23915 23913: 0.427330 + 23921 23919: 0.777585 + 23923 23919: 0.440883 + 23922 23920: 0.589099 + 23924 23920: 0.433590 + 23943 23945: 1.00000 + 23947 23945: 0.797121 + 23944 23946: 1.00000 + 23948 23946: 0.614589 + 23957 23955: 0.440883 + 23959 23955: 0.777585 + 23958 23956: 0.433590 + 23960 23956: 0.589099 + 23971 23967: 0.789776 + 23975 23967: 0.789776 + 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 + 24170 24166: 0.418366 + 24185 = 0 + 24187 24183: 0.768531 + 24186 = 0 + 24188 24184: 0.576341 + 24199 24195: 0.288063 + 24203 24195: 0.774446 + 24200 24196: 0.141216 + 24204 24196: 0.771431 + 24201 24197: 0.282381 + 24205 24197: 0.584650 + 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 + 24388 24386: 0.294815 + 24385 24387: 1.00000 + 24389 24387: 0.145063 + 24398 24396: 0.422732 + 24400 24396: 0.277533 + 24399 24397: 0.418366 + 24401 24397: 0.135275 + 24412 24408: 0.774446 + 24416 24408: 0.288063 + 24413 24409: 0.584650 + 24417 24409: 0.282381 + 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 + 24640 24636: 0.274456 + 24644 24636: 0.274456 + 24641 24637: 0.133733 + 24645 24637: 0.271536 + 24642 24638: 0.271536 + 24646 24638: 0.133733 + 25420 25419: -0.427330 + 25421 25419: 0.427330 + 25427 25425: -0.135275 + 25429 25425: 0.418366 + 25428 25426: -0.277533 + 25430 25426: 0.422732 + 25445 25443: -0.440883 + 25447 25443: 0.777585 + 25446 25444: -0.433590 + 25448 25444: 0.589099 + 25459 25455: -0.141216 + 25463 25455: 0.771431 + 25460 25456: -0.288063 + 25464 25456: 0.774446 + 25461 25457: -0.138002 + 25465 25457: 0.580402 + 25608 25609: -1.00000 + 25610 25609: -0.449490 + 25616 25614: -0.589099 + 25618 25614: 0.433590 + 25617 25615: -0.777585 + 25619 25615: 0.440883 + 25632 25634: -1.00000 + 25636 25634: -0.797121 + 25633 25635: -1.00000 + 25637 25635: -0.614589 + 25648 25644: -0.604838 + 25652 25644: 0.783313 + 25649 25645: -0.789776 + 25653 25645: 0.789776 + 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 + 25825 25821: 0.277533 + 25824 25822: -0.418366 + 25826 25822: 0.135275 + 25837 25833: -0.133733 + 25841 25833: 0.271536 + 25838 25834: -0.274456 + 25842 25834: 0.274456 + 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 + 26014 26012: -0.294815 + 26011 26013: -1.00000 + 26015 26013: -0.145063 + 26026 26022: -0.584650 + 26030 26022: 0.282381 + 26027 26023: -0.774446 + 26031 26023: 0.288063 + 26028 26024: -0.580402 + 26032 26024: 0.138002 + 26715 26716: 1.00000 + 26717 26716: -0.449490 + 26722 26721: 0.427330 + 26723 26721: -0.427330 + 26729 26727: 0.777585 + 26731 26727: -0.440883 + 26730 26728: 0.589099 + 26732 26728: -0.433590 + 26751 26753: 1.00000 + 26755 26753: -0.145063 + 26752 26754: 1.00000 + 26756 26754: -0.294815 + 26765 26763: 0.418366 + 26767 26763: -0.135275 + 26766 26764: 0.422732 + 26768 26764: -0.277533 + 26779 26775: 0.771431 + 26783 26775: -0.141216 + 26780 26776: 0.580402 + 26784 26776: -0.138002 + 26781 26777: 0.774446 + 26785 26777: -0.288063 + 26968 = 0 + 26969 26967: -0.414214 + 26975 26973: 0.277533 + 26977 26973: -0.422732 + 26976 26974: 0.135275 + 26978 26974: -0.418366 + 26993 = 0 + 26995 26991: -0.130882 + 26994 = 0 + 26996 26992: -0.268761 + 27007 27003: 0.271536 + 27011 27003: -0.133733 + 27008 27004: 0.132271 + 27012 27004: -0.132271 + 27009 27005: 0.274456 + 27013 27005: -0.274456 + 27156 27158: 1.00000 + 27160 27158: -0.614589 + 27157 27159: 1.00000 + 27161 27159: -0.797121 + 27170 27168: 0.433590 + 27172 27168: -0.589099 + 27171 27169: 0.440883 + 27173 27169: -0.777585 + 27184 27180: 0.783313 + 27188 27180: -0.604838 + 27185 27181: 0.596427 + 27189 27181: -0.596427 + 27186 27182: 0.789776 + 27190 27182: -0.789776 + 27326 = 0 + 27328 27324: -0.576341 + 27327 = 0 + 27329 27325: -0.768531 + 27340 27336: 0.282381 + 27344 27336: -0.584650 + 27341 27337: 0.138002 + 27345 27337: -0.580402 + 27342 27338: 0.288063 + 27346 27338: -0.774446 + 27976 27975: -0.427330 + 27977 27975: -0.427330 + 27983 27981: -0.135275 + 27985 27981: -0.418366 + 27984 27982: -0.277533 + 27986 27982: -0.422732 + 28001 27999: -0.418366 + 28003 27999: -0.135275 + 28002 28000: -0.422732 + 28004 28000: -0.277533 + 28015 28011: -0.132271 + 28019 28011: -0.132271 + 28016 28012: -0.271536 + 28020 28012: -0.133733 + 28017 28013: -0.133733 + 28021 28013: -0.271536 + 28164 28165: -1.00000 + 28166 28165: 0.449490 + 28172 28170: -0.589099 + 28174 28170: -0.433590 + 28173 28171: -0.777585 + 28175 28171: -0.440883 + 28188 28190: -1.00000 + 28192 28190: 0.145063 + 28189 28191: -1.00000 + 28193 28191: 0.294815 + 28204 28200: -0.580402 + 28208 28200: -0.138002 + 28205 28201: -0.771431 + 28209 28201: -0.141216 + 28206 28202: -0.584650 + 28210 28202: -0.282381 + 28355 28353: -0.433590 + 28357 28353: -0.589099 + 28356 28354: -0.440883 + 28358 28354: -0.777585 + 28369 28365: -0.138002 + 28373 28365: -0.580402 + 28370 28366: -0.282381 + 28374 28366: -0.584650 + 28371 28367: -0.141216 + 28375 28367: -0.771431 + 28479 28481: -1.00000 + 28483 28481: 0.614589 + 28480 28482: -1.00000 + 28484 28482: 0.797121 + 28495 28491: -0.596427 + 28499 28491: -0.596427 + 28496 28492: -0.783313 + 28500 28492: -0.604838 + 28497 28493: -0.604838 + 28501 28493: -0.783313 + 29055 29056: 0.427330 + 29057 29056: 0.427330 + 29067 29069: 0.777585 + 29071 29069: 0.440883 + 29068 29070: 0.589099 + 29072 29070: 0.433590 + 29079 29081: 0.440883 + 29083 29081: 0.777585 + 29080 29082: 0.433590 + 29084 29082: 0.589099 + 29103 29107: 0.789776 + 29111 29107: 0.789776 + 29104 29108: 0.783313 + 29112 29108: 0.604838 + 29105 29109: 0.604838 + 29113 29109: 0.783313 + 29163 = 0 + 29165 29164: 0.414214 + 29175 29177: 0.277533 + 29179 29177: 0.422732 + 29176 29178: 0.135275 + 29180 29178: 0.418366 + 29187 = 0 + 29191 29189: 0.768531 + 29188 = 0 + 29192 29190: 0.576341 + 29211 29215: 0.288063 + 29219 29215: 0.774446 + 29212 29216: 0.282381 + 29220 29216: 0.584650 + 29213 29217: 0.141216 + 29221 29217: 0.771431 + 29433 29434: 0.414214 + 29435 = 0 + 29445 29447: 0.768531 + 29449 = 0 + 29446 29448: 0.576341 + 29450 = 0 + 29457 29459: 0.422732 + 29461 29459: 0.277533 + 29458 29460: 0.418366 + 29462 29460: 0.135275 + 29481 29485: 0.774446 + 29489 29485: 0.288063 + 29482 29486: 0.771431 + 29490 29486: 0.141216 + 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 + 29589 29593: 0.274456 + 29597 29593: 0.274456 + 29590 29594: 0.271536 + 29598 29594: 0.133733 + 29591 29595: 0.133733 + 29599 29595: 0.271536 + 29811 29812: -0.427330 + 29813 29812: 0.427330 + 29823 29825: -0.135275 + 29827 29825: 0.418366 + 29824 29826: -0.277533 + 29828 29826: 0.422732 + 29835 29837: -0.440883 + 29839 29837: 0.777585 + 29836 29838: -0.433590 + 29840 29838: 0.589099 + 29859 29863: -0.141216 + 29867 29863: 0.771431 + 29860 29864: -0.138002 + 29868 29864: 0.580402 + 29861 29865: -0.288063 + 29869 29865: 0.774446 + 29919 29921: -0.589099 + 29923 29921: 0.433590 + 29920 29922: -0.777585 + 29924 29922: 0.440883 + 29931 29935: -0.604838 + 29939 29935: 0.783313 + 29932 29936: -0.596427 + 29940 29936: 0.596427 + 29933 29937: -0.789776 + 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 + 30154 30152: 0.277533 + 30151 30153: -0.418366 + 30155 30153: 0.135275 + 30174 30178: -0.133733 + 30182 30178: 0.271536 + 30175 30179: -0.132271 + 30183 30179: 0.132271 + 30176 30180: -0.274456 + 30184 30180: 0.274456 + 30234 30236: -0.576341 + 30238 = 0 + 30235 30237: -0.768531 + 30239 = 0 + 30246 30250: -0.584650 + 30254 30250: 0.282381 + 30247 30251: -0.580402 + 30255 30251: 0.138002 + 30248 30252: -0.774446 + 30256 30252: 0.288063 + 31431 31432: 0.427330 + 31433 31432: -0.427330 + 31443 31445: 0.777585 + 31447 31445: -0.440883 + 31444 31446: 0.589099 + 31448 31446: -0.433590 + 31455 31457: 0.418366 + 31459 31457: -0.135275 + 31456 31458: 0.422732 + 31460 31458: -0.277533 + 31479 31483: 0.771431 + 31487 31483: -0.141216 + 31480 31484: 0.774446 + 31488 31484: -0.288063 + 31481 31485: 0.580402 + 31489 31485: -0.138002 + 31539 = 0 + 31541 31540: -0.414214 + 31551 31553: 0.277533 + 31555 31553: -0.422732 + 31552 31554: 0.135275 + 31556 31554: -0.418366 + 31563 = 0 + 31567 31565: -0.130882 + 31564 = 0 + 31568 31566: -0.268761 + 31587 31591: 0.271536 + 31595 31591: -0.133733 + 31588 31592: 0.274456 + 31596 31592: -0.274456 + 31589 31593: 0.132271 + 31597 31593: -0.132271 + 31809 31811: 0.433590 + 31813 31811: -0.589099 + 31810 31812: 0.440883 + 31814 31812: -0.777585 + 31833 31837: 0.783313 + 31841 31837: -0.604838 + 31834 31838: 0.789776 + 31842 31838: -0.789776 + 31835 31839: 0.596427 + 31843 31839: -0.596427 + 31881 = 0 + 31885 31883: -0.576341 + 31882 = 0 + 31886 31884: -0.768531 + 31905 31909: 0.282381 + 31913 31909: -0.584650 + 31906 31910: 0.288063 + 31914 31910: -0.774446 + 31907 31911: 0.138002 + 31915 31911: -0.580402 + 32061 32062: -0.427330 + 32063 32062: -0.427330 + 32073 32075: -0.135275 + 32077 32075: -0.418366 + 32074 32076: -0.277533 + 32078 32076: -0.422732 + 32085 32087: -0.418366 + 32089 32087: -0.135275 + 32086 32088: -0.422732 + 32090 32088: -0.277533 + 32109 32113: -0.132271 + 32117 32113: -0.132271 + 32110 32114: -0.133733 + 32118 32114: -0.271536 + 32111 32115: -0.271536 + 32119 32115: -0.133733 + 32169 32171: -0.589099 + 32173 32171: -0.433590 + 32170 32172: -0.777585 + 32174 32172: -0.440883 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33608: -0.277533 + 33610 33608: -0.422732 + 33607 33609: -0.135275 + 33611 33609: -0.418366 + 33624 = 0 + 33628 33626: -0.768531 + 33625 = 0 + 33629 33627: -0.576341 + 33636 