From: bangerth Date: Wed, 23 Jan 2008 23:42:30 +0000 (+0000) Subject: Implement VectorTools::compute_no_normal_flux_constraints. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=b38a22c02dea7b6e473e339fab0d0fa5d2ce3047;p=dealii-svn.git Implement VectorTools::compute_no_normal_flux_constraints. git-svn-id: https://svn.dealii.org/trunk@15654 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/deal.II/include/numerics/vectors.h b/deal.II/deal.II/include/numerics/vectors.h index 5273ed4b13..4d229dbf4a 100644 --- a/deal.II/deal.II/include/numerics/vectors.h +++ b/deal.II/deal.II/include/numerics/vectors.h @@ -2,7 +2,7 @@ // $Id$ // Version: $Name$ // -// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors +// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by the deal.II authors // // This file is subject to QPL and may not be distributed // without copyright and license information. Please refer @@ -18,6 +18,8 @@ #include #include #include +#include + #include #include #include @@ -326,7 +328,8 @@ class VectorTools * following possibilities are * implemented: */ - enum NormType { + enum NormType + { /** * The function or * difference of functions @@ -716,6 +719,262 @@ class VectorTools const Quadrature &q, std::map &boundary_values); + + /** + * 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 + * @ref step_22 "step-22". 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 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 last argument is denoted to + * compute the normal vector $\vec n$ at + * the boundary points. + * + * + *

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 + *

+ * + * 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: + * + *

+ * @image html no_normal_flux_2.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. + * + * + *

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: + * + *

+ * @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. + */ + template class DH> + static + void + compute_no_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); + + //@} /** * @name Assembling of right hand sides diff --git a/deal.II/deal.II/include/numerics/vectors.templates.h b/deal.II/deal.II/include/numerics/vectors.templates.h index 773d2b0d76..3c071a17e6 100644 --- a/deal.II/deal.II/include/numerics/vectors.templates.h +++ b/deal.II/deal.II/include/numerics/vectors.templates.h @@ -42,6 +42,7 @@ #include #include #include +#include DEAL_II_NAMESPACE_OPEN @@ -1824,6 +1825,752 @@ VectorTools::project_boundary_values (const DoFHandler &dof, +namespace internal +{ + namespace VectorTools + { + /** + * A structure that stores the dim DoF + * indices that correspond to a + * vector-valued quantity at a single + * support point. + */ + template + struct VectorDoFTuple + { + unsigned int dof_indices[dim]; + + bool operator < (const VectorDoFTuple &other) const + { + for (unsigned int i=0; i other.dof_indices[i]) + return false; + return false; + } + + bool operator == (const VectorDoFTuple &other) const + { + for (unsigned int i=0; i &other) const + { + return ! (*this == other); + } + }; + + + + /** + * Add the constraint + * $\vec n \cdot \vec u = 0$ + * to the list of constraints. + * + * Here, $\vec u$ is represented + * by the set of given DoF + * indices, and $\vec n$ by the + * vector specified as the second + * argument. + */ + template + void + add_constraint (const VectorDoFTuple &dof_indices, + const Tensor<1,dim> &constraining_vector, + ConstraintMatrix &constraints) + { + // choose the DoF that has the + // largest component in the + // constraining_vector as the + // one to be constrained as + // this makes the process + // stable in cases where the + // constraining_vector has the + // form n=(1,0) or n=(0,1) + // + // we get constraints of the form + // x0 = a_1*x1 + a2*x2 + ... + // if one of the weights is + // essentially zero then skip + // this part. the ConstraintMatrix + // can also deal with cases like + // x0 = 0 + // if necessary + switch (dim) + { + case 2: + { + if (std::fabs(constraining_vector[0]) > std::fabs(constraining_vector[1])) + { + constraints.add_line (dof_indices.dof_indices[0]); + + if (std::fabs (constraining_vector[1]/constraining_vector[0]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[0], + dof_indices.dof_indices[1], + -constraining_vector[1]/constraining_vector[0]); + } + else + { + constraints.add_line (dof_indices.dof_indices[1]); + + if (std::fabs (constraining_vector[0]/constraining_vector[1]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[1], + dof_indices.dof_indices[0], + -constraining_vector[0]/constraining_vector[1]); + } + break; + } + + case 3: + { + if ((std::fabs(constraining_vector[0]) >= std::fabs(constraining_vector[1])) + && + (std::fabs(constraining_vector[0]) >= std::fabs(constraining_vector[2]))) + { + constraints.add_line (dof_indices.dof_indices[0]); + + if (std::fabs (constraining_vector[1]/constraining_vector[0]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[0], + dof_indices.dof_indices[1], + -constraining_vector[1]/constraining_vector[0]); + + if (std::fabs (constraining_vector[2]/constraining_vector[0]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[0], + dof_indices.dof_indices[2], + -constraining_vector[2]/constraining_vector[0]); + } + else + if ((std::fabs(constraining_vector[1]) >= std::fabs(constraining_vector[0])) + && + (std::fabs(constraining_vector[1]) >= std::fabs(constraining_vector[2]))) + { + constraints.add_line (dof_indices.dof_indices[1]); + + if (std::fabs (constraining_vector[0]/constraining_vector[1]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[1], + dof_indices.dof_indices[0], + -constraining_vector[0]/constraining_vector[1]); + + if (std::fabs (constraining_vector[2]/constraining_vector[1]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[1], + dof_indices.dof_indices[2], + -constraining_vector[2]/constraining_vector[1]); + } + else + { + constraints.add_line (dof_indices.dof_indices[2]); + + if (std::fabs (constraining_vector[0]/constraining_vector[2]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[2], + dof_indices.dof_indices[0], + -constraining_vector[0]/constraining_vector[2]); + + if (std::fabs (constraining_vector[1]/constraining_vector[2]) + > std::numeric_limits::epsilon()) + constraints.add_entry (dof_indices.dof_indices[2], + dof_indices.dof_indices[1], + -constraining_vector[1]/constraining_vector[2]); + } + + break; + } + + default: + Assert (false, ExcNotImplemented()); + } + + } + + + + /** + * Given a vector, compute a set + * of dim-1 vectors that are + * orthogonal to the first one + * and mutually orthonormal as + * well. + */ + template + void + compute_orthonormal_vectors (const Tensor<1,dim> &vector, + Tensor<1,dim> (&orthonormals)[dim-1]) + { + switch (dim) + { + case 3: + { + // to do this in 3d, take + // one vector that is + // guaranteed to be not + // aligned with the + // average tangent and + // form the cross + // product. this yields + // one vector that is + // certainly + // perpendicular to the + // tangent; then take the + // cross product between + // this vector and the + // tangent and get one + // vector that is + // perpendicular to both + + // construct a + // temporary vector + // by swapping the + // larger two + // components and + // flipping one + // sign; this can + // not be collinear + // with the average + // tangent + Tensor<1,dim> tmp = vector; + if ((std::fabs(tmp[0]) > std::fabs(tmp[1])) + && + (std::fabs(tmp[0]) > std::fabs(tmp[2]))) + { + // entry zero + // is the + // largest + if ((std::fabs(tmp[1]) > std::fabs(tmp[2]))) + std::swap (tmp[0], tmp[1]); + else + std::swap (tmp[0], tmp[2]); + + tmp[0] *= -1; + } + else if ((std::fabs(tmp[1]) > std::fabs(tmp[0])) + && + (std::fabs(tmp[1]) > std::fabs(tmp[2]))) + { + // entry one + // is the + // largest + if ((std::fabs(tmp[0]) > std::fabs(tmp[2]))) + std::swap (tmp[1], tmp[0]); + else + std::swap (tmp[1], tmp[2]); + + tmp[1] *= -1; + } + else + { + // entry two + // is the + // largest + if ((std::fabs(tmp[0]) > std::fabs(tmp[1]))) + std::swap (tmp[2], tmp[0]); + else + std::swap (tmp[2], tmp[1]); + + tmp[2] *= -1; + } + + Assert (std::fabs(vector * tmp) < 1e-12, + ExcInternalError()); + + // now compute the + // two normals + cross_product (orthonormals[0], vector, tmp); + cross_product (orthonormals[1], vector, orthonormals[0]); + + break; + } + + default: + Assert (false, ExcNotImplemented()); + } + } + + } +} + + + +template class DH> +void +VectorTools::compute_no_normal_flux_constraints (const DH &dof_handler, + const unsigned int first_vector_component, + const std::set &boundary_ids, + ConstraintMatrix &constraints, + const Mapping &mapping) +{ + Assert (dim > 1, + ExcMessage ("This function is not useful in 1d because it amounts " + "to imposing Dirichlet values on the vector-valued " + "quantity.")); + + const FiniteElement &fe = dof_handler.get_fe(); + + std::vector face_dofs (fe.dofs_per_face); + std::vector > dof_locations (fe.dofs_per_face); + + // have a map that stores normal vectors + // for each vector-dof tuple we want to + // constrain. since we can get at the same + // vector dof tuple more than once (for + // example if it is located at a vertex + // that we visit from all adjacent cells), + // we will want to average later on the + // normal vectors computed on different + // cells as described in the documentation + // of this function. however, we can only + // average if the contributions came from + // different cells, whereas we want to + // constrain twice or more in case the + // contributions came from different faces + // of the same cell. consequently, we also + // have to store which cell a normal vector + // was computed on + typedef + std::multimap, + std::pair, typename DH::active_cell_iterator> > + DoFToNormalsMap; + + DoFToNormalsMap dof_to_normals_map; + + // now loop over all cells and all faces + typename DH::active_cell_iterator + cell = dof_handler.begin_active(), + endc = dof_handler.end(); + for (; cell!