mesh.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    mesh.cc
 * @ingroup mesh
 * @brief   Mesh construction
 */
 
 
#include <unistd.h>
#include <set>
#include <unordered_map>
 
#include "system/system.hh"
#include "system/exceptions.hh"
#include "system/index_types.hh"
#include "input/reader_to_storage.hh"
#include "input/input_type.hh"
#include "input/accessors.hh"
#include "system/sys_profiler.hh"
#include "la/distribution.hh"
 
#include "mesh/mesh.h"
#include "mesh/bc_mesh.hh"
#include "mesh/ref_element.hh"
#include "mesh/region_set.hh"
#include "mesh/range_wrapper.hh"
 
// think about following dependencies
#include "mesh/accessors.hh"
#include "mesh/node_accessor.hh"
#include "mesh/partitioning.hh"
#include "mesh/neighbours.h"
 
 
#include "mesh/bih_tree.hh"
#include "mesh/duplicate_nodes.h"
#include "mesh/mesh_optimizer.hh"
 
#include "intersection/mixed_mesh_intersections.hh"
 
 
 
//TODO: sources, concentrations, initial condition  and similarly boundary conditions should be
// instances of a Element valued field
// concentrations is in fact reimplemented in transport REMOVE it HERE
 
// After removing non-geometrical things from mesh, this should be part of mash initializing.
#include "mesh/region.hh"
 
#define NDEF  -1
 
namespace IT = Input::Type;
 
const unsigned int MeshBase::undef_idx;
 
MeshBase::MeshBase()
:   nodes_(make_shared<Armor::Array<double>>(3, 1, 0)),
    node_ids_(make_shared<BidirectionalMap<int>>()),
    row_4_el(nullptr),
    el_4_loc(nullptr),
    el_ds(nullptr),
    duplicate_nodes_(nullptr),
    region_db_(make_shared<RegionDB>())
{
        // Initialize numbering of nodes on sides.
    // This is temporary solution, until class Element is templated
    // by dimension. Then we can replace Mesh::side_nodes by
    // RefElement<dim>::side_nodes.
 
    // indices of side nodes in element node array
    // Currently this is made ad libitum
    // with some ordering here we can get sides with correct orientation.
    // This speedup normal calculation.
 
    side_nodes.resize(3); // three side dimensions
    for(int dim=0; dim < 3; dim++) {
        side_nodes[dim].resize(dim+2); // number of sides
        for(int i_side=0; i_side < dim+2; i_side++)
            side_nodes[dim][i_side].resize(dim+1);
    }
 
    for (unsigned int sid=0; sid<RefElement<1>::n_sides; sid++)
        for (unsigned int nid=0; nid<RefElement<1>::n_nodes_per_side; nid++)
            side_nodes[0][sid][nid] = RefElement<1>::interact(Interaction<0,0>(sid))[nid];
 
    for (unsigned int sid=0; sid<RefElement<2>::n_sides; sid++)
            for (unsigned int nid=0; nid<RefElement<2>::n_nodes_per_side; nid++)
                side_nodes[1][sid][nid] = RefElement<2>::interact(Interaction<0,1>(sid))[nid];
 
    for (unsigned int sid=0; sid<RefElement<3>::n_sides; sid++)
            for (unsigned int nid=0; nid<RefElement<3>::n_nodes_per_side; nid++)
                side_nodes[2][sid][nid] = RefElement<3>::interact(Interaction<0,2>(sid))[nid];
 
    for (int d=0; d<3; d++) max_edge_sides_[d] = 0;
}
 
MeshBase::~MeshBase()
{
    for(EdgeData &edg : this->edges)
        if (edg.side_) delete[] edg.side_;
 
    for (unsigned int idx=0; idx < element_vec_.size(); idx++) {
        Element *ele=&(element_vec_[idx]);
        if (ele->boundary_idx_) delete[] ele->boundary_idx_;
        if (ele->neigh_vb) delete[] ele->neigh_vb;
    }
 
    if (row_4_el != nullptr) delete[] row_4_el;
    if (el_4_loc != nullptr) delete[] el_4_loc;
    if (el_ds != nullptr) delete el_ds;
    if (duplicate_nodes_ != nullptr) delete duplicate_nodes_;
}
 
