feat3/space_2cro__rav__ran__tur_2evaluator_8hpp_source.html

// FEAT3: Finite Element Analysis Toolbox, Version 3

// Copyright (C) 2010 by Stefan Turek & the FEAT group

// FEAT3 is released under the GNU General Public License version 3,

// see the file 'copyright.txt' in the top level directory for details.


#pragma once


// includes, FEAT

#include <kernel/space/parametric_evaluator.hpp>


namespace FEAT

{

  namespace Space

  {

    namespace CroRavRanTur

    {

      static constexpr SpaceTags ref_caps = SpaceTags::ref_value | SpaceTags::ref_grad;


      template<

        typename Space_,

        typename TrafoEvaluator_,

        typename SpaceEvalTraits_,

        typename Shape_ = typename Space_::ShapeType>

      class Evaluator DOXY({});


      template<

        typename Space_,

        typename TrafoEvaluator_,

        typename SpaceEvalTraits_>

      class Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex<2> > :

        public ParametricEvaluator<

          Evaluator<

            Space_,

            TrafoEvaluator_,

            SpaceEvalTraits_,

            Shape::Simplex<2> >,

          TrafoEvaluator_,

          SpaceEvalTraits_,

          ref_caps>

      {

      public:

        typedef ParametricEvaluator<Evaluator, TrafoEvaluator_, SpaceEvalTraits_, ref_caps> BaseClass;


        typedef Space_ SpaceType;


        typedef SpaceEvalTraits_ SpaceEvalTraits;


        typedef typename SpaceEvalTraits::EvalPolicy EvalPolicy;


        typedef typename EvalPolicy::DomainPointType DomainPointType;


        typedef typename SpaceEvalTraits::DataType DataType;


      public:

        explicit Evaluator(const SpaceType& DOXY(space))

        {

        }


        int get_num_local_dofs() const

        {

          return 3;

        }


        template<typename EvalData_>

        void eval_ref_values(

          EvalData_& data,

          const DomainPointType& point) const

        {

          data.phi[0].ref_value = DataType(2) * (point[0] + point[1]) - DataType(1);

          data.phi[1].ref_value = DataType(1) - DataType(2)*point[0];

          data.phi[2].ref_value = DataType(1) - DataType(2)*point[1];

        }


        template<typename EvalData_>

        void eval_ref_gradients(

          EvalData_& data,

          const DomainPointType& DOXY(point)) const

        {

          data.phi[0].ref_grad[0] = DataType(2);

          data.phi[0].ref_grad[1] = DataType(2);

          data.phi[1].ref_grad[0] = -DataType(2);

          data.phi[1].ref_grad[1] = DataType(0);

          data.phi[2].ref_grad[0] = DataType(0);

          data.phi[2].ref_grad[1] = -DataType(2);

        }

      }; // class Evaluator<...,Simplex<2>>


      template<

        typename Space_,

        typename TrafoEvaluator_,

        typename SpaceEvalTraits_>

      class Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex<3> > :

        public ParametricEvaluator<

        Evaluator<

        Space_,

        TrafoEvaluator_,

        SpaceEvalTraits_,

        Shape::Simplex<3> >,

        TrafoEvaluator_,

        SpaceEvalTraits_,

        ref_caps>

      {

      public:

        typedef ParametricEvaluator<Evaluator, TrafoEvaluator_, SpaceEvalTraits_, ref_caps> BaseClass;


        typedef Space_ SpaceType;


        typedef SpaceEvalTraits_ SpaceEvalTraits;


        typedef typename SpaceEvalTraits::EvalPolicy EvalPolicy;


        typedef typename EvalPolicy::DomainPointType DomainPointType;


        typedef typename SpaceEvalTraits::DataType DataType;


      public:

        explicit Evaluator(const SpaceType& DOXY(space))

        {

        }


        int get_num_local_dofs() const

        {

          return 4;

        }


        template<typename EvalData_>

        void eval_ref_values(

          EvalData_& data,

          const DomainPointType& point) const

        {

          data.phi[0].ref_value = DataType(3) * (point[0] + point[1] + point[2]) - DataType(2);

          data.phi[1].ref_value = DataType(1) - DataType(3)*point[0];

          data.phi[2].ref_value = DataType(1) - DataType(3)*point[1];

          data.phi[3].ref_value = DataType(1) - DataType(3)*point[2];