33640: -0.288063 + 33644 33640: -0.774446 + 33637 33641: -0.141216 + 33645 33641: -0.771431 + 33638 33642: -0.282381 + 33646 33642: -0.584650 + 33789 33790: -0.414214 + 33791 = 0 + 33795 33797: -0.768531 + 33799 = 0 + 33796 33798: -0.576341 + 33800 = 0 + 33813 33815: -0.422732 + 33817 33815: -0.277533 + 33814 33816: -0.418366 + 33818 33816: -0.135275 + 33825 33829: -0.774446 + 33833 33829: -0.288063 + 33826 33830: -0.584650 + 33834 33830: -0.282381 + 33827 33831: -0.771431 + 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 + 34014 34018: -0.274456 + 34022 34018: -0.274456 + 34015 34019: -0.133733 + 34023 34019: -0.271536 + 34016 34020: -0.271536 + 34024 34020: -0.133733 + 34707 34708: 0.427330 + 34709 34708: -0.427330 + 34713 34715: 0.135275 + 34717 34715: -0.418366 + 34714 34716: 0.277533 + 34718 34716: -0.422732 + 34731 34733: 0.440883 + 34735 34733: -0.777585 + 34732 34734: 0.433590 + 34736 34734: -0.589099 + 34743 34747: 0.141216 + 34751 34747: -0.771431 + 34744 34748: 0.288063 + 34752 34748: -0.774446 + 34745 34749: 0.138002 + 34753 34749: -0.580402 + 34896 34898: 0.589099 + 34900 34898: -0.433590 + 34897 34899: 0.777585 + 34901 34899: -0.440883 + 34908 34912: 0.604838 + 34916 34912: -0.783313 + 34909 34913: 0.789776 + 34917 34913: -0.789776 + 34910 34914: 0.596427 + 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 + 35047 35049: 0.418366 + 35051 35049: -0.135275 + 35058 35062: 0.133733 + 35066 35062: -0.271536 + 35059 35063: 0.274456 + 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 + 35224 35228: 0.774446 + 35232 35228: -0.288063 + 35225 35229: 0.580402 + 35233 35229: -0.138002 + 35787 35788: -0.427330 + 35789 35788: 0.427330 + 35793 35795: -0.777585 + 35797 35795: 0.440883 + 35794 35796: -0.589099 + 35798 35796: 0.433590 + 35811 35813: -0.418366 + 35815 35813: 0.135275 + 35812 35814: -0.422732 + 35816 35814: 0.277533 + 35823 35827: -0.771431 + 35831 35827: 0.141216 + 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 + 36021 36017: 0.132271 + 36014 36018: -0.274456 + 36022 36018: 0.274456 + 36165 36167: -0.433590 + 36169 36167: 0.589099 + 36166 36168: -0.440883 + 36170 36168: 0.777585 + 36177 36181: -0.783313 + 36185 36181: 0.604838 + 36178 36182: -0.596427 + 36186 36182: 0.596427 + 36179 36183: -0.789776 + 36187 36183: 0.789776 + 36291 = 0 + 36295 36293: 0.576341 + 36292 = 0 + 36296 36294: 0.768531 + 36303 36307: -0.282381 + 36311 36307: 0.584650 + 36304 36308: -0.138002 + 36312 36308: 0.580402 + 36305 36309: -0.288063 + 36313 36309: 0.774446 + 36867 36868: 0.427330 + 36869 36868: 0.427330 + 36873 36875: 0.135275 + 36877 36875: 0.418366 + 36874 36876: 0.277533 + 36878 36876: 0.422732 + 36891 36893: 0.418366 + 36895 36893: 0.135275 + 36892 36894: 0.422732 + 36896 36894: 0.277533 + 36903 36907: 0.132271 + 36911 36907: 0.132271 + 36904 36908: 0.271536 + 36912 36908: 0.133733 + 36905 36909: 0.133733 + 36913 36909: 0.271536 + 37056 37058: 0.589099 + 37060 37058: 0.433590 + 37057 37059: 0.777585 + 37061 37059: 0.440883 + 37068 37072: 0.580402 + 37076 37072: 0.138002 + 37069 37073: 0.771431 + 37077 37073: 0.141216 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