field_fe.cc

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/*!
 *
 * Copyright (C) 2015 Technical University of Liberec.  All rights reserved.
 * 
 * This program is free software; you can redistribute it and/or modify it under
 * the terms of the GNU General Public License version 3 as published by the
 * Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)
 * 
 * This program is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
 *
 * 
 * @file    field_fe.cc
 * @brief   
 */


#include <limits>

#include "fields/field_fe.hh"
#include "la/vector_mpi.hh"
#include "fields/field_instances.hh"    // for instantiation macros
#include "fields/fe_value_handler.hh"
#include "input/input_type.hh"
#include "fem/fe_p.hh"
#include "fem/fe_system.hh"
#include "fem/dh_cell_accessor.hh"
#include "fem/mapping_p1.hh"
#include "io/reader_cache.hh"
#include "io/msh_gmshreader.h"
#include "mesh/accessors.hh"
#include "mesh/range_wrapper.hh"
#include "mesh/bc_mesh.hh"
#include "quadrature/quadrature_lib.hh"

#include "system/sys_profiler.hh"
#include "intersection/intersection_aux.hh"
#include "intersection/intersection_local.hh"
#include "intersection/compute_intersection.hh"




/// Implementation.

namespace it = Input::Type;




FLOW123D_FORCE_LINK_IN_CHILD(field_fe)



/************************************************************************************
 * Implementation of FieldFE methods
 */
template <int spacedim, class Value>
const Input::Type::Record & FieldFE<spacedim, Value>::get_input_type()
{
    return it::Record("FieldFE", FieldAlgorithmBase<spacedim,Value>::template_name()+" Field given by finite element approximation.")
        .derive_from(FieldAlgorithmBase<spacedim, Value>::get_input_type())
        .copy_keys(FieldAlgorithmBase<spacedim, Value>::get_field_algo_common_keys())
        .declare_key("mesh_data_file", IT::FileName::input(), IT::Default::obligatory(),
                "GMSH mesh with data. Can be different from actual computational mesh.")
        .declare_key("input_discretization", FieldFE<spacedim, Value>::get_disc_selection_input_type(), IT::Default::optional(),
                "Section where to find the field.\n Some sections are specific to file format: "
                "point_data/node_data, cell_data/element_data, -/element_node_data, native/-.\n"
                "If not given by a user, we try to find the field in all sections, but we report an error "
                "if it is found in more than one section.")
        .declare_key("field_name", IT::String(), IT::Default::obligatory(),
                "The values of the Field are read from the ```$ElementData``` section with field name given by this key.")
        .declare_key("default_value", IT::Double(), IT::Default::optional(),
                "Default value is set on elements which values have not been listed in the mesh data file.")
        .declare_key("time_unit", IT::String(), IT::Default::read_time("Common unit of TimeGovernor."),
                "Definition of the unit of all times defined in the mesh data file.")
        .declare_key("read_time_shift", TimeGovernor::get_input_time_type(), IT::Default("0.0"),
                "This key allows reading field data from the mesh data file shifted in time. Considering the time 't', field descriptor with time 'T', "
                "time shift 'S', then if 't > T', we read the time frame 't + S'.")
        .declare_key("interpolation", FieldFE<spacedim, Value>::get_interp_selection_input_type(),
                IT::Default("\"equivalent_mesh\""), "Type of interpolation applied to the input spatial data.\n"
                "The default value 'equivalent_mesh' assumes the data being constant on elements living on the same mesh "
                "as the computational mesh, but possibly with different numbering. In the case of the same numbering, "
                "the user can set 'identical_mesh' to omit algorithm for guessing node and element renumbering. "
                "Alternatively, in case of different input mesh, several interpolation algorithms are available.")
        .close();
}

template <int spacedim, class Value>
const Input::Type::Selection & FieldFE<spacedim, Value>::get_disc_selection_input_type()
{
    return it::Selection("FE_discretization",
            "Specify the section in mesh input file where field data is listed.\nSome sections are specific to file format.")
        .add_value(OutputTime::DiscreteSpace::NODE_DATA, "node_data", "point_data (VTK) / node_data (GMSH)")
        .add_value(OutputTime::DiscreteSpace::ELEM_DATA, "element_data", "cell_data (VTK) / element_data (GMSH)")
        .add_value(OutputTime::DiscreteSpace::CORNER_DATA, "element_node_data", "element_node_data (only for GMSH)")
        .add_value(OutputTime::DiscreteSpace::NATIVE_DATA, "native_data", "native_data (only for VTK)")
        .close();
}