        }


        template<typename EvalData_>

        void eval_ref_gradients(

          EvalData_& data,

          const DomainPointType& DOXY(point)) const

        {

          data.phi[0].ref_grad[0] = DataType(3);

          data.phi[0].ref_grad[1] = DataType(3);

          data.phi[0].ref_grad[2] = DataType(3);

          data.phi[1].ref_grad[0] = -DataType(3);

          data.phi[1].ref_grad[1] = DataType(0);

          data.phi[1].ref_grad[2] = DataType(0);

          data.phi[2].ref_grad[0] = DataType(0);

          data.phi[2].ref_grad[1] = -DataType(3);

          data.phi[2].ref_grad[2] = DataType(0);

          data.phi[3].ref_grad[0] = DataType(0);

          data.phi[3].ref_grad[1] = DataType(0);

          data.phi[3].ref_grad[2] = -DataType(3);

        }

      }; // class Evaluator<...,Simplex<3>>


      template<

        typename Space_,

        typename TrafoEvaluator_,

        typename SpaceEvalTraits_>

      class Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral> :

        public EvaluatorBase<

          Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral>,

          TrafoEvaluator_,

          SpaceEvalTraits_>

      {

      public:

        typedef EvaluatorBase<Evaluator, TrafoEvaluator_, SpaceEvalTraits_> BaseClass;


        typedef Space_ SpaceType;


        typedef SpaceEvalTraits_ SpaceEvalTraits;


        typedef TrafoEvaluator_ TrafoEvaluator;


        typedef typename TrafoEvaluator::EvalTraits TrafoEvalTraits;


        typedef typename TrafoEvaluator::TrafoType TrafoType;


        typedef typename TrafoType::MeshType MeshType;


        typedef typename MeshType::template IndexSet<2,1>::Type FacetIndexSetType;


        typedef typename SpaceEvalTraits::DataType DataType;


        typedef typename SpaceEvalTraits::EvalPolicy EvalPolicy;


        typedef typename EvalPolicy::DomainPointType DomainPointType;

        typedef typename EvalPolicy::ImagePointType ImagePointType;


        typedef typename EvalPolicy::JacobianMatrixType JacobianMatrixType;

        typedef typename EvalPolicy::JacobianInverseType JacobianInverseType;


        static constexpr SpaceTags eval_caps = SpaceTags::value | SpaceTags::grad;


        template<SpaceTags cfg_>

        struct ConfigTraits

        {

          static constexpr SpaceTags config = cfg_;


          static constexpr TrafoTags trafo_config = TrafoTags::img_point;


          typedef Space::EvalData<SpaceEvalTraits, config> EvalDataType;

        };


      protected:

        static constexpr TrafoTags inv_lin_trafo_config = TrafoTags::dom_point | TrafoTags::img_point | TrafoTags::jac_inv;


        typedef typename TrafoEvaluator::template ConfigTraits<inv_lin_trafo_config>::EvalDataType InvLinTrafoData;


        typedef typename TrafoType::template Evaluator<Shape::Hypercube<1>, DataType>::Type FacetTrafoEvaluator;

        typedef typename FacetTrafoEvaluator::EvalTraits FacetEvalTraits;


        static constexpr TrafoTags facet_trafo_config = TrafoTags::img_point | TrafoTags::jac_det;


        typedef typename FacetTrafoEvaluator::template ConfigTraits<facet_trafo_config>::EvalDataType FacetTrafoData;


        typedef Tiny::Matrix<DataType, 4, 4> CoeffMatrixType;


        JacobianInverseType _inv_lin_mat;


        // inverse linearized trafo vector

        ImagePointType _inv_lin_vec;


        CoeffMatrixType _coeff_mat;


        void _build_inv_lin_trafo(const TrafoEvaluator& trafo_eval)

        {

          // create a domain point in the barycentre of the cell

          DomainPointType dom_point(DataType(0));


          // create the trafo data

          InvLinTrafoData trafo_data;

          trafo_eval(trafo_data, dom_point);


          // store inverse trafo linearization

          _inv_lin_mat = trafo_data.jac_inv;

          _inv_lin_vec = trafo_data.img_point;

        }


        void _build_coeff_matrix(const TrafoEvaluator& trafo_eval)

        {

          // fetch the trafo

          const TrafoType& trafo = trafo_eval.get_trafo();


          // fetch the mesh

          const MeshType& mesh = trafo.get_mesh();


          // fetch the facet-index-set of the mesh

          const FacetIndexSetType& facet_index_set = mesh.template get_index_set<2,1>();


          // fetch the cell index of the currently active cell

          const Index cell = trafo_eval.get_cell_index();


          // create a nodal matrix

          CoeffMatrixType _nodal_mat(DataType(0));


          // create a facet trafo evaluator

          FacetTrafoEvaluator facet_eval(trafo);


          // create facet evaluation data

          FacetTrafoData facet_data;


          // define 2-point Gauss cubature point coordinate

          const DataType g = Math::sqrt(DataType(1) / DataType(3));

          const typename FacetEvalTraits::DomainPointType g1(-g), g2(+g);

          DomainPointType q1, q2;