Range<Edge> MeshBase::edge_range() const {
    auto bgn_it = make_iter<Edge>( Edge(this, 0) );
    auto end_it = make_iter<Edge>( Edge(this, edges.size()) );
    return Range<Edge>(bgn_it, end_it);
}
 
Edge MeshBase::edge(uint edge_idx) const
{
    ASSERT_LT(edge_idx, edges.size());
    return Edge(this, edge_idx);
}
 
unsigned int MeshBase::n_vb_neighbours() const
{ 
    return vb_neighbours_.size();
}
 
//void Mesh::array_sort(std::array<uint, 4> &nodes) {
//    // TODO: use templated insert sort with recursion over length of array so that compiler can
//    // optimize for the small array size.
//
//    std::sort(nodes.begin(), nodes.end());
//}
 
std::array<std::pair<uint,uint>, 6> _comparisons = { {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}} };
 
 
void MeshBase::canonical_faces() {
    // Fill mappings from canonical element nodes to original
    // for individual permitations.
    // Permutations are numbered by the bifield of all six _comparisons.
    element_nodes_original_[0] = {0,1,2,3};
    element_nodes_original_[1] = {0,1,3,2};
    element_nodes_original_[4] = {0,2,1,3};
    element_nodes_original_[6] = {0,2,3,1};
    element_nodes_original_[3] = {0,3,1,2};
    element_nodes_original_[7] = {0,3,2,1};
    element_nodes_original_[32] = {1,0,2,3};
    element_nodes_original_[33] = {1,0,3,2};
    element_nodes_original_[48] = {1,2,0,3};
    element_nodes_original_[56] = {1,2,3,0};
    element_nodes_original_[41] = {1,3,0,2};
    element_nodes_original_[57] = {1,3,2,0};
    element_nodes_original_[20] = {2,0,1,3};
    element_nodes_original_[22] = {2,0,3,1};
    element_nodes_original_[52] = {2,1,0,3};
    element_nodes_original_[60] = {2,1,3,0};
    element_nodes_original_[30] = {2,3,0,1};
    element_nodes_original_[62] = {2,3,1,0};
    element_nodes_original_[11] = {3,0,1,2};
    element_nodes_original_[15] = {3,0,2,1};
    element_nodes_original_[43] = {3,1,0,2};
    element_nodes_original_[59] = {3,1,2,0};
    element_nodes_original_[31] = {3,2,0,1};
    element_nodes_original_[63] = {3,2,1,0};
 
 
    // element_vec_ still contains both bulk and boundary elements
    for (uint i_el=0; i_el < element_vec_.size(); i_el++) {
        Element &ele = element_vec_[i_el];
        uint cmp_bits = 0;
        for(uint i=0; i<6; i++) {
            cmp_bits <<=1;
            cmp_bits += (ele.nodes_[_comparisons[i].first] > ele.nodes_[_comparisons[i].second]);
        }
        ele.permutation_ = cmp_bits;
        std::sort(ele.nodes_.begin(), ele.nodes_.end());
    }
 
    if (bc_mesh() != nullptr) bc_mesh()->canonical_faces();
 
}
 
 
 
 
 
const Input::Type::Selection & Mesh::get_input_intersection_variant() {
    return Input::Type::Selection("Types of search algorithm for finding intersection candidates.")
        .add_value(Mesh::BIHsearch, "BIHsearch",
            "Use BIH for finding initial candidates, then continue by prolongation.")
        .add_value(Mesh::BIHonly, "BIHonly",
            "Use BIH for finding all candidates.")
        .add_value(Mesh::BBsearch, "BBsearch",
            "Use bounding boxes for finding initial candidates, then continue by prolongation.")
        .close();
}
 