template <int spacedim, class Value>
const Input::Type::Selection & FieldFE<spacedim, Value>::get_interp_selection_input_type()
{
    return it::Selection("interpolation", "Specify interpolation of the input data from its input mesh to the computational mesh.")
        .add_value(DataInterpolation::identic_msh, "identic_mesh", "Topology and indices of nodes and elements of"
                "the input mesh and the computational mesh are identical. "
                "This interpolation is typically used for GMSH input files containing only the field values without "
                "explicit mesh specification.")
        .add_value(DataInterpolation::equivalent_msh, "equivalent_mesh", "Topologies of the input mesh and the computational mesh "
                "are the same, the node and element numbering may differ. "
                "This interpolation can be used also for VTK input data.") // default value
        .add_value(DataInterpolation::gauss_p0, "P0_gauss", "Topologies of the input mesh and the computational mesh may differ. "
                "Constant values on the elements of the computational mesh are evaluated using the Gaussian quadrature of the fixed order 4, "
                "where the quadrature points and their values are found in the input mesh and input data using the BIH tree search."
                )
        .add_value(DataInterpolation::interp_p0, "P0_intersection", "Topologies of the input mesh and the computational mesh may differ. "
                "Can be applied only for boundary fields. For every (boundary) element of the computational mesh the "
                "intersection with the input mesh is computed. Constant values on the elements of the computational mesh "
                "are evaluated as the weighted average of the (constant) values on the intersecting elements of the input mesh.")
        .close();
}

template <int spacedim, class Value>
const int FieldFE<spacedim, Value>::registrar =
        Input::register_class< FieldFE<spacedim, Value>, unsigned int >("FieldFE") +
        FieldFE<spacedim, Value>::get_input_type().size();



template <int spacedim, class Value>
FieldFE<spacedim, Value>::FieldFE( unsigned int n_comp)
: FieldAlgorithmBase<spacedim, Value>(n_comp),
  field_name_("")
{
    this->is_constant_in_space_ = false;
}


template <int spacedim, class Value>
VectorMPI FieldFE<spacedim, Value>::set_fe_data(std::shared_ptr<DOFHandlerMultiDim> dh,
        unsigned int component_index, VectorMPI dof_values)
{
    dh_ = dh;
    if (dof_values.size()==0) { //create data vector according to dof handler - Warning not tested yet
        data_vec_ = dh_->create_vector();
        data_vec_.zero_entries();
    } else {
        data_vec_ = dof_values;
    }

    unsigned int ndofs = dh_->max_elem_dofs();

    // initialization data of value handlers
    FEValueInitData init_data;
    init_data.dh = dh_;
    init_data.data_vec = data_vec_;
    init_data.ndofs = ndofs;
    init_data.n_comp = this->n_comp();
    init_data.comp_index = component_index;

    // initialize value handler objects
    value_handler0_.initialize(init_data);
    value_handler1_.initialize(init_data);
    value_handler2_.initialize(init_data);
    value_handler3_.initialize(init_data);

    // set discretization
    discretization_ = OutputTime::DiscreteSpace::UNDEFINED;
    interpolation_ = DataInterpolation::equivalent_msh;

    return data_vec_;
}


/**
 * Returns one value in one given point. ResultType can be used to avoid some costly calculation if the result is trivial.
 */
template <int spacedim, class Value>
typename Value::return_type const & FieldFE<spacedim, Value>::value(const Point &p, const ElementAccessor<spacedim> &elm)
{
    switch (elm.dim()) {
    case 0:
        return value_handler0_.value(p, elm);
    case 1:
        return value_handler1_.value(p, elm);
    case 2:
        return value_handler2_.value(p, elm);
    case 3:
        return value_handler3_.value(p, elm);
    default:
        ASSERT(false).error("Invalid element dimension!");
    }

    return this->r_value_;
}



/**
 * Returns std::vector of scalar values in several points at once.
 */
template <int spacedim, class Value>
void FieldFE<spacedim, Value>::value_list (const Armor::array &point_list, const ElementAccessor<spacedim> &elm,
                   std::vector<typename Value::return_type> &value_list)
{
    ASSERT_EQ( point_list.size(), value_list.size() ).error();
    ASSERT_DBG( point_list.n_rows() == spacedim && point_list.n_cols() == 1).error("Invalid point size.\n");

    switch (elm.dim()) {
    case 0:
        value_handler0_.value_list(point_list, elm, value_list);
        break;
    case 1:
        value_handler1_.value_list(point_list, elm, value_list);
        break;
    case 2:
        value_handler2_.value_list(point_list, elm, value_list);
        break;
    case 3:
        value_handler3_.value_list(point_list, elm, value_list);
        break;
    default:
        ASSERT(false).error("Invalid element dimension!");
    }
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::cache_update(FieldValueCache<typename Value::element_type> &data_cache,
        ElementCacheMap &cache_map, unsigned int region_idx)
{
    ASSERT( !boundary_dofs_ ).error("boundary field NOT supported!!\n");
    std::shared_ptr<EvalPoints> eval_points = cache_map.eval_points();
    Armor::ArmaMat<typename Value::element_type, Value::NRows_, Value::NCols_> mat_value;