          // loop over all 4 edges of the quad

          for(int i(0); i < 4; ++i)

          {

            // initialize facet evaluator

            facet_eval.prepare(Index(facet_index_set(cell, i)));


            // map first cubature point

            facet_eval(facet_data, g1);

            DataType w1(facet_data.jac_det);

            q1.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // map second cubature point

            facet_eval(facet_data, g2);

            DataType w2(facet_data.jac_det);

            q2.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // release facet evaluator

            facet_eval.finish();


            // compute reciprocal edge length

            DataType v = DataType(1) / (w1 + w2);


            // evaluate node functionals

            _nodal_mat(0,i) = DataType(1); // = v*(w1 + w2)

            _nodal_mat(1,i) = v*(w1*q1[0] + w2*q2[0]);

            _nodal_mat(2,i) = v*(w1*q1[1] + w2*q2[1]);

            _nodal_mat(3,i) = v*(w1*((q1[0]+q1[1])*(q1[0]-q1[1])) + w2*((q2[0]+q2[1])*(q2[0]-q2[1])));

          }


          // invert nodal matrix to obtain coefficient matrix

          _coeff_mat.set_inverse(_nodal_mat);

        }


      public:

        explicit Evaluator(const SpaceType& DOXY(space))

        {

        }


        virtual ~Evaluator()

        {

        }


        int get_num_local_dofs() const

        {

          return 4;

        }


        void prepare(const TrafoEvaluator& trafo_eval)

        {

          // prepare inverse linearized trafo

          _build_inv_lin_trafo(trafo_eval);


          // build coefficient matrix

          _build_coeff_matrix(trafo_eval);

        }


        template<SpaceTags space_cfg_, TrafoTags trafo_cfg_>

        void eval_values(

          EvalData<SpaceEvalTraits, space_cfg_>& data,

          const Trafo::EvalData<TrafoEvalTraits, trafo_cfg_>& trafo_data) const

        {

          // transform image point

          DomainPointType pt;

          pt.set_mat_vec_mult(_inv_lin_mat, trafo_data.img_point - _inv_lin_vec);


          // "evaluate" monomials

          DataType x(pt[0]);

          DataType y(pt[1]);

          DataType r((x+y)*(x-y));


          // loop over all basis functions

          for(int i(0); i < 4; ++i)

          {

            data.phi[i].value = _coeff_mat(i,0) + _coeff_mat(i,1)*x + _coeff_mat(i,2)*y + _coeff_mat(i,3)*r;

          }

        }


        template<SpaceTags space_cfg_, TrafoTags trafo_cfg_>

        void eval_gradients(

          EvalData<SpaceEvalTraits, space_cfg_>& data,

          const Trafo::EvalData<TrafoEvalTraits, trafo_cfg_>& trafo_data) const

        {

          // transform image point to local coordinate system

          DomainPointType pt, loc_grad;

          pt.set_mat_vec_mult(_inv_lin_mat, trafo_data.img_point - _inv_lin_vec);


          // loop over all basis functions

          for(int i(0); i < 4; ++i)

          {

            // calculate local gradients

            loc_grad(0) = _coeff_mat(i,1) + DataType(2) * _coeff_mat(i,3) * pt[0];

            loc_grad(1) = _coeff_mat(i,2) - DataType(2) * _coeff_mat(i,3) * pt[1];


            // multiply by transpose inverse linearized trafo matrix for chain rule

            data.phi[i].grad.set_vec_mat_mult(loc_grad, _inv_lin_mat);

          }

        }

      }; // Evaluator<..., Shape::Quadrilateral>


      template<

        typename Space_,

        typename TrafoEvaluator_,

        typename SpaceEvalTraits_>

      class Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron> :

        public EvaluatorBase<

          Evaluator<Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron>,

          TrafoEvaluator_,

          SpaceEvalTraits_>

      {

      public:

        typedef EvaluatorBase<Evaluator, TrafoEvaluator_, SpaceEvalTraits_> BaseClass;


        typedef Space_ SpaceType;


        typedef SpaceEvalTraits_ SpaceEvalTraits;


        typedef TrafoEvaluator_ TrafoEvaluator;


        typedef typename TrafoEvaluator::EvalTraits TrafoEvalTraits;


        typedef typename TrafoEvaluator::TrafoType TrafoType;


        typedef typename TrafoType::MeshType MeshType;


        typedef typename MeshType::template IndexSet<3,2>::Type FacetIndexSetType;


        typedef typename SpaceEvalTraits::DataType DataType;


        typedef typename SpaceEvalTraits::EvalPolicy EvalPolicy;


        typedef typename EvalPolicy::DomainPointType DomainPointType;

        typedef typename EvalPolicy::ImagePointType ImagePointType;


        typedef typename EvalPolicy::JacobianMatrixType JacobianMatrixType;

        typedef typename EvalPolicy::JacobianInverseType JacobianInverseType;


        static constexpr SpaceTags eval_caps = SpaceTags::value | SpaceTags::grad;


        template<SpaceTags cfg_>

        struct ConfigTraits

        {

          static constexpr SpaceTags config = cfg_;


          static constexpr TrafoTags trafo_config = TrafoTags::img_point;


          typedef Space::EvalData<SpaceEvalTraits, config> EvalDataType;