=endc; ++cell) + 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()) + { + typename DH::face_iterator face = cell->face(face_no); + + // get the indices of the + // dofs on this cell... + face->get_dof_indices (face_dofs, cell->active_fe_index()); + + // ...and the normal + // vectors at the locations + // where they are defined: + const std::vector > & + unit_support_points = fe.get_unit_face_support_points(); + Quadrature aux_quad (unit_support_points); + FEFaceValues fe_values (mapping, fe, aux_quad, + update_normal_vectors); + fe_values.reinit(cell, face_no); + + // then identify which of + // them correspond to the + // selected set of vector + // components + for (unsigned int i=0; i vector_dofs; + vector_dofs.dof_indices[0] = face_dofs[i]; + + for (unsigned int k=0; k= + first_vector_component) + && + (fe.face_system_to_component_index(k).first < + first_vector_component + dim)) + vector_dofs.dof_indices[fe.face_system_to_component_index(k).first] + = face_dofs[k]; + + // and enter the + // (dofs,(normal_vector,cell)) + // entry into the map + dof_to_normals_map + .insert (std::make_pair (vector_dofs, + std::make_pair (fe_values.normal_vector(i), + cell))); + } + } + + // Now do something with the + // collected information. To this + // end, loop through all sets of + // pairs (dofs,normal_vector) and + // identify which entries belong to + // the same set of dofs and then do + // as described in the + // documentation, i.e. either + // average the normal vector or + // don't for this particular set of + // dofs + typename DoFToNormalsMap::const_iterator + p = dof_to_normals_map.begin(); + + while (p != dof_to_normals_map.end()) + { + // first find the range of entries in + // the multimap that corresponds to the + // same vector-dof tuple. as usual, we + // define the range half-open. the + // first entry of course is 'p' + typename DoFToNormalsMap::const_iterator same_dof_range[2] + = { p }; + for (++p; p != dof_to_normals_map.end(); ++p) + if (p->first != same_dof_range[0]->first) + { + same_dof_range[1] = p; + break; + } + if (p == dof_to_normals_map.end()) + same_dof_range[1] = dof_to_normals_map.end(); + + // now compute the reverse mapping: for + // each of the cells that contributed + // to the current set of vector dofs, + // add up the normal vectors. the + // values of the map are pairs of + // normal vectors and number of cells + // that have contributed + typedef + std::map + ::active_cell_iterator, + std::pair, unsigned int> > + CellToNormalsMap; + + CellToNormalsMap cell_to_normals_map; + for (typename DoFToNormalsMap::const_iterator + q = same_dof_range[0]; + q != same_dof_range[1]; ++q) + if (cell_to_normals_map.find (q->second.second) + == cell_to_normals_map.end()) + cell_to_normals_map[q->second.second] + = std::make_pair (q->second.first, 1U); + else + { + const Tensor<1,dim> old_normal + = cell_to_normals_map[q->second.second].first; + const unsigned int old_count + = cell_to_normals_map[q->second.second].second; + + Assert (old_count > 0, ExcInternalError()); + + // in the same entry, + // store again the now + // averaged normal vector + // and the new count + cell_to_normals_map[q->second.second] + = std::make_pair ((old_normal * old_count + q->second.first) / (old_count + 1), + old_count + 1); + } + + Assert (cell_to_normals_map.size() >= 1, ExcInternalError()); + + // count the maximum number of + // contributions from each cell + unsigned int max_n_contributions_per_cell = 1; + for (typename CellToNormalsMap::const_iterator + x = cell_to_normals_map.begin(); + x != cell_to_normals_map.end(); ++x) + max_n_contributions_per_cell + = std::max (max_n_contributions_per_cell, + x->second.second); + + // verify that each cell can have only + // contributed at most dim times, since + // that is the maximum number of faces + // that come together at a single place + Assert (max_n_contributions_per_cell <= dim, ExcInternalError()); + + switch (max_n_contributions_per_cell) + { + // first deal with the case that a + // number of cells all have + // registered that they have a + // normal vector defined at the + // location of a given vector dof, + // and that each of them have + // encountered this vector dof + // exactly once while looping over + // all their faces. as stated in + // the documentation, this is the + // case where we want to simply + // average over all normal vectors + case 1: + { + + // compute the average + // normal vector from all + // the ones that have the + // same set of dofs. we + // could add them up and + // divide them by the + // number of additions, + // or simply normalize + // them right away since + // we want them to have + // unit length anyway + Tensor<1,dim> normal; + for (typename CellToNormalsMap::const_iterator + x = cell_to_normals_map.begin(); + x != cell_to_normals_map.end(); ++x) + normal += x->second.first; + normal /= normal.norm(); + + // then construct constraints + // from this: + const internal::VectorTools::VectorDoFTuple & + dof_indices = same_dof_range[0]->first; + internal::VectorTools::add_constraint (dof_indices, normal, + constraints); + + break; + } + + + // this is the slightly + // more complicated case + // that a single cell has + // contributed with exactly + // DIM normal vectors to + // the same set of vector + // dofs. this is what + // happens in a corner in + // 2d and 3d (but not on an + // edge in 3d, where we + // have only 2, i.e. t; + + typename DoFToNormalsMap::const_iterator x = same_dof_range[0]; + for (unsigned int i=0; isecond.first[j]; + + Assert (std::fabs(determinant (t)) > 1e-3, + ExcMessage("Found a set of normal vectors that are nearly collinear.")); + } + + // so all components of + // this vector dof are + // constrained. enter + // this into the + // constraint matrix + for (unsigned int i=0; ifirst.dof_indices[i]); + // no add_entries here + } + + break; + } + + + // this is the case of an + // edge contribution in 3d, + // i.e. the vector is + // constrained in two + // directions but not the + // third. + default: + { + Assert (dim >= 3, ExcNotImplemented()); + Assert (max_n_contributions_per_cell == 2, ExcInternalError()); + + // as described in the + // documentation, let us + // first collect what + // each of the cells + // contributed at the + // current point. we use + // a std::list instead of + // a std::set (which + // would be more natural) + // because std::set + // requires that the + // stored elements are + // comparable with + // operator< + typedef + std::map::active_cell_iterator, std::list > > + CellContributions; + CellContributions cell_contributions; + + for (typename DoFToNormalsMap::const_iterator + q = same_dof_range[0]; + q != same_dof_range[1]; ++q) + cell_contributions[q->second.second].push_back (q->second.first); + Assert (cell_contributions.size() >= 1, ExcInternalError()); + + // now for each cell that + // has contributed + // determine the number + // of normal vectors it + // has contributed. we + // currently only + // implement if this is + // dim-1 for all cells + // (if a single cell has + // contributed dim, or if + // all adjacent cells + // have contributed 1 + // normal vector, this is + // already handled above) + // + // for each contributing + // cell compute the + // tangential vector that + // remains unconstrained + std::list > tangential_vectors; + for (typename CellContributions::const_iterator + contribution = cell_contributions.begin(); + contribution != cell_contributions.end(); + ++contribution) + { + Assert (contribution->second.size() == dim-1, ExcNotImplemented()); + + Tensor<1,dim> normals[dim-1]; + { + unsigned int index=0; + for (typename std::list >::const_iterator + t = contribution->second.begin(); + t != contribution->second.end(); + ++t, ++index) + normals[index] = *t; + Assert (index == dim-1, ExcInternalError()); + } + + // calculate the + // tangent as the + // outer product of + // the normal vectors + Tensor<1,dim> tangent; + switch (dim) + { + case 3: + cross_product (tangent, normals[0], normals[1]); + break; + default: + Assert (false, ExcNotImplemented()); + } + + Assert (std::fabs (tangent.norm()-1) < 1e-12, + ExcInternalError()); + + tangential_vectors.push_back (tangent); + } + + // go through the list of + // tangents and make sure + // that they all roughly + // point in the same + // direction as the first + // one (i.e. have an + // angle less than 90 + // degrees); if they + // don't then flip their + // sign + { + const Tensor<1,dim> first_tangent = tangential_vectors.front(); + typename std::list >::iterator + t = tangential_vectors.begin(); + ++t; + for (; t != tangential_vectors.end(); ++t) + if (*t * first_tangent < 0) + *t *= -1; + } + + // now compute the + // average tangent and + // normalize it + Tensor<1,dim> average_tangent; + for (typename std::list >::const_iterator + t = tangential_vectors.begin(); + t != tangential_vectors.end(); + ++t) + average_tangent += *t; + average_tangent /= average_tangent.norm(); + + // from the tangent + // vector we now need to + // again reconstruct dim-1 + // normal directions in + // which the vector field + // is to be constrained + Tensor<1,dim> constraining_normals[dim-1]; + internal::VectorTools:: + compute_orthonormal_vectors (average_tangent, + constraining_normals); + + // now all that is left + // is that we add the + // constraints for these + // dim-1 vectors + const internal::VectorTools::VectorDoFTuple & + dof_indices = same_dof_range[0]->first; + for (unsigned int c=0; c std::map &); +#if deal_II_dimension != 1 +template +void +VectorTools::compute_no_normal_flux_constraints (const DoFHandler &dof_handler, + const unsigned int first_vector_component, + const std::set &boundary_ids, + ConstraintMatrix &constraints, + const Mapping &mapping); +#endif + // // Due to introducing the DoFHandler as a template parameter, // // the following instantiations are required in 1d diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h index 5cd975c516..6f4be3939f 100644 --- a/deal.II/doc/news/changes.h +++ b/deal.II/doc/news/changes.h @@ -232,6 +232,14 @@ constraints individually.