    if (fe_values_.size() == 0) {
        // initialize FEValues objects (when first using)
        std::array<Quadrature, 4> quads{QGauss(0, 1), this->init_quad<1>(eval_points), this->init_quad<2>(eval_points), this->init_quad<3>(eval_points)};
        fe_values_.resize(4);
        fe_values_[0].initialize(quads[0], *fe_[0_d], update_values);
        fe_values_[1].initialize(quads[1], *fe_[1_d], update_values);
        fe_values_[2].initialize(quads[2], *fe_[2_d], update_values);
        fe_values_[3].initialize(quads[3], *fe_[3_d], update_values);
    }

    auto update_cache_data = cache_map.update_cache_data();
    unsigned int region_in_cache = update_cache_data.region_cache_indices_range_.find(region_idx)->second;

    for (unsigned int i_elm=update_cache_data.region_element_cache_range_[region_in_cache];
            i_elm<update_cache_data.region_element_cache_range_[region_in_cache+1]; ++i_elm) {
        unsigned int elm_idx = cache_map.elm_idx_on_position(i_elm);
        ElementAccessor<spacedim> elm(dh_->mesh(), elm_idx);
        fe_values_[elm.dim()].reinit( elm );

        DHCellAccessor cell = dh_->cell_accessor_from_element( elm_idx );
        LocDofVec loc_dofs = cell.get_loc_dof_indices();

        for (unsigned int i_ep=0; i_ep<eval_points->max_size(); ++i_ep) { // i_eval_point
            //DHCellAccessor cache_cell = cache_map(cell);
            int field_cache_idx = cache_map.get_field_value_cache_index(cache_map(cell).element_cache_index(), i_ep);
            if (field_cache_idx < 0) continue; // skip
            mat_value.fill(0.0);
            for (unsigned int i_dof=0; i_dof<loc_dofs.n_elem; i_dof++) {
                mat_value += data_vec_[loc_dofs[i_dof]] * this->handle_fe_shape(elm.dim(), i_dof, i_ep, 0);
            }
            data_cache.data().set(field_cache_idx) = mat_value;
        }
    }
}


template <int spacedim, class Value>
template <unsigned int dim>
Quadrature FieldFE<spacedim, Value>::init_quad(std::shared_ptr<EvalPoints> eval_points)
{
    Quadrature quad(dim, eval_points->size(dim));
    for (unsigned int k=0; k<eval_points->size(dim); k++)
        quad.set(k) = eval_points->local_point<dim>(k);
    return quad;
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::init_from_input(const Input::Record &rec, const struct FieldAlgoBaseInitData& init_data) {
    this->init_unit_conversion_coefficient(rec, init_data);
    this->in_rec_ = rec;
    flags_ = init_data.flags_;


    // read data from input record
    reader_file_ = FilePath( rec.val<FilePath>("mesh_data_file") );
    field_name_ = rec.val<std::string>("field_name");
    if (! rec.opt_val<OutputTime::DiscreteSpace>("input_discretization", discretization_) ) {
        discretization_ = OutputTime::DiscreteSpace::UNDEFINED;
    }
    if (! rec.opt_val<DataInterpolation>("interpolation", interpolation_) ) {
        interpolation_ = DataInterpolation::equivalent_msh;
    }
    if (! rec.opt_val("default_value", default_value_) ) {
        default_value_ = numeric_limits<double>::signaling_NaN();
    }
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::set_mesh(const Mesh *mesh, bool boundary_domain) {
    // Mesh can be set only for field initialized from input.
    if ( flags_.match(FieldFlag::equation_input) && flags_.match(FieldFlag::declare_input) ) {
        ASSERT(field_name_ != "").error("Uninitialized FieldFE, did you call init_from_input()?\n");
        this->boundary_domain_ = boundary_domain;
        if (this->interpolation_ == DataInterpolation::identic_msh) {
            ReaderCache::get_element_ids(reader_file_, *mesh);
        } else {
            auto source_mesh = ReaderCache::get_mesh(reader_file_);
            ReaderCache::get_element_ids(reader_file_, *(source_mesh.get()));
            if (this->interpolation_ == DataInterpolation::equivalent_msh) {
                source_target_mesh_elm_map_ = ReaderCache::get_target_mesh_element_map(reader_file_, const_cast<Mesh *>(mesh));
                if (source_target_mesh_elm_map_->size() == 0) { // incompatible meshes
                    this->interpolation_ = DataInterpolation::gauss_p0;
                    WarningOut().fmt("Source mesh of FieldFE '{}' is not compatible with target mesh.\nInterpolation of input data will be changed to 'P0_gauss'.\n",
                            field_name_);
                }
            } else if (this->interpolation_ == DataInterpolation::interp_p0) {
                if (!boundary_domain) {
                    this->interpolation_ = DataInterpolation::gauss_p0;
                    WarningOut().fmt("Interpolation 'P0_intersection' of FieldFE '{}' can't be used on bulk region.\nIt will be changed to 'P0_gauss'.\n",
                            field_name_);
                }
            }
        }
        this->make_dof_handler(mesh);
    }
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::fill_boundary_dofs() {
    ASSERT(this->boundary_domain_);