        };


      protected:

        static constexpr TrafoTags inv_lin_trafo_config = TrafoTags::dom_point | TrafoTags::img_point | TrafoTags::jac_inv;


        typedef typename TrafoEvaluator::template ConfigTraits<inv_lin_trafo_config>::EvalDataType InvLinTrafoData;


        typedef typename TrafoType::template Evaluator<Shape::Hypercube<2>, DataType>::Type FacetTrafoEvaluator;

        typedef typename FacetTrafoEvaluator::EvalTraits FacetEvalTraits;


        static constexpr TrafoTags facet_trafo_config = TrafoTags::img_point | TrafoTags::jac_det;


        typedef typename FacetTrafoEvaluator::template ConfigTraits<facet_trafo_config>::EvalDataType FacetTrafoData;


        typedef Tiny::Matrix<DataType, 6, 6> CoeffMatrixType;


        JacobianInverseType _inv_lin_mat;


        // inverse linearized trafo vector

        ImagePointType _inv_lin_vec;


        CoeffMatrixType _coeff_mat;


        void _build_inv_lin_trafo(const TrafoEvaluator& trafo_eval)

        {

          // create a domain point in the barycentre of the cell

          DomainPointType dom_point(DataType(0));


          // create the trafo data

          InvLinTrafoData trafo_data;

          trafo_eval(trafo_data, dom_point);


          // store inverse trafo linearization

          _inv_lin_mat = trafo_data.jac_inv;

          _inv_lin_vec = trafo_data.img_point;

        }


        void _build_coeff_matrix(const TrafoEvaluator& trafo_eval)

        {

          // fetch the trafo

          const TrafoType& trafo = trafo_eval.get_trafo();


          // fetch the mesh

          const MeshType& mesh = trafo.get_mesh();


          // fetch the facet-index-set of the mesh

          const FacetIndexSetType& facet_index_set = mesh.template get_index_set<3,2>();


          // fetch the cell index of the currently active cell

          const Index cell = trafo_eval.get_cell_index();


          // create a nodal matrix

          CoeffMatrixType _nodal_mat(DataType(0));


          // create a facet trafo evaluator

          FacetTrafoEvaluator facet_eval(trafo);


          // create facet evaluation data

          FacetTrafoData facet_data;


          // define 2-point Gauss cubature point coordinate

          const DataType g = Math::sqrt(DataType(1) / DataType(3));

          typename FacetEvalTraits::DomainPointType g1, g2, g3, g4;

          DomainPointType q1, q2, q3, q4;


          // set up cubature points

          g1[0] = g2[0] = -g;

          g3[0] = g4[0] = +g;

          g1[1] = g3[1] = -g;

          g2[1] = g4[1] = +g;


          // loop over all 6 faces of the hexa

          for(int i(0); i < 6; ++i)

          {

            // initialize facet evaluator

            facet_eval.prepare(Index(facet_index_set(cell, i)));


            // map first cubature point

            facet_eval(facet_data, g1);

            DataType w1(facet_data.jac_det);

            q1.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // map second cubature point

            facet_eval(facet_data, g2);

            DataType w2(facet_data.jac_det);

            q2.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // map third cubature point

            facet_eval(facet_data, g3);

            DataType w3(facet_data.jac_det);

            q3.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // map fourth cubature point

            facet_eval(facet_data, g4);

            DataType w4(facet_data.jac_det);

            q4.set_mat_vec_mult(_inv_lin_mat, facet_data.img_point - _inv_lin_vec);


            // release facet evaluator

            facet_eval.finish();


            // compute reciprocal quad area

            DataType v = DataType(1) / (w1 + w2 + w3 + w4);


            // evaluate node functionals

            _nodal_mat(0,i) = DataType(1); // = v*(w1 + w2 + w3 + w4)

            _nodal_mat(1,i) = v*(w1*q1[0] + w2*q2[0] + w3*q3[0] + w4*q4[0]);

            _nodal_mat(2,i) = v*(w1*q1[1] + w2*q2[1] + w3*q3[1] + w4*q4[1]);

            _nodal_mat(3,i) = v*(w1*q1[2] + w2*q2[2] + w3*q3[2] + w4*q4[2]);