const IT::Record & Mesh::get_input_type() {
    return IT::Record("Mesh","Record with mesh related data." )
        .allow_auto_conversion("mesh_file")
        .declare_key("mesh_file", IT::FileName::input(), IT::Default::obligatory(),
                "Input file with mesh description.")
        .declare_key("regions", IT::Array( RegionSetBase::get_input_type() ), IT::Default::optional(),
                "List of additional region and region set definitions not contained in the mesh. "
                "There are three region sets implicitly defined:\n\n"
                "- ALL (all regions of the mesh)\n"
                "- .BOUNDARY (all boundary regions)\n"
                "- BULK (all bulk regions)")
        .declare_key("partitioning", Partitioning::get_input_type(), IT::Default("\"any_neighboring\""), "Parameters of mesh partitioning algorithms.\n" )
        .declare_key("print_regions", IT::Bool(), IT::Default("true"), "If true, print table of all used regions.")
        .declare_key("intersection_search", Mesh::get_input_intersection_variant(), 
                     IT::Default("\"BIHsearch\""), "Search algorithm for element intersections.")
        .declare_key("global_snap_radius", IT::Double(0.0), IT::Default("1E-3"),
                     "Maximal snapping distance from the mesh in various search operations. In particular, it is used "
                     "to find the closest mesh element of an observe point; and in FieldFormula to find closest surface "
                     "element in plan view (Z projection).")
        .declare_key("raw_ngh_output", IT::FileName::output(), IT::Default::optional(),
                     "Output file with neighboring data from mesh.")
        .declare_key("optimize_mesh", IT::Bool(), IT::Default("true"), "If true, permute nodes and elements in order to increase cache locality. "
                     "This will speed up the calculations. GMSH output preserves original ordering but is slower. All variants of VTK output use the permuted.")
        .close();
}
 
Mesh::Mesh()
: comm_(MPI_COMM_WORLD),
  node_4_loc_(nullptr),
  node_ds_(nullptr),  
  bc_mesh_(new BCMesh(this))
  
{init();}
 
 
 
Mesh::Mesh(Input::Record in_record, MPI_Comm com)
: optimize_memory_locality(true),
  in_record_(in_record),
  comm_(com),
  node_4_loc_(nullptr),
  node_ds_(nullptr),
  bc_mesh_(new BCMesh(this))
{
 
    init();
}
 
 
Mesh::Mesh(Mesh &other)
  : optimize_memory_locality(other.optimize_memory_locality),
  in_record_(other.in_record_),
  comm_(other.comm_),
  node_4_loc_(nullptr),
  node_ds_(nullptr),
  bc_mesh_(new BCMesh(this))
{
    init();
}
 
 
 
Mesh::IntersectionSearch Mesh::get_intersection_search()
{
    return in_record_.val<Mesh::IntersectionSearch>("intersection_search");
}
 
 
void Mesh::init()
{
    // set in_record_, if input accessor is empty
    if (in_record_.is_empty()) {
        istringstream is("{mesh_file=\"\", optimize_mesh=false}");
        Input::ReaderToStorage reader;
        IT::Record &in_rec = const_cast<IT::Record &>(Mesh::get_input_type());
        in_rec.finish();
        reader.read_stream(is, in_rec, Input::FileFormat::format_JSON);
        in_record_ = reader.get_root_interface<Input::Record>();
    }
 
    optimize_memory_locality = in_record_.val<bool>("optimize_mesh");
 
    n_insides = NDEF;
    n_exsides = NDEF;
    n_sides_ = NDEF;
}
 
 
Mesh::~Mesh() {
    if (node_4_loc_ != nullptr) delete[] node_4_loc_;
    if (node_ds_ != nullptr) delete node_ds_;
    if (bc_mesh_ != nullptr) delete bc_mesh_;
}
 
 
unsigned int Mesh::n_sides() const
{
    if (n_sides_ == NDEF) {
        n_sides_=0;
        for (auto ele : this->elements_range()) n_sides_ += ele->n_sides();
    }
    return n_sides_;
}
 
 
unsigned int Mesh::n_corners() {
    unsigned int li, count = 0;
    for (auto ele : this->elements_range()) {
        for (li=0; li<ele->n_nodes(); li++) {
            count++;
        }
    }
    return count;
}
 
Boundary Mesh::boundary(uint bc_idx) const
{
    ASSERT_LT(bc_idx, boundary_.size());
    return Boundary(&boundary_[bc_idx]);
}
 
Partitioning *Mesh::get_part() {
    return part_.get();
}
 
const LongIdx *Mesh::get_local_part() {
    return (LongIdx*)this->get_part()->get_loc_part();
}
 