    auto bc_mesh = dh_->mesh()->get_bc_mesh();
    unsigned int n_comp = this->value_.n_rows() * this->value_.n_cols();
    boundary_dofs_ = std::make_shared< std::vector<IntIdx> >( n_comp * bc_mesh->n_elements() );
    std::vector<IntIdx> &in_vec = *( boundary_dofs_.get() );
    unsigned int j = 0; // actual index to boundary_dofs_ vector

    for (auto ele : bc_mesh->elements_range()) {
        IntIdx elm_shift = n_comp * ele.idx();
        for (unsigned int i=0; i<n_comp; ++i, ++j) {
            in_vec[j] = elm_shift + i;
        }
    }

    value_handler0_.set_boundary_dofs_vector(boundary_dofs_);
    value_handler1_.set_boundary_dofs_vector(boundary_dofs_);
    value_handler2_.set_boundary_dofs_vector(boundary_dofs_);
    value_handler3_.set_boundary_dofs_vector(boundary_dofs_);

    data_vec_.resize(boundary_dofs_->size());
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::make_dof_handler(const Mesh *mesh) {
    // temporary solution - these objects will be set through FieldCommon
    switch (this->value_.n_rows() * this->value_.n_cols()) { // by number of components
        case 1: { // scalar
            fe_ = MixedPtr<FE_P_disc>(0);
            break;
        }
        case 3: { // vector
             MixedPtr<FE_P_disc>   fe_base(0) ;
            fe_ = mixed_fe_system(fe_base, FEType::FEVector, 3);
            break;
        }
        case 9: { // tensor
            MixedPtr<FE_P_disc>   fe_base(0) ;
            fe_ = mixed_fe_system(fe_base, FEType::FETensor, 9);
            break;
        }
        default:
            ASSERT(false).error("Should not happen!\n");
    }

    std::shared_ptr<DOFHandlerMultiDim> dh_par = std::make_shared<DOFHandlerMultiDim>( const_cast<Mesh &>(*mesh) );
    std::shared_ptr<DiscreteSpace> ds = std::make_shared<EqualOrderDiscreteSpace>( &const_cast<Mesh &>(*mesh), fe_);
    dh_par->distribute_dofs(ds);
    dh_ = dh_par;
    unsigned int ndofs = dh_->max_elem_dofs();

    if (this->boundary_domain_) fill_boundary_dofs(); // temporary solution for boundary mesh
    else data_vec_ = VectorMPI::sequential( dh_->lsize() ); // allocate data_vec_

    // initialization data of value handlers
    FEValueInitData init_data;
    init_data.dh = dh_;
    init_data.data_vec = data_vec_;
    init_data.ndofs = ndofs;
    init_data.n_comp = this->n_comp();
    init_data.comp_index = 0;

    // initialize value handler objects
    value_handler0_.initialize(init_data);
    value_handler1_.initialize(init_data);
    value_handler2_.initialize(init_data);
    value_handler3_.initialize(init_data);
}



template <int spacedim, class Value>
bool FieldFE<spacedim, Value>::set_time(const TimeStep &time) {
    // Time can be set only for field initialized from input.
    if ( flags_.match(FieldFlag::equation_input) && flags_.match(FieldFlag::declare_input) ) {
        ASSERT(field_name_ != "").error("Uninitialized FieldFE, did you call init_from_input()?\n");
        ASSERT_PTR(dh_)(field_name_).error("Null target mesh pointer of finite element field, did you call set_mesh()?\n");
        if ( reader_file_ == FilePath() ) return false;