    +
  1. New: The function VectorTools::compute_no_normal_flux_constraints computes + the constraints that correspond to boundary conditions of the + form $\vec u \cdot \vec n = 0$. The use of the function is demonstrated in the + @ref step_22 "step-22" tutorial program. +
    + (WB 2008/01/23) +

  2. +
  3. Fixed: Neither ConstraintMatrix::print nor ConstraintMatrix::write_dot produced any output for constraints of the form $x_i=0$, i.e. where the right hand side is a trivial linear combination of other degrees of freedom. This diff --git a/tests/deal.II/Makefile b/tests/deal.II/Makefile index eebc4ba894..f48213a374 100644 --- a/tests/deal.II/Makefile +++ b/tests/deal.II/Makefile @@ -1,6 +1,6 @@ ############################################################ # $Id$ -# Copyright (C) 2000, 2001, 2002, 2003, 2005, 2006, 2007 by the deal.II authors +# Copyright (C) 2000, 2001, 2002, 2003, 2005, 2006, 2007, 2008 by the deal.II authors ############################################################ ############################################################ @@ -24,7 +24,11 @@ default: run-tests tests_x = block_matrices \ user_data_* \ constraints \ + constraints_zero \ + constraints_zero_merge \ + constraints_zero_condense \ constraint_graph \ + constraint_graph_zero \ data_out \ derivative_* \ derivatives \ @@ -68,7 +72,8 @@ tests_x = block_matrices \ maximal_cell_diameter \ union_triangulation \ create_* \ - line_coarsening_3d + line_coarsening_3d \ + no_flux_* # from above list of regular expressions, generate the real set of # tests diff --git a/tests/deal.II/no_flux_01.cc b/tests/deal.II/no_flux_01.cc new file mode 100644 index 0000000000..db8ff53584 --- /dev/null +++ b/tests/deal.II/no_flux_01.cc @@ -0,0 +1,90 @@ +//---------------------------------------------------------------------- +// $Id$ +// Version: $Name$ +// +// Copyright (C) 2007, 2008 by the deal.II authors +// +// This file is subject to QPL and may not be distributed +// without copyright and license information. Please refer +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +//---------------------------------------------------------------------- + + +// check the creation of no-flux boundary conditions for a finite +// element that consists of only a single set of vector components +// (i.e. it has dim components) + +#include "../tests.h" +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + + +template +void test_projection (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_no_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_projection(tr, fe); + } +} + + +int main() +{ + std::ofstream logfile ("no_flux_01/output"); + logfile.precision (2); + logfile.setf(std::ios::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/no_flux_01/cmp/generic b/tests/deal.II/no_flux_01/cmp/generic new file mode 100644 index 0000000000..56d7e3d9df --- /dev/null +++ b/tests/deal.II/no_flux_01/cmp/generic @@ -0,0 +1,6076 @@ +JobId unknown Wed Jan 23 17:37:56 2008 +DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=0 + 0 = 0 + 4 = 0 + 12 = 0 + 30 = 0 + 36 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=1 + 0 = 0 + 4 = 0 + 12 = 0 + 22 = 0 + 24 = 0 + 28 = 0 + 30 = 0 + 36 = 0 + 44 = 0 + 48 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=2 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 9 = 0 + 12 = 0 + 19 = 0 + 22 = 0 + 23 = 0 + 24 = 0 + 28 = 0 + 30 = 0 + 36 = 0 + 44 = 0 + 48 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(1)^2], case=3 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 9 = 0 + 12 = 0 + 19 = 0 + 22 = 0 + 23 = 0 + 24 = 0 + 28 = 0 + 30 = 0 + 36 = 0 + 37 = 0 + 39 = 0 + 41 = 0 + 44 = 0 + 47 = 0 + 48 = 0 + 49 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=0 + 0 = 0 + 4 = 0 + 8 = 0 + 30 = 0 + 34 = 0 + 90 = 0 + 94 = 0 + 110 = 0 + 114 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=1 + 0 = 0 + 4 = 0 + 8 = 0 + 30 = 0 + 34 = 0 + 62 = 0 + 64 = 0 + 66 = 0 + 82 = 0 + 84 = 0 + 90 = 0 + 94 = 0 + 110 = 0 + 114 = 0 + 138 = 0 + 140 = 0 + 154 = 0 + 156 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=2 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 8 = 0 + 13 = 0 + 19 = 0 + 25 = 0 + 30 = 0 + 34 = 0 + 51 = 0 + 57 = 0 + 62 = 0 + 63 = 0 + 64 = 0 + 66 = 0 + 69 = 0 + 82 = 0 + 84 = 0 + 90 = 0 + 94 = 0 + 110 = 0 + 114 = 0 + 138 = 0 + 140 = 0 + 154 = 0 + 156 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)^2], case=3 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 8 = 0 + 13 = 0 + 19 = 0 + 25 = 0 + 30 = 0 + 34 = 0 + 51 = 0 + 57 = 0 + 62 = 0 + 63 = 0 + 64 = 0 + 66 = 0 + 69 = 0 + 82 = 0 + 84 = 0 + 90 = 0 + 94 = 0 + 110 = 0 + 111 = 0 + 113 = 0 + 114 = 0 + 119 = 0 + 123 = 0 + 127 = 0 + 138 = 0 + 140 = 0 + 147 = 0 + 151 = 0 + 154 = 0 + 155 = 0 + 156 = 0 + 159 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=0 + 0 = 0 + 4 = 0 + 8 = 0 + 9 = 0 + 56 = 0 + 60 = 0 + 61 = 0 + 182 = 0 + 186 = 0 + 187 = 0 + 224 = 0 + 228 = 0 + 229 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=1 + 0 = 0 + 4 = 0 + 