+
+
+
+
+
+// Nonparametric version of P1 Nonconforming FE
+class FE_P1NCNonparametric : public FiniteElement<2,2>
+{
+private:
+
+
+ static
+ std::vector<ComponentMask>
+ get_nonzero_component();
+
+
+ static
+ std::vector<unsigned int>
+ get_dpo_vector ();
+
+
+
+ virtual FiniteElement<2,2>::InternalDataBase *
+ get_data (const UpdateFlags update_flags,
+ const Mapping<2,2> &,
+ const Quadrature<2> &) const ;
+
+
+
+
+ virtual
+ void
+ fill_fe_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const Quadrature<2> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data,
+ const CellSimilarity::Similarity cell_similarity) const;
+
+
+
+
+ virtual
+ void
+ fill_fe_face_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const Quadrature<1> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const;
+
+
+
+
+ virtual
+ void
+ fill_fe_subface_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const unsigned int sub_no,
+ const Quadrature<1> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const;
+
+
+
+public:
+ FE_P1NCNonparametric() ;
+
+ virtual std::string get_name () const ;
+
+ virtual UpdateFlags update_once (const UpdateFlags flags) const ;
+
+ virtual UpdateFlags update_each (const UpdateFlags flags) const ;
+
+ virtual FiniteElement<2,2> *clone () const ;
+
+ virtual ~FE_P1NCNonparametric ();
+
+
+protected:
+
+ void initialize_constraints () ;
+
+};
+
+
+
+
/** @}*/
DEAL_II_NAMESPACE_CLOSE
+
+
+
+
+
+// FE_P1NCNonparametric
+
+std::vector<ComponentMask>
+FE_P1NCNonparametric::get_nonzero_component()
+{
+ const unsigned int dofs_per_cell = 4;
+ std::vector<ComponentMask> masks (dofs_per_cell);
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ masks[i] = ComponentMask(1,true);
+ return masks;
+}
+
+
+std::vector<unsigned int>
+FE_P1NCNonparametric::get_dpo_vector ()
+{
+ std::vector<unsigned int> dpo(3);
+ dpo[0] = 1; // dofs per object: vertex
+ dpo[1] = 0; // line
+ dpo[2] = 0; // quad
+ return dpo;
+}
+
+
+FiniteElement<2,2>::InternalDataBase *
+FE_P1NCNonparametric::get_data (const UpdateFlags update_flags,
+ const Mapping<2,2> &,
+ const Quadrature<2> &) const
+{
+ FiniteElement<2,2>::InternalDataBase *data = new FiniteElement<2,2>::InternalDataBase;
+
+ data->update_once = update_once(update_flags);
+ data->update_each = update_each(update_flags);
+ data->update_flags = data->update_once | data->update_each;
+
+ return data;
+
+
+
+
+}
+
+
+
+void
+FE_P1NCNonparametric::fill_fe_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const Quadrature<2> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data,
+ const CellSimilarity::Similarity cell_similarity) const
+
+{
+ const UpdateFlags flags(fe_internal.current_update_flags()) ;
+
+ const unsigned int n_q_points = mapping_data.quadrature_points.size();
+
+ std::vector<double> values(flags & update_values ? this->dofs_per_cell : 0);
+ std::vector<Tensor<1,2> > grads(flags & update_gradients ? this->dofs_per_cell : 0);
+
+
+
+ // edge midpoints
+ std::vector<Point<2> > mpt(4) ;
+
+ mpt[0](0) = (cell->vertex(0)(0) + cell->vertex(2)(0))/2.0 ;
+ mpt[0](1) = (cell->vertex(0)(1) + cell->vertex(2)(1))/2.0 ;
+
+ mpt[1](0) = (cell->vertex(1)(0) + cell->vertex(3)(0))/2.0 ;
+ mpt[1](1) = (cell->vertex(1)(1) + cell->vertex(3)(1))/2.0 ;
+
+ mpt[2](0) = (cell->vertex(0)(0) + cell->vertex(1)(0))/2.0 ;
+ mpt[2](1) = (cell->vertex(0)(1) + cell->vertex(1)(1))/2.0 ;
+
+ mpt[3](0) = (cell->vertex(2)(0) + cell->vertex(3)(0))/2.0 ;
+ mpt[3](1) = (cell->vertex(2)(1) + cell->vertex(3)(1))/2.0 ;
+
+ // center point
+ Point<2> cpt ;
+ cpt(0) = (mpt[0](0) + mpt[1](0) + mpt[2](0) + mpt[3](0))/4.0 ;
+ cpt(1) = (mpt[0](1) + mpt[1](1) + mpt[2](1) + mpt[3](1))/4.0 ;
+
+
+ // basis functions with a half value: phi(x,y) = ax + by + c
+ std::vector<double> a(4), b(4), c(4) ;
+ double det ;
+
+ det = (mpt[0](0)-mpt[1](0))*(mpt[2](1)-mpt[3](1)) - (mpt[2](0)-mpt[3](0))*(mpt[0](1)-mpt[1](1)) ;
+
+ a[0] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ;
+ a[1] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(0.5))/det ;
+ a[2] = ((mpt[2](1)-mpt[3](1))*(0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ;
+ a[3] = ((mpt[2](1)-mpt[3](1))*(-0.5) -(mpt[0](1)-mpt[1](1))*(-0.5))/det ;
+
+ b[0] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ;
+ b[1] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(0.5))/det ;
+ b[2] = (-(mpt[2](0)-mpt[3](0))*(0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ;
+ b[3] = (-(mpt[2](0)-mpt[3](0))*(-0.5) +(mpt[0](0)-mpt[1](0))*(-0.5))/det ;
+
+ c[0] = 0.25 - cpt(0)*a[0] - cpt(1)*b[0] ;
+ c[1] = 0.25 - cpt(0)*a[1] - cpt(1)*b[1] ;
+ c[2] = 0.25 - cpt(0)*a[2] - cpt(1)*b[2] ;
+ c[3] = 0.25 - cpt(0)*a[3] - cpt(1)*b[3] ;
+
+
+
+ // compute basis functions
+ if (flags & (update_values | update_gradients))
+ for (unsigned int i=0; i<n_q_points; ++i)
+ {
+ for (unsigned int k=0; k<this->dofs_per_cell; ++k)
+ {
+ if (flags & update_values)
+ {
+ values[k] = a[k]*mapping_data.quadrature_points[i](0) + b[k]*mapping_data.quadrature_points[i](1) + c[k] ;
+ output_data.shape_values[k][i] = values[k];
+ }
+
+ if (flags & update_gradients)
+ {
+ grads[k][0] = a[k] ;
+ grads[k][1] = b[k] ;
+ output_data.shape_gradients[k][i] = grads[k];
+ }
+ }
+
+ }
+
+ // When this function is called for the graphic out,
+ // MappingRelatedData does not work properly.