        unsigned int n_components = this->value_.n_rows() * this->value_.n_cols();
        double time_unit_coef = time.read_coef(in_rec_.find<string>("time_unit"));
        double time_shift = time.read_time( in_rec_.find<Input::Tuple>("read_time_shift") );
        double read_time = (time.end()+time_shift) / time_unit_coef;
        BaseMeshReader::HeaderQuery header_query(field_name_, read_time, this->discretization_, dh_->hash());
        ReaderCache::get_reader(reader_file_)->find_header(header_query);
        // TODO: use default and check NaN values in data_vec

        unsigned int n_entities;
        bool is_native = (header_query.discretization == OutputTime::DiscreteSpace::NATIVE_DATA);
        bool boundary;
        if (is_native || this->interpolation_==DataInterpolation::identic_msh || this->interpolation_==DataInterpolation::equivalent_msh) {
            boundary = this->boundary_domain_;
        } else {
            boundary = false;
        }
        if (this->interpolation_==DataInterpolation::identic_msh) {
            n_entities = dh_->mesh()->n_elements(boundary);
        } else {
            n_entities = ReaderCache::get_mesh(reader_file_)->n_elements(boundary);
        }
        auto input_data_cache = ReaderCache::get_reader(reader_file_)->template get_element_data<double>(n_entities, n_components,
                boundary, this->component_idx_);
        CheckResult checked_data = ReaderCache::get_reader(reader_file_)->scale_and_check_limits(field_name_,
                this->unit_conversion_coefficient_, default_value_);


        if (checked_data == CheckResult::not_a_number) {
            THROW( ExcUndefElementValue() << EI_Field(field_name_) );
        }

        if (is_native) {
            this->calculate_native_values(input_data_cache);
        } else if (this->interpolation_==DataInterpolation::identic_msh) {
            this->calculate_identic_values(input_data_cache);
        } else if (this->interpolation_==DataInterpolation::equivalent_msh) {
            this->calculate_equivalent_values(input_data_cache);
        } else if (this->interpolation_==DataInterpolation::gauss_p0) {
            this->interpolate_gauss(input_data_cache);
        } else { // DataInterpolation::interp_p0
            this->interpolate_intersection(input_data_cache);
        }

        return true;
    } else return false;

}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::interpolate_gauss(ElementDataCache<double>::ComponentDataPtr data_vec)
{
    static const unsigned int quadrature_order = 4; // parameter of quadrature
    std::shared_ptr<Mesh> source_mesh = ReaderCache::get_mesh(reader_file_);
    std::vector<unsigned int> searched_elements; // stored suspect elements in calculating the intersection
    std::vector<arma::vec::fixed<3>> q_points; // real coordinates of quadrature points
    std::vector<double> q_weights; // weights of quadrature points
    unsigned int quadrature_size=0; // size of quadrature point and weight vector
    std::vector<double> sum_val(dh_->max_elem_dofs()); // sum of value of one quadrature point
    unsigned int elem_count; // count of intersect (source) elements of one quadrature point
    std::vector<double> elem_value(dh_->max_elem_dofs()); // computed value of one (target) element
    bool contains; // sign if source element contains quadrature point

    {
        // set size of vectors to maximal count of quadrature points
        QGauss quad(3, quadrature_order);
        q_points.resize(quad.size());
        q_weights.resize(quad.size());
    }

    for (auto cell : dh_->own_range()) {
        auto ele = cell.elm();
        std::fill(elem_value.begin(), elem_value.end(), 0.0);
        switch (cell.dim()) {
        case 0:
            quadrature_size = 1;
            q_points[0] = *ele.node(0);
            q_weights[0] = 1.0;
            break;
        case 1:
            quadrature_size = value_handler1_.compute_quadrature(q_points, q_weights, ele, quadrature_order);
            break;
        case 2:
            quadrature_size = value_handler2_.compute_quadrature(q_points, q_weights, ele, quadrature_order);
            break;
        case 3:
            quadrature_size = value_handler3_.compute_quadrature(q_points, q_weights, ele, quadrature_order);
            break;
        }
        searched_elements.clear();
        source_mesh->get_bih_tree().find_bounding_box(ele.bounding_box(), searched_elements);

        for (unsigned int i=0; i<quadrature_size; ++i) {
            std::fill(sum_val.begin(), sum_val.end(), 0.0);
            elem_count = 0;
            for (std::vector<unsigned int>::iterator it = searched_elements.begin(); it!=searched_elements.end(); it++) {
                ElementAccessor<3> elm = source_mesh->element_accessor(*it);
                contains=false;
                switch (elm->dim()) {
                case 0:
                    contains = arma::norm(*elm.node(0) - q_points[i], 2) < 4*std::numeric_limits<double>::epsilon();
                    break;
                case 1:
                    contains = MappingP1<1,3>::contains_point(q_points[i], elm);
                    break;
                case 2:
                    contains = MappingP1<2,3>::contains_point(q_points[i], elm);
                    break;
                case 3:
                    contains = MappingP1<3,3>::contains_point(q_points[i], elm);
                    break;
                default:
                    ASSERT(false).error("Invalid element dimension!");
                }
                if ( contains ) {
                    // projection point in element
                    unsigned int index = sum_val.size() * (*it);
                    for (unsigned int j=0; j < sum_val.size(); j++) {
                        sum_val[j] += (*data_vec)[index+j];
                    }
                    ++elem_count;
                }
            }