8 = 0 + 9 = 0 + 56 = 0 + 60 = 0 + 61 = 0 + 122 = 0 + 124 = 0 + 126 = 0 + 127 = 0 + 164 = 0 + 166 = 0 + 167 = 0 + 182 = 0 + 186 = 0 + 187 = 0 + 224 = 0 + 228 = 0 + 229 = 0 + 284 = 0 + 286 = 0 + 287 = 0 + 320 = 0 + 322 = 0 + 323 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=2 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 8 = 0 + 9 = 0 + 18 = 0 + 19 = 0 + 33 = 0 + 42 = 0 + 43 = 0 + 56 = 0 + 60 = 0 + 61 = 0 + 99 = 0 + 108 = 0 + 109 = 0 + 122 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 127 = 0 + 132 = 0 + 133 = 0 + 164 = 0 + 166 = 0 + 167 = 0 + 182 = 0 + 186 = 0 + 187 = 0 + 224 = 0 + 228 = 0 + 229 = 0 + 284 = 0 + 286 = 0 + 287 = 0 + 320 = 0 + 322 = 0 + 323 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)^2], case=3 + 0 = 0 + 1 = 0 + 3 = 0 + 4 = 0 + 8 = 0 + 9 = 0 + 18 = 0 + 19 = 0 + 33 = 0 + 42 = 0 + 43 = 0 + 56 = 0 + 60 = 0 + 61 = 0 + 99 = 0 + 108 = 0 + 109 = 0 + 122 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 127 = 0 + 132 = 0 + 133 = 0 + 164 = 0 + 166 = 0 + 167 = 0 + 182 = 0 + 186 = 0 + 187 = 0 + 224 = 0 + 225 = 0 + 227 = 0 + 228 = 0 + 229 = 0 + 238 = 0 + 239 = 0 + 249 = 0 + 256 = 0 + 257 = 0 + 284 = 0 + 286 = 0 + 287 = 0 + 303 = 0 + 310 = 0 + 311 = 0 + 320 = 0 + 321 = 0 + 322 = 0 + 323 = 0 + 328 = 0 + 329 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=0 + 0 = 0 + 6 = 0 + 12 = 0 + 18 = 0 + 36 = 0 + 42 = 0 + 54 = 0 + 60 = 0 + 72 = 0 + 135 = 0 + 141 = 0 + 153 = 0 + 159 = 0 + 171 = 0 + 180 = 0 + 225 = 0 + 231 = 0 + 243 = 0 + 252 = 0 + 258 = 0 + 270 = 0 + 315 = 0 + 324 = 0 + 333 = 0 + 342 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=1 + 0 = 0 + 6 = 0 + 12 = 0 + 18 = 0 + 36 = 0 + 42 = 0 + 54 = 0 + 60 = 0 + 72 = 0 + 93 = 0 + 96 = 0 + 99 = 0 + 102 = 0 + 111 = 0 + 114 = 0 + 123 = 0 + 126 = 0 + 132 = 0 + 135 = 0 + 141 = 0 + 153 = 0 + 159 = 0 + 171 = 0 + 180 = 0 + 195 = 0 + 198 = 0 + 207 = 0 + 210 = 0 + 216 = 0 + 222 = 0 + 225 = 0 + 231 = 0 + 243 = 0 + 252 = 0 + 258 = 0 + 270 = 0 + 285 = 0 + 288 = 0 + 294 = 0 + 303 = 0 + 306 = 0 + 312 = 0 + 315 = 0 + 324 = 0 + 333 = 0 + 342 = 0 + 354 = 0 + 360 = 0 + 366 = 0 + 372 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=2 + 0 = 0 + 1 = 0 + 4 = 0 + 6 = 0 + 12 = 0 + 13 = 0 + 16 = 0 + 18 = 0 + 25 = 0 + 31 = 0 + 36 = 0 + 42 = 0 + 54 = 0 + 55 = 0 + 58 = 0 + 60 = 0 + 67 = 0 + 72 = 0 + 82 = 0 + 88 = 0 + 93 = 0 + 94 = 0 + 96 = 0 + 99 = 0 + 100 = 0 + 102 = 0 + 111 = 0 + 114 = 0 + 118 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 132 = 0 + 135 = 0 + 141 = 0 + 153 = 0 + 159 = 0 + 171 = 0 + 180 = 0 + 195 = 0 + 198 = 0 + 207 = 0 + 210 = 0 + 216 = 0 + 222 = 0 + 225 = 0 + 226 = 0 + 229 = 0 + 231 = 0 + 238 = 0 + 243 = 0 + 252 = 0 + 253 = 0 + 256 = 0 + 258 = 0 + 265 = 0 + 270 = 0 + 280 = 0 + 285 = 0 + 286 = 0 + 288 = 0 + 294 = 0 + 298 = 0 + 303 = 0 + 304 = 0 + 306 = 0 + 312 = 0 + 315 = 0 + 324 = 0 + 333 = 0 + 342 = 0 + 354 = 0 + 360 = 0 + 366 = 0 + 372 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=3 + 0 = 0 + 1 = 0 + 4 = 0 + 6 = 0 + 12 = 0 + 13 = 0 + 16 = 0 + 18 = 0 + 25 = 0 + 31 = 0 + 36 = 0 + 42 = 0 + 54 = 0 + 55 = 0 + 58 = 0 + 60 = 0 + 67 = 0 + 72 = 0 + 82 = 0 + 88 = 0 + 93 = 0 + 94 = 0 + 96 = 0 + 99 = 0 + 100 = 0 + 102 = 0 + 111 = 0 + 114 = 0 + 118 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 132 = 0 + 135 = 0 + 141 = 0 + 153 = 0 + 154 = 0 + 157 = 0 + 159 = 0 + 160 = 0 + 163 = 0 + 166 = 0 + 169 = 0 + 171 = 0 + 180 = 0 + 181 = 0 + 184 = 0 + 187 = 0 + 195 = 0 + 198 = 0 + 202 = 0 + 205 = 0 + 207 = 0 + 208 = 0 + 210 = 0 + 211 = 0 + 216 = 0 + 220 = 0 + 222 = 0 + 223 = 0 + 225 = 0 + 226 = 0 + 229 = 0 + 231 = 0 + 238 = 0 + 243 = 0 + 252 = 0 + 253 = 0 + 256 = 0 + 258 = 0 + 265 = 0 + 270 = 0 + 280 = 0 + 285 = 0 + 286 = 0 + 288 = 0 + 294 = 0 + 298 = 0 + 303 = 0 + 304 = 0 + 306 = 0 + 312 = 0 + 315 = 0 + 324 = 0 + 325 = 0 + 328 = 0 + 331 = 0 + 333 = 0 + 342 = 0 + 343 = 0 + 346 = 0 + 349 = 0 + 354 = 0 + 358 = 0 + 360 = 0 + 361 = 0 + 366 = 0 + 370 = 0 + 372 = 0 + 373 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=4 + 0 = 0 + 1 = 0 + 2 = 0 + 4 = 0 + 5 = 0 + 6 = 0 + 8 = 0 + 11 = 0 + 12 = 0 + 13 = 0 + 16 = 0 + 18 = 0 + 25 = 0 + 26 = 0 + 29 = 0 + 31 = 0 + 36 = 0 + 38 = 0 + 41 = 0 + 42 = 0 + 50 = 0 + 54 = 0 + 55 = 0 + 58 = 0 + 60 = 0 + 67 = 0 + 72 = 0 + 82 = 0 + 83 = 0 + 86 = 0 + 88 = 0 + 93 = 0 + 94 = 0 + 95 = 0 + 96 = 0 + 98 = 0 + 99 = 0 + 100 = 0 + 102 = 0 + 107 = 0 + 111 = 0 + 113 = 0 + 114 = 0 + 118 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 132 = 0 + 135 = 0 + 137 = 0 + 140 = 0 + 141 = 0 + 149 = 0 + 153 = 0 + 154 = 0 + 155 = 0 + 157 = 0 + 158 = 0 + 159 = 0 + 160 = 0 + 163 = 0 + 166 = 0 + 167 = 0 + 169 = 0 + 171 = 0 + 180 = 0 + 181 = 0 + 184 = 0 + 187 = 0 + 191 = 0 + 195 = 0 + 197 = 0 + 198 = 0 + 202 = 0 + 203 = 0 + 205 = 0 + 207 = 0 + 208 = 0 + 209 = 0 + 210 = 0 + 211 = 0 + 216 = 0 + 220 = 0 + 222 = 0 + 223 = 0 + 225 = 0 + 226 = 0 + 229 = 0 + 231 = 0 + 238 = 0 + 243 = 0 + 252 = 0 + 253 = 0 + 256 = 0 + 258 = 0 + 265 = 0 + 270 = 0 + 280 = 0 + 285 = 0 + 286 = 0 + 288 = 0 + 294 = 0 + 298 = 0 + 303 = 0 + 304 = 0 + 306 = 0 + 312 = 0 + 315 = 0 + 324 = 0 + 325 = 0 + 328 = 0 + 331 = 0 + 333 = 0 + 342 = 0 + 343 = 0 + 346 = 0 + 349 = 0 + 354 = 0 + 358 = 0 + 360 = 0 + 361 = 0 + 366 = 0 + 370 = 0 + 372 = 0 + 373 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(1)^3], case=5 + 0 = 0 + 1 = 0 + 2 = 0 + 4 = 0 + 5 = 0 + 6 = 0 + 8 = 0 + 11 = 0 + 12 = 0 + 13 = 0 + 16 = 0 + 18 = 0 + 25 = 0 + 26 = 0 + 29 = 0 + 31 = 0 + 36 = 0 + 38 = 0 + 41 = 0 + 42 = 0 + 50 = 0 + 54 = 0 + 55 = 0 + 58 = 0 + 60 = 0 + 67 = 0 + 72 = 0 + 82 = 0 + 83 = 0 + 86 = 0 + 88 = 0 + 93 = 0 + 94 = 0 + 95 = 0 + 96 = 0 + 98 = 0 + 99 = 0 + 100 = 0 + 102 = 0 + 107 = 0 + 111 = 0 + 113 = 0 + 114 = 0 + 118 = 0 + 123 = 0 + 124 = 0 + 126 = 0 + 132 = 0 + 135 = 0 + 137 = 0 + 140 = 0 + 141 = 0 + 149 = 0 + 153 = 0 + 154 = 0 + 155 = 0 + 157 = 0 + 158 = 0 + 159 = 0 + 160 = 0 + 163 = 0 + 166 = 0 + 167 = 0 + 169 = 0 + 171 = 0 + 180 = 0 + 181 = 0 + 184 = 0 + 187 = 0 + 191 = 0 + 195 = 0 + 197 = 0 + 198 = 0 + 202 = 0 + 203 = 0 + 205 = 0 + 207 = 0 + 208 = 0 + 209 = 0 + 210 = 0 + 211 = 0 + 216 = 0 + 220 = 0 + 222 = 0 + 223 = 0 + 225 = 0 + 226 = 0 + 229 = 0 + 231 = 0 + 238 = 0 + 243 = 0 + 252 = 0 + 253 = 0 + 254 = 0 + 256 = 0 + 257 = 0 + 258 = 0 + 260 = 0 + 263 = 0 + 265 = 0 + 266 = 0 + 269 = 0 + 270 = 0 + 272 = 0 + 275 = 0 + 278 = 0 + 280 = 0 + 285 = 0 + 286 = 0 + 288 = 0 + 294 = 0 + 298 = 0 + 299 = 0 + 302 = 0 + 303 = 0 + 304 = 0 + 305 = 0 + 306 = 0 + 308 = 0 + 311 = 0 + 312 = 0 + 314 = 0 + 315 = 0 + 324 = 0 + 325 = 0 + 328 = 0 + 331 = 0 + 333 = 0 + 335 = 0 + 338 = 0 + 341 = 0 + 342 = 0 + 343 = 0 + 344 = 0 + 346 = 0 + 347 = 0 + 349 = 0 + 350 = 0 + 354 = 0 + 358 = 0 + 360 = 0 + 361 = 0 + 365 = 0 + 366 = 0 + 368 = 0 + 370 = 0 + 371 = 0 + 372 = 0 + 373 = 0 + 374 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=0 + 0 = 0 + 6 = 0 + 12 = 0 + 18 = 0 + 24 = 0 + 36 = 0 + 48 = 0 + 54 = 0 + 60 = 0 + 135 = 0 + 141 = 0 + 147 = 0 + 156 = 0 + 165 = 0 + 171 = 0 + 225 = 0 + 231 = 0 + 237 = 0 + 249 = 0 + 255 = 0 + 261 = 0 + 315 = 0 + 321 = 0 + 330 = 0 + 336 = 0 + 675 = 0 + 681 = 0 + 687 = 0 + 696 = 0 + 705 = 0 + 711 = 0 + 765 = 0 + 771 = 0 + 777 = 0 + 786 = 0 + 795 = 0 + 801 = 0 + 855 = 0 + 861 = 0 + 870 = 0 + 876 = 0 + 915 = 0 + 921 = 0 + 930 = 0 + 936 = 0 + 1215 = 0 + 1221 = 0 + 1227 = 0 + 1239 = 0 + 1245 = 0 + 1251 = 0 + 1305 = 0 + 1311 = 0 + 1320 = 0 + 1326 = 0 + 1365 = 0 + 1371 = 0 + 1377 = 0 + 1389 = 0 + 1395 = 0 + 1401 = 0 + 1455 = 0 + 1461 = 0 + 1470 = 0 + 1476 = 0 + 1755 = 0 + 1761 = 0 + 1770 = 0 + 1776 = 0 + 1815 = 0 + 1821 = 0 + 1830 = 0 + 1836 = 0 + 1875 = 0 + 1881 = 0 + 1890 = 0 + 1896 = 0 + 1935 = 0 + 1941 = 0 + 1950 = 0 + 1956 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=1 + 0 = 0 + 6 = 0 + 12 = 0 + 18 = 0 + 24 = 0 + 36 = 0 + 48 = 0 + 54 = 0 + 60 = 0 + 135 = 0 + 141 = 0 + 147 = 0 + 156 = 0 + 165 = 0 + 171 = 0 + 225 = 0 + 231 = 0 + 237 = 0 + 249 = 0 + 255 = 0 + 261 = 0 + 315 = 0 + 321 = 0 + 330 = 0 + 336 = 0 + 429 = 0 + 432 = 0 + 435 = 0 + 438 = 0 + 441 = 0 + 450 = 0 + 459 = 0 + 462 = 0 + 465 = 0 + 519 = 0 + 522 = 0 + 525 = 0 + 531 = 0 + 537 = 0 + 540 = 0 + 591 = 0 + 594 = 0 + 597 = 0 + 606 = 0 + 609 = 0 + 612 = 0 + 651 = 0 + 654 = 0 + 660 = 0 + 663 = 0 + 675 = 0 + 681 = 0 + 687 = 0 + 696 = 0 + 705 = 0 + 711 = 0 + 765 = 0 + 771 = 0 + 777 = 0 + 786 = 0 + 795 = 0 + 801 = 0 + 855 = 0 + 861 = 0 + 870 = 0 + 876 = 0 + 915 = 0 + 921 = 0 + 930 = 0 + 936 = 0 + 1011 = 0 + 1014 = 0 + 1017 = 0 + 1023 = 0 + 1029 = 0 + 1032 = 0 + 1083 = 0 + 1086 = 0 + 1089 = 0 + 1095 = 0 + 1101 = 0 + 1104 = 0 + 1143 = 0 + 1146 = 0 + 1152 = 0 + 1155 = 0 + 1191 = 0 + 1194 = 0 + 1200 = 0 + 1203 = 0 + 1215 = 0 + 1221 = 0 + 1227 = 0 + 1239 = 0 + 1245 = 0 + 1251 = 0 + 1305 = 0 + 1311 = 0 + 1320 = 0 + 1326 = 0 + 1365 = 0 + 1371 = 0 + 1377 = 0 + 1389 = 0 + 1395 = 0 + 1401 = 0 + 1455 = 0 + 1461 = 0 + 1470 = 0 + 1476 = 0 + 1551 = 0 + 1554 = 0 + 1557 = 0 + 1566 = 0 + 1569 = 0 + 1572 = 0 + 1611 = 0 + 1614 = 0 + 1620 = 0 + 1623 = 0 + 1671 = 0 + 1674 = 0 + 1677 = 0 + 1686 = 0 + 1689 = 0 + 1692 = 0 + 1731 = 0 + 1734 = 0 + 1740 = 0 + 1743 = 0 + 1755 = 0 + 1761 = 0 + 1770 = 0 + 1776 = 0 + 1815 = 0 + 1821 = 0 + 1830 = 0 + 1836 = 0 + 1875 = 0 + 1881 = 0 + 1890 = 0 + 1896 = 0 + 1935 = 0 + 1941 = 0 + 1950 = 0 + 1956 = 0 + 2019 = 0 + 2022 = 0 + 2028 = 0 + 2031 = 0 + 2067 = 0 + 2070 = 0 + 2076 = 0 + 2079 = 0 + 2115 = 0 + 2118 = 0 + 2124 = 0 + 2127 = 0 + 2163 = 0 + 2166 = 0 + 2172 = 0 + 2175 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)^3], case=2 + 0 = 0 + 1 = 0 + 4 = 0 + 6 = 0 + 12 = 0 + 13 = 0 + 16 = 0 + 18 = 0 + 24 = 0 + 31 = 0 + 36 = 0 + 43 = 0 + 48 = 0 + 49 = 0 + 52 = 0 + 54 = 0 + 60 = 0 + 67 = 0 + 82 = 0 + 88 = 0 + 97 = 0 + 106 = 0 + 112 = 0 + 121 = 0 + 135 = 0 + 141 = 0 + 147 = 0 + 156 = 0 + 165 = 0 + 171 = 0 + 225 = 0 + 226 = 0 + 229 = 0 + 231 = 0 + 237 = 0 + 244 = 0 + 249 = 0 + 250 = 0 + 253 = 0 + 255 = 0 + 261 = 0 + 268 = 0 + 280 = 0 + 289 = 0 + 295 = 0 + 304 = 0 + 315 = 0 + 321 = 0 + 330 = 0 + 336 = 0 + 376 = 0 + 382 = 0 + 391 = 0 + 400 = 0 + 406 = 0 + 415 = 0 + 429 = 0 + 430 = 0 + 432 = 0 + 