            _nodal_mat(4,i) = v*( // x^2 - y^2

              w1*(q1[0] + q1[1])*(q1[0] - q1[1]) + w2*(q2[0] + q2[1])*(q2[0] - q2[1]) +

              w3*(q3[0] + q3[1])*(q3[0] - q3[1]) + w4*(q4[0] + q4[1])*(q4[0] - q4[1]));

            _nodal_mat(5,i) = v*( // y^2 - z^2

              w1*(q1[1] + q1[2])*(q1[1] - q1[2]) + w2*(q2[1] + q2[2])*(q2[1] - q2[2]) +

              w3*(q3[1] + q3[2])*(q3[1] - q3[2]) + w4*(q4[1] + q4[2])*(q4[1] - q4[2]));

          }


          // invert nodal matrix to obtain coefficient matrix

          _coeff_mat.set_inverse(_nodal_mat);

        }


      public:

        explicit Evaluator(const SpaceType& DOXY(space))

        {

        }


        virtual ~Evaluator()

        {

        }


        int get_num_local_dofs() const

        {

          return 6;

        }


        void prepare(const TrafoEvaluator& trafo_eval)

        {

          // prepare inverse linearized trafo

          _build_inv_lin_trafo(trafo_eval);


          // build coefficient matrix

          _build_coeff_matrix(trafo_eval);

        }


        template<SpaceTags space_cfg_, TrafoTags trafo_cfg_>

        void eval_values(

          EvalData<SpaceEvalTraits, space_cfg_>& data,

          const Trafo::EvalData<TrafoEvalTraits, trafo_cfg_>& trafo_data) const

        {

          // transform image point

          DomainPointType pt;

          pt.set_mat_vec_mult(_inv_lin_mat, trafo_data.img_point - _inv_lin_vec);


          // "evaluate" monomials

          DataType x(pt[0]);

          DataType y(pt[1]);

          DataType z(pt[2]);

          DataType rxy((x+y)*(x-y)); // = x^2 - y^2

          DataType ryz((y+z)*(y-z)); // = y^2 - z^2


          // loop over all basis functions

          for(int i(0); i < 6; ++i)

          {

            data.phi[i].value = _coeff_mat(i,0) + _coeff_mat(i,1)*x + _coeff_mat(i,2)*y + _coeff_mat(i,3)*z

                              + _coeff_mat(i,4)*rxy + _coeff_mat(i,5)*ryz;

          }

        }


        template<SpaceTags space_cfg_, TrafoTags trafo_cfg_>

        void eval_gradients(

          EvalData<SpaceEvalTraits, space_cfg_>& data,

          const Trafo::EvalData<TrafoEvalTraits, trafo_cfg_>& trafo_data) const

        {

          // transform image point to local coordinate system

          DomainPointType pt, loc_grad;

          pt.set_mat_vec_mult(_inv_lin_mat, trafo_data.img_point - _inv_lin_vec);


          // loop over all basis functions

          for(int i(0); i < 6; ++i)

          {

            // calculate local gradients

            loc_grad[0] = _coeff_mat(i,1) + DataType(2) * pt[0] * _coeff_mat(i,4);

            loc_grad[1] = _coeff_mat(i,2) + DataType(2) * pt[1] * (_coeff_mat(i,5) - _coeff_mat(i,4));

            loc_grad[2] = _coeff_mat(i,3) - DataType(2) * pt[2] * _coeff_mat(i,5);


            // multiply by transpose inverse linearized trafo matrix for chain rule

            data.phi[i].grad.set_vec_mat_mult(loc_grad, _inv_lin_mat);

          }

        }

      }; // Evaluator<..., Shape::Quadrilateral>

    } // namespace CroRavRanTur

  } // namespace Space

} // namespace FEAT

FEAT::Space::BasisData::value
EvalTraits_::BasisValueType value
basis function value object
Definition: eval_data.hpp:47

FEAT::Space::BasisData::grad
EvalTraits_::BasisGradientType grad
basis gradient object
Definition: eval_data.hpp:45

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::prepare
void prepare(const TrafoEvaluator &trafo_eval)
Prepares the evaluator for a given cell.
Definition: evaluator.hpp:459

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::EvalPolicy
SpaceEvalTraits::EvalPolicy EvalPolicy
evaluation policy
Definition: evaluator.hpp:293

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::DataType
SpaceEvalTraits::DataType DataType
data type
Definition: evaluator.hpp:290

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::TrafoType
TrafoEvaluator::TrafoType TrafoType
trafo type
Definition: evaluator.hpp:281

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::DomainPointType
EvalPolicy::DomainPointType DomainPointType
domain point type
Definition: evaluator.hpp:296

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::get_num_local_dofs
int get_num_local_dofs() const
Returns the number of local DOFs.
Definition: evaluator.hpp:448