 
 
 
void Mesh::modify_element_ids(const RegionDB::MapElementIDToRegionID &map) {
 
    // get dim of the first element in the map, if it exists
    uint dim_to_check = RegionDB::undefined_dim;
    std::string reg_name = "UndefinedRegion";
    if(map.size() > 0){
        Element &ele = element_vec_[ elem_index(map.begin()->first) ];
        dim_to_check = ele.dim();
        reg_name = region_db_->find_id(map.begin()->second).label();
    }
 
    for (auto elem_to_region : map) {
        Element &ele = element_vec_[ elem_index(elem_to_region.first) ];
        
        if( ele.dim() != dim_to_check){
            THROW(ExcRegionElmDiffDim() << EI_Region(reg_name) << EI_RegIdx(elem_to_region.second) << EI_Dim(dim_to_check)
                    << EI_DimOther(ele.dim()) << EI_ElemId(elem_to_region.first) );
        }
 
        ele.region_idx_ = region_db_->get_region( elem_to_region.second, ele.dim() );
        region_db_->mark_used_region(ele.region_idx_.idx());
    }
}
 
 
void Mesh::check_mesh_on_read() {
    std::vector<uint> nodes_new_idx( this->n_nodes(), undef_idx );
 
    // check element quality and flag used nodes
    for (auto ele : this->elements_range()) {
        // element quality
        double quality = ele.quality_measure_smooth();
        if (quality < 0) {
            ASSERT_LT(ele.jacobian_S3(), 0);
            element_vec_[ele.idx()].inverted = true;
            quality = -quality;
        }
        if (quality < 4*std::numeric_limits<double>::epsilon())
            THROW( ExcBadElement() << EI_Quality(quality) << EI_ElemId(ele.idx()) );
        if ( quality< 0.001)
            WarningOut().fmt("Bad quality element ID={}, ({}<0.001).\n", ele.idx(), quality);
 
        // flag used nodes
        for (uint ele_node=0; ele_node<ele->n_nodes(); ele_node++) {
            uint inode = ele->node_idx(ele_node);
            nodes_new_idx[inode] = inode;
        }
    }
 
    // possibly build new node ids map
    BidirectionalMap<int> new_node_ids_;
    new_node_ids_.reserve(node_ids_->size());
 
    // remove unused nodes from the mesh
    uint inode_new = 0;
    for(uint inode = 0; inode < nodes_new_idx.size(); inode++) {
        if(nodes_new_idx[inode] == undef_idx){
            WarningOut().fmt("A node {} does not belong to any element "
                         " and will be removed.",
                         find_node_id(inode));
        }
        else{
            // map new node numbering
            nodes_new_idx[inode] = inode_new;
            
            // possibly move the nodes
            nodes_->vec<3>(inode_new) = nodes_->vec<3>(inode);
            new_node_ids_.add_item((*node_ids_)[inode]);
 
            inode_new++;
        }
    }
 
    uint n_nodes_new = inode_new;
 
    // if some node erased, update node ids in elements
    if(n_nodes_new < nodes_new_idx.size()){
        
        DebugOut() << "Updating node-element numbering due to unused nodes: "
            << print_var(n_nodes_new) << print_var(nodes_new_idx.size()) << "\n";
 
        // throw away unused nodes
        nodes_->resize(n_nodes_new);
        *node_ids_ = new_node_ids_;
 
        // update node-element numbering
        for (auto ele : this->elements_range()) {
            for (uint ele_node=0; ele_node<ele->n_nodes(); ele_node++) {
                uint inode_orig = ele->node_idx(ele_node);
                uint inode = nodes_new_idx[inode_orig];
                ASSERT(inode != undef_idx);
                const_cast<Element*>(ele.element())->nodes_[ele_node] = inode;
            }
        }
    }
}
 
 
 
void Mesh::setup_topology() {
    if (optimize_memory_locality) {
        START_TIMER("MESH - optimizer");
        this->optimize();
        END_TIMER("MESH - optimizer");
    }
 
    START_TIMER("MESH - setup topology");
 
    canonical_faces();
    check_mesh_on_read();
 
 
    make_neighbours_and_edges();
    element_to_neigh_vb();
    count_side_types();
    
    this->duplicate_nodes_ = new DuplicateNodes(this);
 
    part_ = std::make_shared<Partitioning>(this, in_record_.val<Input::Record>("partitioning") );
 