435 = 0 + 436 = 0 + 438 = 0 + 441 = 0 + 445 = 0 + 450 = 0 + 454 = 0 + 459 = 0 + 460 = 0 + 462 = 0 + 465 = 0 + 469 = 0 + 519 = 0 + 522 = 0 + 525 = 0 + 531 = 0 + 537 = 0 + 540 = 0 + 556 = 0 + 565 = 0 + 571 = 0 + 580 = 0 + 591 = 0 + 592 = 0 + 594 = 0 + 597 = 0 + 601 = 0 + 606 = 0 + 607 = 0 + 609 = 0 + 612 = 0 + 616 = 0 + 651 = 0 + 654 = 0 + 660 = 0 + 663 = 0 + 675 = 0 + 681 = 0 + 687 = 0 + 696 = 0 + 705 = 0 + 711 = 0 + 765 = 0 + 771 = 0 + 777 = 0 + 786 = 0 + 795 = 0 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4406 = 0 + 4432 = 0 + 4445 = 0 + 4446 = 0 + 4457 = 0 + 4458 = 0 + 4483 = 0 + 4484 = 0 + 4485 = 0 + 4486 = 0 + 4539 = 0 + 4540 = 0 + 4542 = 0 + 4545 = 0 + 4546 = 0 + 4553 = 0 + 4554 = 0 + 4563 = 0 + 4565 = 0 + 4564 = 0 + 4566 = 0 + 4569 = 0 + 4570 = 0 + 4575 = 0 + 4576 = 0 + 4577 = 0 + 4578 = 0 + 4591 = 0 + 4592 = 0 + 4593 = 0 + 4594 = 0 + 4728 = 0 + 4731 = 0 + 4732 = 0 + 4743 = 0 + 4744 = 0 + 4749 = 0 + 4750 = 0 + 4751 = 0 + 4752 = 0 + 4810 = 0 + 4811 = 0 + 4814 = 0 + 4819 = 0 + 4820 = 0 + 4823 = 0 + 4825 = 0 + 4824 = 0 + 4826 = 0 + 4831 = 0 + 4832 = 0 + 4835 = 0 + 4836 = 0 + 4861 = 0 + 4862 = 0 + 4863 = 0 + 4864 = 0 + 4889 = 0 + 4890 = 0 + 4891 = 0 + 4892 = 0 + 4917 = 0 + 4918 = 0 + 4919 = 0 + 4920 = 0 + 4922 = 0 + 4923 = 0 + 4927 = 0 + 4924 = 0 + 4928 = 0 + 4931 = 0 + 4933 = 0 + 4932 = 0 + 4934 = 0 + 4939 = 0 + 4940 = 0 + 4941 = 0 + 4943 = 0 + 4942 = 0 + 4944 = 0 + 4947 = 0 + 4948 = 0 + 4953 = 0 + 4954 = 0 + 4955 = 0 + 4956 = 0 + 4969 = 0 + 4970 = 0 + 4971 = 0 + 4972 = 0 + 4997 = 0 + 4998 = 0 + 4999 = 0 + 5000 = 0 + 5027 = 0 + 5032 = 0 + 5033 = 0 + 5038 = 0 + 5039 = 0 + 5078 = 0 + 5079 = 0 + 5080 = 0 + 5081 = 0 + 5106 = 0 + 5108 = 0 + 5109 = 0 + 5113 = 0 + 5110 = 0 + 5114 = 0 + 5119 = 0 + 5120 = 0 + 5121 = 0 + 5122 = 0 + 5127 = 0 + 5128 = 0 + 5129 = 0 + 5130 = 0 + 5159 = 0 + 5160 = 0 + 5161 = 0 + 5162 = 0 + 5187 = 0 + 5193 = 0 + 5194 = 0 + 5211 = 0 + 5212 = 0 + 5223 = 0 + 5224 = 0 + 5225 = 0 + 5226 = 0 + 5376 = 0 + 5377 = 0 + 5380 = 0 + 5382 = 0 + 5383 = 0 + 5396 = 0 + 5397 = 0 + 5400 = 0 + 5402 = 0 + 5401 = 0 + 5403 = 0 + 5408 = 0 + 5409 = 0 + 5412 = 0 + 5413 = 0 + 5414 = 0 + 5415 = 0 + 5440 = 0 + 5441 = 0 + 5442 = 0 + 5443 = 0 + 5485 = 0 + 5495 = 0 + 5496 = 0 + 5501 = 0 + 5502 = 0 + 5521 = 0 + 5522 = 0 + 5523 = 0 + 5524 = 0 + 5565 = 0 + 5567 = 0 + 5570 = 0 + 5571 = 0 + 5575 = 0 + 5572 = 0 + 5576 = 0 + 5581 = 0 + 5582 = 0 + 5587 = 0 + 5588 = 0 + 5589 = 0 + 5590 = 0 + 5601 = 0 + 5602 = 0 + 5603 = 0 + 5604 = 0 + 5645 = 0 + 5646 = 0 + 5647 = 0 + 5648 = 0 + 5675 = 0 + 5680 = 0 + 5681 = 0 + 5686 = 0 + 5687 = 0 + 5726 = 0 + 5727 = 0 + 5728 = 0 + 5729 = 0 + 5754 = 0 + 5755 = 0 + 5756 = 0 + 5758 = 0 + 5759 = 0 + 5760 = 0 + 5764 = 0 + 5761 = 0 + 5765 = 0 + 5770 = 0 + 5771 = 0 + 5774 = 0 + 5776 = 0 + 5775 = 0 + 5777 = 0 + 5778 = 0 + 5780 = 0 + 5779 = 0 + 5781 = 0 + 5786 = 0 + 5787 = 0 + 5790 = 0 + 5791 = 0 + 5792 = 0 + 5793 = 0 + 5818 = 0 + 5819 = 0 + 5820 = 0 + 5821 = 0 + 5834 = 0 + 5835 = 0 + 5836 = 0 + 5837 = 0 + 5863 = 0 + 5864 = 0 + 5869 = 0 + 5870 = 0 + 5873 = 0 + 5875 = 0 + 5874 = 0 + 5876 = 0 + 5879 = 0 + 5880 = 0 + 5899 = 0 + 5900 = 0 + 5901 = 0 + 5902 = 0 + 5915 = 0 + 5916 = 0 + 5917 = 0 + 5918 = 0 + 6024 = 0 + 6027 = 0 + 6028 = 0 + 6039 = 0 + 6040 = 0 + 6045 = 0 + 6046 = 0 + 6047 = 0 + 6048 = 0 + 6106 = 0 + 6116 = 0 + 6117 = 0 + 6122 = 0 + 6123 = 0 + 6142 = 0 + 6143 = 0 + 6144 = 0 + 6145 = 0 + 6186 = 0 + 6187 = 0 + 6189 = 0 + 6190 = 0 + 6197 = 0 + 6198 = 0 + 6201 = 0 + 6203 = 0 + 6202 = 0 + 6204 = 0 + 6207 = 0 + 6208 = 0 + 6209 = 0 + 6210 = 0 + 6223 = 0 + 6224 = 0 + 6225 = 0 + 6226 = 0 + 6269 = 0 + 6274 = 0 + 6275 = 0 + 6280 = 0 + 6281 = 0 + 6320 = 0 + 6321 = 0 + 6322 = 0 + 6323 = 0 + 6348 = 0 + 6350 = 0 + 6351 = 0 + 6355 = 0 + 6352 = 0 + 6356 = 0 + 6361 = 0 + 6362 = 0 + 6363 = 0 + 6364 = 0 + 6369 = 0 + 6370 = 0 + 6371 = 0 + 6372 = 0 + 6401 = 0 + 6402 = 0 + 6403 = 0 + 6404 = 0 + 6430 = 0 + 6431 = 0 + 6436 = 0 + 6437 = 0 + 6440 = 0 + 6442 = 0 + 6441 = 0 + 6443 = 0 + 6446 = 0 + 6447 = 0 + 6466 = 0 + 6467 = 0 + 6468 = 0 + 6469 = 0 + 6482 = 0 + 6483 = 0 + 6484 = 0 + 6485 = 0 + 6510 = 0 + 6511 = 0 + 6512 = 0 + 6513 = 0 + 6517 = 0 + 6514 = 0 + 6518 = 0 + 6521 = 0 + 6523 = 0 + 6522 = 0 + 6524 = 0 + 6525 = 0 + 6527 = 0 + 6526 = 0 + 6528 = 0 + 6531 = 0 + 6532 = 0 + 6533 = 0 + 6534 = 0 + 6547 = 0 + 6548 = 0 + 6549 = 0 + 6550 = 0 + 6563 = 0 + 6564 = 0 + 6565 = 0 + 6566 = 0 diff --git a/tests/deal.II/no_flux_02.cc b/tests/deal.II/no_flux_02.cc new file mode 100644 index 0000000000..7dccf6d12f --- /dev/null +++ b/tests/deal.II/no_flux_02.cc @@ -0,0 +1,94 @@ +//---------------------------------------------------------------------- +// $Id$ +// Version: $Name$ +// +// Copyright (C) 2007, 2008 by the deal.II authors +// +// This file is subject to QPL and may not be distributed +// without copyright and license information. Please refer +// to the file deal.II/doc/license.html for the text and +// further information on this license. +// +//---------------------------------------------------------------------- + +// check