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::TrafoEvaluator
TrafoEvaluator_ TrafoEvaluator
trafo evaluator type
Definition: evaluator.hpp:275

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::InvLinTrafoData
TrafoEvaluator::template ConfigTraits< inv_lin_trafo_config >::EvalDataType InvLinTrafoData
inverse linearized trafo data
Definition: evaluator.hpp:325

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_build_coeff_matrix
void _build_coeff_matrix(const TrafoEvaluator &trafo_eval)
computes the basis function coefficient matrix for the current cell
Definition: evaluator.hpp:365

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_coeff_mat
CoeffMatrixType _coeff_mat
basis function coefficient matrix
Definition: evaluator.hpp:348

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::eval_gradients
void eval_gradients(EvalData< SpaceEvalTraits, space_cfg_ > &data, const Trafo::EvalData< TrafoEvalTraits, trafo_cfg_ > &trafo_data) const
Definition: evaluator.hpp:492

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::MeshType
TrafoType::MeshType MeshType
mesh type
Definition: evaluator.hpp:284

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::SpaceType
Space_ SpaceType
space type
Definition: evaluator.hpp:269

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::CoeffMatrixType
Tiny::Matrix< DataType, 4, 4 > CoeffMatrixType
basis function coefficient matrix
Definition: evaluator.hpp:339

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::Evaluator
Evaluator(const SpaceType &space)
Constructor.
Definition: evaluator.hpp:433

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::ImagePointType
EvalPolicy::ImagePointType ImagePointType
image point type
Definition: evaluator.hpp:298

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::JacobianMatrixType
EvalPolicy::JacobianMatrixType JacobianMatrixType
jacobian matrix type
Definition: evaluator.hpp:301

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::FacetTrafoData
FacetTrafoEvaluator::template ConfigTraits< facet_trafo_config >::EvalDataType FacetTrafoData
facet trafo data
Definition: evaluator.hpp:336

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::FacetTrafoEvaluator
TrafoType::template Evaluator< Shape::Hypercube< 1 >, DataType >::Type FacetTrafoEvaluator
trafo evaluator for facets (=edges)
Definition: evaluator.hpp:328

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_inv_lin_mat
JacobianInverseType _inv_lin_mat
inverse linearized trafo matrix
Definition: evaluator.hpp:342

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::FacetIndexSetType
MeshType::template IndexSet< 2, 1 >::Type FacetIndexSetType
facet-index-set type
Definition: evaluator.hpp:287

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::TrafoEvalTraits
TrafoEvaluator::EvalTraits TrafoEvalTraits
trafo evaluator traits
Definition: evaluator.hpp:278

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::SpaceEvalTraits
SpaceEvalTraits_ SpaceEvalTraits
space evaluation traits
Definition: evaluator.hpp:272

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::~Evaluator
virtual ~Evaluator()
virtual destructor
Definition: evaluator.hpp:438

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::eval_values
void eval_values(EvalData< SpaceEvalTraits, space_cfg_ > &data, const Trafo::EvalData< TrafoEvalTraits, trafo_cfg_ > &trafo_data) const
Evaluates the basis function values on the real cell.
Definition: evaluator.hpp:470

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::FacetEvalTraits
FacetTrafoEvaluator::EvalTraits FacetEvalTraits
facet evaluation traits
Definition: evaluator.hpp:330

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::JacobianInverseType
EvalPolicy::JacobianInverseType JacobianInverseType
jacobian inverse matrix type
Definition: evaluator.hpp:303

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::BaseClass
EvaluatorBase< Evaluator, TrafoEvaluator_, SpaceEvalTraits_ > BaseClass
base-class typedef
Definition: evaluator.hpp:266

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::eval_ref_gradients
void eval_ref_gradients(EvalData_ &data, const DomainPointType &point) const
Evaluates the basis function gradients on the reference cell.
Definition: evaluator.hpp:230

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::SpaceType
Space_ SpaceType
space type
Definition: evaluator.hpp:164

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::BaseClass
ParametricEvaluator< Evaluator, TrafoEvaluator_, SpaceEvalTraits_, ref_caps > BaseClass
base-class typedef
Definition: evaluator.hpp:161

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::EvalPolicy
SpaceEvalTraits::EvalPolicy EvalPolicy
evaluation policy
Definition: evaluator.hpp:170

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::DomainPointType
EvalPolicy::DomainPointType DomainPointType
domain point type
Definition: evaluator.hpp:173

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::Evaluator
Evaluator(const SpaceType &space)
Constructor.
Definition: evaluator.hpp:185

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::eval_ref_values
void eval_ref_values(EvalData_ &data, const DomainPointType &point) const
Evaluates the basis function values on the reference cell.
Definition: evaluator.hpp:210

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::get_num_local_dofs
int get_num_local_dofs() const
Returns the number of local DOFs.
Definition: evaluator.hpp:195