            if (elem_count > 0) {
                for (unsigned int j=0; j < sum_val.size(); j++) {
                    elem_value[j] += (sum_val[j] / elem_count) * q_weights[i];
                }
            }
        }

        LocDofVec loc_dofs;
        if (this->boundary_domain_) loc_dofs = value_handler1_.get_loc_dof_indices(cell.elm_idx());
        else loc_dofs = cell.get_loc_dof_indices();

        ASSERT_LE_DBG(loc_dofs.n_elem, elem_value.size());
        for (unsigned int i=0; i < elem_value.size(); i++) {
            ASSERT_LT_DBG( loc_dofs[i], (int)data_vec_.size());
            data_vec_[loc_dofs[i]] = elem_value[i] * this->unit_conversion_coefficient_;
        }
    }
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::interpolate_intersection(ElementDataCache<double>::ComponentDataPtr data_vec)
{
    std::shared_ptr<Mesh> source_mesh = ReaderCache::get_mesh(reader_file_);
    std::vector<unsigned int> searched_elements; // stored suspect elements in calculating the intersection
    std::vector<double> value(dh_->max_elem_dofs());
    double total_measure;
    double measure = 0;

    Mesh *mesh;
    if (this->boundary_domain_) mesh = dh_->mesh()->get_bc_mesh();
    else mesh = dh_->mesh();
    for (auto elm : mesh->elements_range()) {
        if (elm.dim() == 3) {
            xprintf(Err, "Dimension of element in target mesh must be 0, 1 or 2! elm.idx() = %d\n", elm.idx());
        }

        double epsilon = 4* numeric_limits<double>::epsilon() * elm.measure();

        // gets suspect elements
        if (elm.dim() == 0) {
            searched_elements.clear();
            source_mesh->get_bih_tree().find_point(*elm.node(0), searched_elements);
        } else {
            BoundingBox bb = elm.bounding_box();
            searched_elements.clear();
            source_mesh->get_bih_tree().find_bounding_box(bb, searched_elements);
        }

        // set zero values of value object
        std::fill(value.begin(), value.end(), 0.0);
        total_measure=0.0;

        START_TIMER("compute_pressure");
        ADD_CALLS(searched_elements.size());


        for (std::vector<unsigned int>::iterator it = searched_elements.begin(); it!=searched_elements.end(); it++)
        {
            ElementAccessor<3> ele = source_mesh->element_accessor(*it);
            if (ele->dim() == 3) {
                // get intersection (set measure = 0 if intersection doesn't exist)
                switch (elm.dim()) {
                    case 0: {
                        arma::vec::fixed<3> real_point = *elm.node(0);
                        arma::mat::fixed<3, 4> elm_map = MappingP1<3,3>::element_map(ele);
                        arma::vec::fixed<4> unit_point = MappingP1<3,3>::project_real_to_unit(real_point, elm_map);

                        measure = (std::fabs(arma::sum( unit_point )-1) <= 1e-14
                                        && arma::min( unit_point ) >= 0)
                                            ? 1.0 : 0.0;
                        break;
                    }
                    case 1: {
                        IntersectionAux<1,3> is;
                        ComputeIntersection<1,3> CI(elm, ele, source_mesh.get());
                        CI.init();
                        CI.compute(is);

                        IntersectionLocal<1,3> ilc(is);
                        measure = ilc.compute_measure() * elm.measure();
                        break;
                    }
                    case 2: {
                        IntersectionAux<2,3> is;
                        ComputeIntersection<2,3> CI(elm, ele, source_mesh.get());
                        CI.init();
                        CI.compute(is);

                        IntersectionLocal<2,3> ilc(is);
                        measure = 2 * ilc.compute_measure() * elm.measure();
                        break;
                    }
                }

                //adds values to value_ object if intersection exists
                if (measure > epsilon) {
                    unsigned int index = value.size() * (*it);
                    std::vector<double> &vec = *( data_vec.get() );
                    for (unsigned int i=0; i < value.size(); i++) {
                        value[i] += vec[index+i] * measure;
                    }
                    total_measure += measure;
                }
            }
        }