the creation of no-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 + + +#include "../tests.h" +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include + + + +template +void test_projection (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_no_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_projection(tr, fe); + } +} + + +int main() +{ + std::ofstream logfile ("no_flux_02/output"); + logfile.precision (2); + logfile.setf(std::ios::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/no_flux_02/cmp/generic b/tests/deal.II/no_flux_02/cmp/generic new file mode 100644 index 0000000000..3dfa219774 --- /dev/null +++ b/tests/deal.II/no_flux_02/cmp/generic @@ -0,0 +1,4088 @@ +JobId unknown Wed Jan 23 17:39:41 2008 +DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=0 + 1 = 0 + 9 = 0 + 43 = 0 + 121 = 0 + 147 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=1 + 1 = 0 + 9 = 0 + 43 = 0 + 85 = 0 + 89 = 0 + 111 = 0 + 121 = 0 + 147 = 0 + 183 = 0 + 203 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=2 + 1 = 0 + 32767 = 0 + 9 = 0 + 43 = 0 + 85 = 0 + 89 = 0 + 111 = 0 + 121 = 0 + 147 = 0 + 183 = 0 + 203 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(2)-FE_Q<2>(1)^2-FE_Q<2>(2)], case=3 + 1 = 0 + 32767 = 0 + 9 = 0 + 43 = 0 + 85 = 0 + 89 = 0 + 111 = 0 + 121 = 0 + 147 = 0 + 183 = 0 + 203 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=0 + 1 = 0 + 9 = 0 + 18 = 0 + 87 = 0 + 96 = 0 + 273 = 0 + 282 = 0 + 335 = 0 + 344 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=1 + 1 = 0 + 9 = 0 + 18 = 0 + 87 = 0 + 96 = 0 + 185 = 0 + 189 = 0 + 194 = 0 + 247 = 0 + 252 = 0 + 273 = 0 + 282 = 0 + 335 = 0 + 344 = 0 + 423 = 0 + 428 = 0 + 475 = 0 + 480 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=2 + 1 = 0 + 32767 = 0 + 9 = 0 + 18 = 0 + 87 = 0 + 96 = 0 + 185 = 0 + 189 = 0 + 194 = 0 + 247 = 0 + 252 = 0 + 273 = 0 + 282 = 0 + 335 = 0 + 344 = 0 + 423 = 0 + 428 = 0 + 475 = 0 + 480 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(3)-FE_Q<2>(2)^2-FE_Q<2>(3)], case=3 + 1 = 0 + 32767 = 0 + 9 = 0 + 18 = 0 + 87 = 0 + 96 = 0 + 185 = 0 + 189 = 0 + 194 = 0 + 247 = 0 + 252 = 0 + 273 = 0 + 282 = 0 + 335 = 0 + 344 = 0 + 423 = 0 + 428 = 0 + 475 = 0 + 480 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=0 + 1 = 0 + 9 = 0 + 19 = 0 + 20 = 0 + 147 = 0 + 157 = 0 + 158 = 0 + 489 = 0 + 499 = 0 + 500 = 0 + 603 = 0 + 613 = 0 + 614 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=1 + 1 = 0 + 9 = 0 + 19 = 0 + 20 = 0 + 147 = 0 + 157 = 0 + 158 = 0 + 325 = 0 + 329 = 0 + 335 = 0 + 336 = 0 + 439 = 0 + 445 = 0 + 446 = 0 + 489 = 0 + 499 = 0 + 500 = 0 + 603 = 0 + 613 = 0 + 614 = 0 + 767 = 0 + 773 = 0 + 774 = 0 + 867 = 0 + 873 = 0 + 874 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=2 + 1 = 0 + 32767 = 0 + 9 = 0 + 19 = 0 + 20 = 0 + 147 = 0 + 157 = 0 + 158 = 0 + 325 = 0 + 329 = 0 + 335 = 0 + 336 = 0 + 439 = 0 + 445 = 0 + 446 = 0 + 489 = 0 + 499 = 0 + 500 = 0 + 603 = 0 + 613 = 0 + 614 = 0 + 767 = 0 + 773 = 0 + 774 = 0 + 867 = 0 + 873 = 0 + 874 = 0 +DEAL::FE=FESystem<2>[FE_Q<2>(4)-FE_Q<2>(3)^2-FE_Q<2>(4)], case=3 + 1 = 0 + 32767 = 0 + 9 = 0 + 19 = 0 + 20 = 0 + 147 = 0 + 157 = 0 + 158 = 0 + 325 = 0 + 329 = 0 + 335 = 0 + 336 = 0 + 439 = 0 + 445 = 0 + 446 = 0 + 489 = 0 + 499 = 0 + 500 = 0 + 603 = 0 + 613 = 0 + 614 = 0 + 767 = 0 + 773 = 0 + 774 = 0 + 867 = 0 + 873 = 0 + 874 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=0 + 1 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 127 = 0 + 137 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 586 = 0 + 596 = 0 + 664 = 0 + 674 = 0 + 742 = 0 + 791 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1173 = 0 + 1241 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1633 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=1 + 1 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 127 = 0 + 137 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 380 = 0 + 385 = 0 + 390 = 0 + 395 = 0 + 458 = 0 + 463 = 0 + 518 = 0 + 523 = 0 + 567 = 0 + 586 = 0 + 596 = 0 + 664 = 0 + 674 = 0 + 742 = 0 + 791 = 0 + 870 = 0 + 875 = 0 + 930 = 0 + 935 = 0 + 979 = 0 + 1017 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1173 = 0 + 1241 = 0 + 1320 = 0 + 1325 = 0 + 1369 = 0 + 1418 = 0 + 1423 = 0 + 1467 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1633 = 0 + 1701 = 0 + 1739 = 0 + 1777 = 0 + 1815 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=2 + 1 = 0 + 32767 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 127 = 0 + 137 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 380 = 0 + 385 = 0 + 390 = 0 + 395 = 0 + 458 = 0 + 463 = 0 + 518 = 0 + 523 = 0 + 567 = 0 + 586 = 0 + 596 = 0 + 664 = 0 + 674 = 0 + 742 = 0 + 791 = 0 + 870 = 0 + 875 = 0 + 930 = 0 + 935 = 0 + 979 = 0 + 1017 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1173 = 0 + 1241 = 0 + 1320 = 0 + 1325 = 0 + 1369 = 0 + 1418 = 0 + 1423 = 0 + 1467 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1633 = 0 + 1701 = 0 + 1739 = 0 + 1777 = 0 + 1815 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=3 + 1 = 0 + 32767 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 127 = 0 + 137 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 380 = 0 + 385 = 0 + 390 = 0 + 395 = 0 + 458 = 0 + 463 = 0 + 518 = 0 + 523 = 0 + 567 = 0 + 586 = 0 + 596 = 0 + 664 = 0 + 674 = 0 + 742 = 0 + 791 = 0 + 870 = 0 + 875 = 0 + 930 = 0 + 935 = 0 + 979 = 0 + 1017 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1173 = 0 + 1241 = 0 + 1320 = 0 + 1325 = 0 + 1369 = 0 + 1418 = 0 + 1423 = 0 + 1467 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1633 = 0 + 1701 = 0 + 1739 = 0 + 1777 = 0 + 1815 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=4 + 1 = 0 + 32767 = 0 + 2 = 0 + 7 = 0 + 11 = 0 + 12 = 0 + 17 = 0 + 21 = 0 + 31 = 0 + 80 = 0 + 85 = 0 + 127 = 0 + 128 = 0 + 133 = 0 + 137 = 0 + 176 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 333 = 0 + 338 = 0 + 380 = 0 + 381 = 0 + 385 = 0 + 386 = 0 + 390 = 0 + 395 = 0 + 429 = 0 + 458 = 0 + 459 = 0 + 463 = 0 + 518 = 0 + 523 = 0 + 567 = 0 + 586 = 0 + 587 = 0 + 592 = 0 + 596 = 0 + 635 = 0 + 664 = 0 + 665 = 0 + 670 = 0 + 674 = 0 + 713 = 0 + 742 = 0 + 791 = 0 + 841 = 0 + 870 = 0 + 871 = 0 + 875 = 0 + 901 = 0 + 930 = 0 + 931 = 0 + 935 = 0 + 979 = 0 + 1017 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1173 = 0 + 1241 = 0 + 1320 = 0 + 1325 = 0 + 1369 = 0 + 1418 = 0 + 1423 = 0 + 1467 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1633 = 0 + 1701 = 0 + 1739 = 0 + 1777 = 0 + 1815 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(2)-FE_Q<3>(1)^3-FE_Q<3>(2)], case=5 + 1 = 0 + 32767 = 0 + 2 = 0 + 7 = 0 + 11 = 0 + 12 = 0 + 17 = 0 + 21 = 0 + 31 = 0 + 80 = 0 + 85 = 0 + 127 = 0 + 128 = 0 + 133 = 0 + 137 = 0 + 176 = 0 + 205 = 0 + 215 = 0 + 283 = 0 + 333 = 0 + 338 = 0 + 380 = 0 + 381 = 0 + 385 = 0 + 386 = 0 + 390 = 0 + 395 = 0 + 429 = 0 + 458 = 0 + 459 = 0 + 463 = 0 + 518 = 0 + 523 = 0 + 567 = 0 + 586 = 0 + 587 = 0 + 592 = 0 + 596 = 0 + 635 = 0 + 664 = 0 + 665 = 0 + 670 = 0 + 674 = 0 + 713 = 0 + 742 = 0 + 791 = 0 + 841 = 0 + 870 = 0 + 871 = 0 + 875 = 0 + 901 = 0 + 930 = 0 + 931 = 0 + 935 = 0 + 979 = 0 + 1017 = 0 + 1036 = 0 + 1046 = 0 + 1114 = 0 + 1163 = 0 + 1164 = 0 + 1169 = 0 + 1173 = 0 + 1174 = 0 + 1179 = 0 + 1212 = 0 + 1217 = 0 + 1241 = 0 + 1242 = 0 + 1247 = 0 + 1272 = 0 + 1320 = 0 + 1325 = 0 + 1369 = 0 + 1389 = 0 + 1394 = 0 + 1418 = 0 + 1419 = 0 + 1423 = 0 + 1424 = 0 + 1449 = 0 + 1467 = 0 + 1468 = 0 + 1486 = 0 + 1535 = 0 + 1584 = 0 + 1585 = 0 + 1590 = 0 + 1615 = 0 + 1633 = 0 + 1634 = 0 + 1639 = 0 + 1664 = 0 + 1701 = 0 + 1739 = 0 + 1759 = 0 + 1777 = 0 + 1778 = 0 + 1797 = 0 + 1815 = 0 + 1816 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=0 + 1 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 42 = 0 + 70 = 0 + 98 = 0 + 112 = 0 + 128 = 0 + 360 = 0 + 370 = 0 + 381 = 0 + 402 = 0 + 423 = 0 + 439 = 0 + 618 = 0 + 628 = 0 + 639 = 0 + 667 = 0 + 681 = 0 + 697 = 0 + 876 = 0 + 887 = 0 + 908 = 0 + 924 = 0 + 1950 = 0 + 1960 = 0 + 1971 = 0 + 1992 = 0 + 2013 = 0 + 2029 = 0 + 2208 = 0 + 2218 = 0 + 2229 = 0 + 2250 = 0 + 2271 = 0 + 2287 = 0 + 2466 = 0 + 2477 = 0 + 2498 = 0 + 2514 = 0 + 2652 = 0 + 2663 = 0 + 2684 = 0 + 2700 = 0 + 3582 = 0 + 3592 = 0 + 3603 = 0 + 3631 = 0 + 3645 = 0 + 3661 = 0 + 3840 = 0 + 3851 = 0 + 3872 = 0 + 3888 = 0 + 4026 = 0 + 4036 = 0 + 4047 = 0 + 4075 = 0 + 4089 = 0 + 4105 = 0 + 4284 = 0 + 4295 = 0 + 4316 = 0 + 4332 = 0 + 5214 = 0 + 5225 = 0 + 5246 = 0 + 5262 = 0 + 5400 = 0 + 5411 = 0 + 5432 = 0 + 5448 = 0 + 5586 = 0 + 5597 = 0 + 5618 = 0 + 5634 = 0 + 5772 = 0 + 5783 = 0 + 5804 = 0 + 5820 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=1 + 1 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 42 = 0 + 70 = 0 + 98 = 0 + 112 = 0 + 128 = 0 + 360 = 0 + 370 = 0 + 381 = 0 + 402 = 0 + 423 = 0 + 439 = 0 + 618 = 0 + 628 = 0 + 639 = 0 + 667 = 0 + 681 = 0 + 697 = 0 + 876 = 0 + 887 = 0 + 908 = 0 + 924 = 0 + 1212 = 0 + 1217 = 0 + 1222 = 0 + 1227 = 0 + 1233 = 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0 + 4955 = 0 + 4961 = 0 + 4982 = 0 + 4989 = 0 + 4998 = 0 + 5136 = 0 + 5142 = 0 + 5156 = 0 + 5165 = 0 + 5214 = 0 + 5225 = 0 + 5246 = 0 + 5262 = 0 + 5400 = 0 + 5411 = 0 + 5432 = 0 + 5448 = 0 + 5586 = 0 + 5597 = 0 + 5618 = 0 + 5634 = 0 + 5772 = 0 + 5783 = 0 + 5804 = 0 + 5820 = 0 + 6036 = 0 + 6042 = 0 + 6056 = 0 + 6065 = 0 + 6192 = 0 + 6198 = 0 + 6212 = 0 + 6221 = 0 + 6348 = 0 + 6354 = 0 + 6368 = 0 + 6377 = 0 + 6504 = 0 + 6510 = 0 + 6524 = 0 + 6533 = 0 +DEAL::FE=FESystem<3>[FE_Q<3>(3)-FE_Q<3>(2)^3-FE_Q<3>(3)], case=2 + 1 = 0 + 0 = 0 + 11 = 0 + 21 = 0 + 31 = 0 + 42 = 0 + 70 = 0 + 98 = 0 + 112 = 0 + 128 = 0 + 360 = 0 + 370 = 0 + 381 = 0 + 402 = 0 + 423 = 0 + 439 = 0 + 618 = 0 + 628 = 0 + 639 = 0 + 667 = 0 + 681 = 0 + 697 = 0 + 876 = 0 + 887 = 0 + 908 = 0 + 924 = 0 + 1212 = 0 + 1217 = 0 + 1222 = 0 + 1227 = 0 + 1233 = 0 + 1254 = 0 + 1275 = 0 + 1282 = 0 + 1291 = 0 + 1470 = 0 + 1475 = 0 + 1481 = 0 + 1495 = 0 + 1509 = 0 + 1518 = 0 + 1686 = 0 + 1691 = 0 + 1697 = 0 + 1718 = 0 + 1725 = 0 + 1734 = 0 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