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::SpaceEvalTraits
SpaceEvalTraits_ SpaceEvalTraits
space evaluation traits
Definition: evaluator.hpp:167

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 3 > >::DataType
SpaceEvalTraits::DataType DataType
data type
Definition: evaluator.hpp:176

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::~Evaluator
virtual ~Evaluator()
virtual destructor
Definition: evaluator.hpp:725

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::prepare
void prepare(const TrafoEvaluator &trafo_eval)
Prepares the evaluator for a given cell.
Definition: evaluator.hpp:746

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::Evaluator
Evaluator(const SpaceType &space)
Constructor.
Definition: evaluator.hpp:720

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::InvLinTrafoData
TrafoEvaluator::template ConfigTraits< inv_lin_trafo_config >::EvalDataType InvLinTrafoData
inverse linearized trafo data
Definition: evaluator.hpp:590

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::TrafoType
TrafoEvaluator::TrafoType TrafoType
trafo type
Definition: evaluator.hpp:546

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::MeshType
TrafoType::MeshType MeshType
mesh type
Definition: evaluator.hpp:549

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::FacetTrafoData
FacetTrafoEvaluator::template ConfigTraits< facet_trafo_config >::EvalDataType FacetTrafoData
facet trafo data
Definition: evaluator.hpp:601

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::BaseClass
EvaluatorBase< Evaluator, TrafoEvaluator_, SpaceEvalTraits_ > BaseClass
base-class typedef
Definition: evaluator.hpp:531

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::ImagePointType
EvalPolicy::ImagePointType ImagePointType
image point type
Definition: evaluator.hpp:563

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::eval_values
void eval_values(EvalData< SpaceEvalTraits, space_cfg_ > &data, const Trafo::EvalData< TrafoEvalTraits, trafo_cfg_ > &trafo_data) const
Evaluates the basis function values on the real cell.
Definition: evaluator.hpp:757

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::DataType
SpaceEvalTraits::DataType DataType
data type
Definition: evaluator.hpp:555

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_coeff_mat
CoeffMatrixType _coeff_mat
basis function coefficient matrix
Definition: evaluator.hpp:613

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::eval_gradients
void eval_gradients(EvalData< SpaceEvalTraits, space_cfg_ > &data, const Trafo::EvalData< TrafoEvalTraits, trafo_cfg_ > &trafo_data) const
Definition: evaluator.hpp:782

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::EvalPolicy
SpaceEvalTraits::EvalPolicy EvalPolicy
evaluation policy
Definition: evaluator.hpp:558

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::FacetEvalTraits
FacetTrafoEvaluator::EvalTraits FacetEvalTraits
facet evaluation traits
Definition: evaluator.hpp:595

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::JacobianMatrixType
EvalPolicy::JacobianMatrixType JacobianMatrixType
jacobian matrix type
Definition: evaluator.hpp:566

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_build_coeff_matrix
void _build_coeff_matrix(const TrafoEvaluator &trafo_eval)
computes the basis function coefficient matrix for the current cell
Definition: evaluator.hpp:630

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::TrafoEvalTraits
TrafoEvaluator::EvalTraits TrafoEvalTraits
trafo evaluator traits
Definition: evaluator.hpp:543

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::SpaceType
Space_ SpaceType
space type
Definition: evaluator.hpp:534

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::DomainPointType
EvalPolicy::DomainPointType DomainPointType
domain point type
Definition: evaluator.hpp:561

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::TrafoEvaluator
TrafoEvaluator_ TrafoEvaluator
trafo evaluator type
Definition: evaluator.hpp:540

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::FacetTrafoEvaluator
TrafoType::template Evaluator< Shape::Hypercube< 2 >, DataType >::Type FacetTrafoEvaluator
trafo evaluator for facets
Definition: evaluator.hpp:593

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_inv_lin_mat
JacobianInverseType _inv_lin_mat
inverse linearized trafo matrix
Definition: evaluator.hpp:607

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::get_num_local_dofs
int get_num_local_dofs() const
Returns the number of local DOFs.
Definition: evaluator.hpp:735

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::CoeffMatrixType
Tiny::Matrix< DataType, 6, 6 > CoeffMatrixType
basis function coefficient matrix
Definition: evaluator.hpp:604

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::SpaceEvalTraits
SpaceEvalTraits_ SpaceEvalTraits
space evaluation traits
Definition: evaluator.hpp:537

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::JacobianInverseType
EvalPolicy::JacobianInverseType JacobianInverseType
jacobian inverse matrix type
Definition: evaluator.hpp:568

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::FacetIndexSetType
MeshType::template IndexSet< 3, 2 >::Type FacetIndexSetType
facet-index-set type
Definition: evaluator.hpp:552