        // computes weighted average, store it to data vector
        if (total_measure > epsilon) {
            VectorMPI::VectorDataPtr data_vector = data_vec_.data_ptr();

            LocDofVec loc_dofs;
            if (this->boundary_domain_) loc_dofs = value_handler1_.get_loc_dof_indices(elm.idx());
            else{
                DHCellAccessor cell = dh_->cell_accessor_from_element(elm.idx());
                loc_dofs = cell.get_loc_dof_indices();
            }

            ASSERT_LE_DBG(loc_dofs.n_elem, value.size());
            for (unsigned int i=0; i < value.size(); i++) {
                (*data_vector)[ loc_dofs[i] ] = value[i] / total_measure;
            }
        } else {
            WarningOut().fmt("Processed element with idx {} is out of source mesh!\n", elm.idx());
        }
        END_TIMER("compute_pressure");

    }
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::calculate_native_values(ElementDataCache<double>::ComponentDataPtr data_cache)
{
    // Same algorithm as in output of Node_data. Possibly code reuse.
    unsigned int dof_size, data_vec_i;
    std::vector<unsigned int> count_vector(data_vec_.size(), 0);
    data_vec_.zero_entries();
    VectorMPI::VectorDataPtr data_vector = data_vec_.data_ptr();
    std::vector<LongIdx> global_dof_indices(dh_->max_elem_dofs());
    std::vector<LongIdx> &source_target_vec = *(source_target_mesh_elm_map_.get());

    // iterate through cells, assembly MPIVector
    for (auto cell : dh_->own_range()) {
        dof_size = cell.get_dof_indices(global_dof_indices);
        LocDofVec loc_dofs = cell.get_loc_dof_indices();
        data_vec_i = source_target_vec[cell.elm_idx()] * dof_size;
        ASSERT_EQ_DBG(dof_size, loc_dofs.n_elem);
        for (unsigned int i=0; i<dof_size; ++i, ++data_vec_i) {
            (*data_vector)[ loc_dofs[i] ] += (*data_cache)[ data_vec_i ];
            ++count_vector[ loc_dofs[i] ];
        }
    }

    // compute averages of values
    for (unsigned int i=0; i<data_vec_.size(); ++i) {
        if (count_vector[i]>0) (*data_vector)[i] /= count_vector[i];
    }
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::calculate_identic_values(ElementDataCache<double>::ComponentDataPtr data_cache)
{
    // Same algorithm as in output of Node_data. Possibly code reuse.
    unsigned int data_vec_i, i_elm;
    std::vector<unsigned int> count_vector(data_vec_.size(), 0);
    data_vec_.zero_entries();

    if (this->boundary_domain_) {
        // iterate through elements, assembly global vector and count number of writes
        Mesh *mesh = dh_->mesh()->get_bc_mesh();
        i_elm=0;
        for (auto ele : mesh->elements_range()) {
            LocDofVec loc_dofs = value_handler1_.get_loc_dof_indices(ele.idx());
            data_vec_i = i_elm * dh_->max_elem_dofs();
            for (unsigned int i=0; i<loc_dofs.n_elem; ++i, ++data_vec_i) {
                ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                data_vec_[ loc_dofs[i] ] += (*data_cache)[data_vec_i];
                ++count_vector[ loc_dofs[i] ];
            }
            i_elm++;
        }
    }
    else {
        // iterate through cells, assembly global vector and count number of writes - prepared solution for further development
        i_elm=0;
        for (auto cell : dh_->own_range()) {
            LocDofVec loc_dofs = cell.get_loc_dof_indices();
            data_vec_i = i_elm * dh_->max_elem_dofs();
            for (unsigned int i=0; i<loc_dofs.n_elem; ++i, ++data_vec_i) {
                ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                data_vec_[ loc_dofs[i] ] += (*data_cache)[data_vec_i];
                ++count_vector[ loc_dofs[i] ];
            }
            i_elm++;
        }
    }

    // compute averages of values
    for (unsigned int i=0; i<data_vec_.size(); ++i) {
        if (count_vector[i]>0) data_vec_[i] /= count_vector[i];
    }
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::calculate_equivalent_values(ElementDataCache<double>::ComponentDataPtr data_cache)
{
    // Same algorithm as in output of Node_data. Possibly code reuse.
    unsigned int data_vec_i;
    std::vector<unsigned int> count_vector(data_vec_.size(), 0);
    data_vec_.zero_entries();
    std::vector<LongIdx> &source_target_vec = *(source_target_mesh_elm_map_.get());