    // create parallel distribution and numbering of elements
    LongIdx *id_4_old = new LongIdx[n_elements()];
    int i = 0;
    for (auto ele : this->elements_range())
        id_4_old[i++] = ele.idx();
    part_->id_maps(n_elements(), id_4_old, el_ds, el_4_loc, row_4_el);
    bc_mesh_->init_distribution();
    bc_mesh_->duplicate_nodes_ = new DuplicateNodes(bc_mesh_);
 
    delete[] id_4_old;
    
    this->distribute_nodes();
 
    output_internal_ngh_data();
}
 
 
void Mesh::optimize() {
    MeshOptimizer<3> mo(this);
    mo.calculate_sizes();
    mo.calculate_node_curve_values_as_hilbert();
    mo.calculate_element_curve_values_as_hilbert_of_centers();
 
    this->sort_permuted_nodes_elements( mo.sort_nodes(this->node_permutation_), mo.sort_elements(this->elem_permutation_) );
}
 
 
void Mesh::sort_permuted_nodes_elements(std::vector<int> new_node_ids, std::vector<int> new_elem_ids) {
    BidirectionalMap<int> node_ids_backup = *this->node_ids_;
    this->node_ids_->clear();
    this->node_ids_->reserve(this->n_nodes());
    Armor::Array<double> nodes_backup = *this->nodes_;
    for (uint i = 0; i < this->element_vec_.size(); ++i) {
        for (uint j = 0; j < this->element_vec_[i].dim() + 1; ++j) {
            this->element_vec_[i].nodes_[j] = this->node_permutation_[this->element_vec_[i].nodes_[j]];
        }
    }
    for (uint i = 0; i < bc_mesh_->n_elements(); ++i) {
        for (uint j = 0; j < bc_mesh_->element(i).dim() + 1; ++j) {
            bc_mesh_->element_vec_[i].nodes_[j] = this->node_permutation_[bc_mesh_->element_vec_[i].nodes_[j]];
        }
    }
    for (uint i = 0; i < this->n_nodes(); ++i) {
        this->nodes_->set(node_permutation_[i]) = nodes_backup.vec<3>(i);
        this->node_ids_->add_item( node_ids_backup[new_node_ids[i]] );
    }
 
    BidirectionalMap<int> elem_ids_backup = this->element_ids_;
    this->element_ids_.clear();
    this->element_ids_.reserve(element_vec_.size());
    std::vector<Element> elements_backup = this->element_vec_;
    for (uint i = 0; i < element_vec_.size(); ++i) {
        this->element_vec_[elem_permutation_[i]] = elements_backup[i];
        this->element_ids_.add_item( elem_ids_backup[new_elem_ids[i]] );
    }
}
 
 
//
void Mesh::count_side_types()
{
 
    n_insides = 0;
    n_exsides = 0;
    for (auto ele : this->elements_range()) {
        for(SideIter sde = ele.side(0); sde->side_idx() < ele->n_sides(); ++sde) {
            if (sde->is_external()) n_exsides++;
            else n_insides++;
        }
    }
}
 
 
 
void MeshBase::create_node_element_lists() {
    // for each node we make a list of elements that use this node
    node_elements_.resize( this->n_nodes() );
 
    for (auto ele : this->elements_range())
        for (unsigned int n=0; n<ele->n_nodes(); n++)
            node_elements_[ele.node(n).idx()].push_back(ele.idx());
 
    for (vector<vector<unsigned int> >::iterator n=node_elements_.begin(); n!=node_elements_.end(); n++)
        stable_sort(n->begin(), n->end());
}
 
 
void MeshBase::intersect_element_lists(vector<unsigned int> const &nodes_list, vector<unsigned int> &intersection_element_list)
{
    if (node_elements_.size() == 0) {
        this->create_node_element_lists();
    }
 
    if (nodes_list.size() == 0) {
        intersection_element_list.clear();
    } else if (nodes_list.size() == 1) {
        intersection_element_list = node_elements_[ nodes_list[0] ];
    } else {
        vector<unsigned int>::const_iterator it1=nodes_list.begin();
        vector<unsigned int>::const_iterator it2=it1+1;
        intersection_element_list.resize( node_elements_[*it1].size() ); // make enough space
 