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::eval_ref_gradients
void eval_ref_gradients(EvalData_ &data, const DomainPointType &point) const
Evaluates the basis function gradients on the reference cell.
Definition: evaluator.hpp:126

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::SpaceType
Space_ SpaceType
space type
Definition: evaluator.hpp:61

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::Evaluator
Evaluator(const SpaceType &space)
Constructor.
Definition: evaluator.hpp:82

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::BaseClass
ParametricEvaluator< Evaluator, TrafoEvaluator_, SpaceEvalTraits_, ref_caps > BaseClass
base-class typedef
Definition: evaluator.hpp:58

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::EvalPolicy
SpaceEvalTraits::EvalPolicy EvalPolicy
evaluation policy
Definition: evaluator.hpp:67

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::DataType
SpaceEvalTraits::DataType DataType
data type
Definition: evaluator.hpp:73

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::get_num_local_dofs
int get_num_local_dofs() const
Returns the number of local DOFs.
Definition: evaluator.hpp:92

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::eval_ref_values
void eval_ref_values(EvalData_ &data, const DomainPointType &point) const
Evaluates the basis function values on the reference cell.
Definition: evaluator.hpp:107

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::DomainPointType
EvalPolicy::DomainPointType DomainPointType
domain point type
Definition: evaluator.hpp:70

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Simplex< 2 > >::SpaceEvalTraits
SpaceEvalTraits_ SpaceEvalTraits
space evaluation traits
Definition: evaluator.hpp:64

FEAT::Space::CroRavRanTur::Evaluator
Crouzeix-Raviart / Rannacher-Turek Element Evaluator class template declaration.
Definition: evaluator.hpp:34

FEAT::Space::EvalData
Space evaluation data structure.
Definition: eval_data.hpp:141

FEAT::Space::EvalData::phi
BasisDataType phi[max_local_dofs]
the basis function data vector
Definition: eval_data.hpp:150

FEAT::Space::EvaluatorBase
Basic Space Evaluator CRTP base-class template.
Definition: evaluator_base.hpp:46

FEAT::Space::ParametricEvaluator
Finite-Element Parametric Evaluator CRTP base-class template.
Definition: parametric_evaluator.hpp:50

FEAT::Tiny::Matrix
Tiny Matrix class template.
Definition: tiny_algebra.hpp:84

FEAT::Tiny::Matrix::set_inverse
CUDA_HOST_DEVICE Matrix & set_inverse(const Matrix< T_, m_, n_, sma_, sna_ > &a)
Sets this matrix to the inverse of another matrix.
Definition: tiny_algebra.hpp:1810

FEAT::Trafo::EvalData
Trafo evaluation data structure.
Definition: eval_data.hpp:33

FEAT::Trafo::EvalData::img_point
EvalTraits::ImagePointType img_point
image point
Definition: eval_data.hpp:53

FEAT::Math::sqrt
T_ sqrt(T_ x)
Returns the square-root of a value.
Definition: math.hpp:300

FEAT::Space::CroRavRanTur::ref_caps
static constexpr SpaceTags ref_caps
Crouzeix-Raviart Element Evaluator reference capabilities.
Definition: evaluator.hpp:22

FEAT
FEAT namespace.
Definition: adjactor.hpp:12

FEAT::SpaceTags
SpaceTags
Space configuration tags enum.
Definition: eval_tags.hpp:97

FEAT::SpaceTags::value
@ value
specifies whether the space should supply basis function values

FEAT::SpaceTags::ref_value
@ ref_value
specifies whether the space should supply reference basis function values

FEAT::SpaceTags::ref_grad
@ ref_grad
specifies whether the space should supply reference basis function gradients

FEAT::SpaceTags::grad
@ grad
specifies whether the space should supply basis function gradients

FEAT::Index
std::uint64_t Index
Index data type.
Definition: base_header.hpp:122

FEAT::TrafoTags
TrafoTags
Trafo configuration tags enum.
Definition: eval_tags.hpp:22

FEAT::TrafoTags::img_point
@ img_point
specifies whether the trafo should supply image point coordinates

FEAT::TrafoTags::dom_point
@ dom_point
specifies whether the trafo should supply domain point coordinates

FEAT::TrafoTags::jac_inv
@ jac_inv
specifies whether the trafo should supply inverse jacobian matrices

FEAT::TrafoTags::jac_det
@ jac_det
specifies whether the trafo should supply jacobian determinants

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::ConfigTraits::EvalDataType
Space::EvalData< SpaceEvalTraits, config > EvalDataType
evaluation data typedef
Definition: evaluator.hpp:582

FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::ConfigTraits::EvalDataType
Space::EvalData< SpaceEvalTraits, config > EvalDataType
evaluation data typedef
Definition: evaluator.hpp:317