+ // In this case, the quadrature points on the real cell is computed in manual sense, using 'mapping' and 'quadrature'.
+ // This is a temporary solution. It needs to be fixed fundamentally.
+ if (n_q_points==0)
+ {
+ for (unsigned int i=0; i<quadrature.size(); ++i)
+ for (unsigned int k=0; k<this->dofs_per_cell; ++k)
+ {
+ Point<2> realquadrature ;
+
+ realquadrature = mapping.transform_unit_to_real_cell(cell, quadrature.point(i)) ;
+ values[k] = a[k]*realquadrature(0) + b[k]*realquadrature(1) + c[k] ;
+ output_data.shape_values[k][i] = values[k];
+
+ }
+ }
+
+}
+
+
+void
+FE_P1NCNonparametric::fill_fe_face_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const Quadrature<1> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const
+
+
+{}
+
+
+
+
+
+
+void
+FE_P1NCNonparametric::fill_fe_subface_values (const Mapping<2,2> &mapping,
+ const Triangulation<2,2>::cell_iterator &cell,
+ const unsigned int face_no,
+ const unsigned int sub_no,
+ const Quadrature<1> &quadrature,
+ const Mapping<2,2>::InternalDataBase &mapping_internal,
+ const FiniteElement<2,2>::InternalDataBase &fe_internal,
+ const internal::FEValues::MappingRelatedData<2,2> &mapping_data,
+ internal::FEValues::FiniteElementRelatedData<2,2> &output_data) const
+
+{}
+
+
+
+FE_P1NCNonparametric::FE_P1NCNonparametric()
+ :
+ FiniteElement<2,2>(FiniteElementData<2>(get_dpo_vector(),
+ 1,
+ 1,
+ FiniteElementData<2>::L2,
+ numbers::invalid_unsigned_int),
+ std::vector<bool> (1, false),
+ get_nonzero_component())
+{
+
+ // face support points: 2 end vertices
+ unit_face_support_points.resize(2);
+ unit_face_support_points[0][0] = 0.0 ;
+ unit_face_support_points[1][0] = 1.0 ;
+
+
+ // CONSTRAINTS MATRIX INITIALIZATION
+ initialize_constraints () ;
+}
+
+
+
+std::string FE_P1NCNonparametric::get_name () const
+{
+ return "FE_P1NCNonparametric";
+}
+
+
+
+UpdateFlags FE_P1NCNonparametric::update_once (const UpdateFlags flags) const
+{
+ return (update_default );
+
+}
+
+UpdateFlags FE_P1NCNonparametric::update_each (const UpdateFlags flags) const
+{
+ UpdateFlags out = (update_default | (flags & update_values) | (flags & update_quadrature_points)) ;
+
+ if (flags & update_gradients)
+ out |= update_gradients | update_covariant_transformation | update_JxW_values;
+ if (flags & update_cell_normal_vectors)
+ out |= update_cell_normal_vectors | update_JxW_values;
+
+ return out;
+}
+
+
+FiniteElement<2,2> *FE_P1NCNonparametric::clone () const
+{
+ return new FE_P1NCNonparametric(*this);
+}
+
+FE_P1NCNonparametric::~FE_P1NCNonparametric () {}
+
+
+
+
+void FE_P1NCNonparametric::initialize_constraints ()
+{
+
+ std::vector<Point<1> > constraint_points;
+
+ // Add midpoint
+ constraint_points.push_back (Point<1> (0.5));
+
+ // coefficient relation between children and mother
+ interface_constraints
+ .TableBase<2,double>::reinit (interface_constraints_size());
+
+
+ interface_constraints(0,0) = 0.5 ;
+ interface_constraints(0,1) = 0.5 ;
+
+}
+
+
+
+
+
DEAL_II_NAMESPACE_CLOSE