    // iterate through elements, assembly global vector and count number of writes
    if (this->boundary_domain_) {
        Mesh *mesh = dh_->mesh()->get_bc_mesh();
        for (auto ele : mesh->elements_range()) {
            LocDofVec loc_dofs = value_handler1_.get_loc_dof_indices(ele.idx());
            if (source_target_vec[ele.mesh_idx()] == (int)(Mesh::undef_idx)) { // undefined value in input data mesh
                if ( std::isnan(default_value_) )
                    THROW( ExcUndefElementValue() << EI_Field(field_name_) );
                for (unsigned int i=0; i<loc_dofs.n_elem; ++i) {
                    ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                    data_vec_[ loc_dofs[i] ] += default_value_ * this->unit_conversion_coefficient_;
                    ++count_vector[ loc_dofs[i] ];
                }
            } else {
                data_vec_i = source_target_vec[ele.mesh_idx()] * dh_->max_elem_dofs();
                for (unsigned int i=0; i<loc_dofs.n_elem; ++i, ++data_vec_i) {
                    ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                    data_vec_[ loc_dofs[i] ] += (*data_cache)[data_vec_i];
                    ++count_vector[ loc_dofs[i] ];
                }
            }
        }
    }
    else {
        // iterate through cells, assembly global vector and count number of writes - prepared solution for further development
        for (auto cell : dh_->own_range()) {
            LocDofVec loc_dofs = cell.get_loc_dof_indices();
            if (source_target_vec[cell.elm_idx()] == (int)(Mesh::undef_idx)) { // undefined value in input data mesh
                if ( std::isnan(default_value_) )
                    THROW( ExcUndefElementValue() << EI_Field(field_name_) );
                for (unsigned int i=0; i<loc_dofs.n_elem; ++i) {
                    ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                    data_vec_[ loc_dofs[i] ] += default_value_ * this->unit_conversion_coefficient_;
                    ++count_vector[ loc_dofs[i] ];
                }
            } else {
                data_vec_i = source_target_vec[cell.elm_idx()] * dh_->max_elem_dofs();
                for (unsigned int i=0; i<loc_dofs.n_elem; ++i, ++data_vec_i) {
                    ASSERT_LT_DBG(loc_dofs[i], (LongIdx)data_vec_.size());
                    data_vec_[ loc_dofs[i] ] += (*data_cache)[data_vec_i];
                    ++count_vector[ loc_dofs[i] ];
                }
            }
        }
    }

    // compute averages of values
    for (unsigned int i=0; i<data_vec_.size(); ++i) {
        if (count_vector[i]>0) data_vec_[i] /= count_vector[i];
    }
}


template <int spacedim, class Value>
void FieldFE<spacedim, Value>::native_data_to_cache(ElementDataCache<double> &output_data_cache) {
    ASSERT_EQ(output_data_cache.n_values() * output_data_cache.n_comp(), dh_->distr()->lsize()).error();
    double loc_values[output_data_cache.n_comp()];
    unsigned int i;

    VectorMPI::VectorDataPtr data_vec = data_vec_.data_ptr();
    for (auto dh_cell : dh_->own_range()) {
        LocDofVec loc_dofs = dh_cell.get_loc_dof_indices();
        for (i=0; i<loc_dofs.n_elem; ++i) loc_values[i] = (*data_vec)[ loc_dofs[i] ];
        for ( ; i<output_data_cache.n_comp(); ++i) loc_values[i] = numeric_limits<double>::signaling_NaN();
        output_data_cache.store_value( dh_cell.local_idx(), loc_values );
    }

    output_data_cache.set_dof_handler_hash( dh_->hash() );
}



template <int spacedim, class Value>
inline unsigned int FieldFE<spacedim, Value>::data_size() const {
    return data_vec_.size();
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::local_to_ghost_data_scatter_begin() {
    data_vec_.local_to_ghost_begin();
}



template <int spacedim, class Value>
void FieldFE<spacedim, Value>::local_to_ghost_data_scatter_end() {
    data_vec_.local_to_ghost_end();
}



template <int spacedim, class Value>
Armor::ArmaMat<typename Value::element_type, Value::NRows_, Value::NCols_> FieldFE<spacedim, Value>::handle_fe_shape(unsigned int dim,
        unsigned int i_dof, unsigned int i_qp, unsigned int comp_index)
{
    Armor::ArmaMat<typename Value::element_type, Value::NCols_, Value::NRows_> v;
    for (unsigned int c=0; c<Value::NRows_*Value::NCols_; ++c)
        v(c/spacedim,c%spacedim) = fe_values_[dim].shape_value_component(i_dof, i_qp, comp_index+c);
    if (Value::NRows_ == Value::NCols_)
        return v;
    else
        return v.t();
}



template <int spacedim, class Value>
FieldFE<spacedim, Value>::~FieldFE()
{}


// Instantiations of FieldFE
INSTANCE_ALL(FieldFE)