        it1=set_intersection(
                node_elements_[*it1].begin(), node_elements_[*it1].end(),
                node_elements_[*it2].begin(), node_elements_[*it2].end(),
                intersection_element_list.begin());
        intersection_element_list.resize(it1-intersection_element_list.begin()); // resize to true size
 
        for(;it2<nodes_list.end();++it2) {
            it1=set_intersection(
                    intersection_element_list.begin(), intersection_element_list.end(),
                    node_elements_[*it2].begin(), node_elements_[*it2].end(),
                    intersection_element_list.begin());
            intersection_element_list.resize(it1-intersection_element_list.begin()); // resize to true size
        }
    }
}
 
 
bool MeshBase::find_lower_dim_element( vector<unsigned int> &element_list, unsigned int dim, unsigned int &element_idx) {
    bool is_neighbour = false;
 
    vector<unsigned int>::iterator e_dest=element_list.begin();
    for( vector<unsigned int>::iterator ele = element_list.begin(); ele!=element_list.end(); ++ele) {
        //DebugOut() << "Eid: " << this->elem_index(*ele)
        //        << format(element_vec_[*ele].nodes_);
 
        if (element_vec_[*ele].dim() == dim) { // keep only indexes of elements of same dimension
            *e_dest=*ele;
            ++e_dest;
        } else if (element_vec_[*ele].dim() == dim-1) { // get only first element of lower dimension
            if (is_neighbour) THROW(ExcTooMatchingIds() << EI_ElemId(this->elem_index(*ele)) << EI_ElemIdOther(this->elem_index(element_idx)) );
 
            is_neighbour = true;
            element_idx = *ele;
        }
    }
    element_list.resize( e_dest - element_list.begin());
    return is_neighbour;
}
 
bool MeshBase::same_sides(const SideIter &si, vector<unsigned int> &side_nodes) {
    // check if nodes lists match (this is slow and will be faster only when we convert whole mesh into hierarchical design like in deal.ii)
    unsigned int ni=0;
    while ( ni < si->n_nodes()
        && find(side_nodes.begin(), side_nodes.end(), si->node(ni).idx() ) != side_nodes.end() ) ni++;
    return ( ni == si->n_nodes() );
}
 
/**
 * TODO:
 * - use std::is_any for setting is_neigbour
 * - possibly make appropriate constructors for Edge and Neighbour
 * - check side!=-1 when searching neigbouring element
 * - process boundary elements first, there should be no Neigh, but check it
 *   set Edge and boundary there
 */
 
void Mesh::make_neighbours_and_edges()
{
    Neighbour neighbour;
    EdgeData *edg = nullptr;
    unsigned int ngh_element_idx;
    unsigned int last_edge_idx = undef_idx;
 
    neighbour.mesh_ = this;
 
    create_node_element_lists();
 
    // pointers to created edges
    //vector<Edge *> tmp_edges;
    edges.resize(0); // be sure that edges are empty
 
    vector<unsigned int> side_nodes;
    vector<unsigned int> intersection_list; // list of elements in intersection of node element lists
 
    for( unsigned int i=0; i<bc_mesh()->n_elements(); ++i) {
 
        ElementAccessor<3> bc_ele = bc_mesh_->element_accessor(i);
        ASSERT(bc_ele.region().is_boundary());
        // Find all elements that share this side.
        side_nodes.resize(bc_ele->n_nodes());
        for (unsigned n=0; n<bc_ele->n_nodes(); n++) side_nodes[n] = bc_ele->node_idx(n);
        intersect_element_lists(side_nodes, intersection_list);
        bool is_neighbour = find_lower_dim_element(intersection_list, bc_ele->dim() +1, ngh_element_idx);
        if (is_neighbour) {
            THROW( ExcBdrElemMatchRegular() << EI_ElemId(bc_ele.idx()) << EI_ElemIdOther(this->elem_index(ngh_element_idx)) );
        } else {
            if (intersection_list.size() == 0) {
                // no matching dim+1 element found
                WarningOut().fmt("Lonely boundary element, id: {}, region: {}, dimension {}.\n",
                        bc_ele.idx(), bc_ele.region().id(), bc_ele->dim());
                continue; // skip the boundary element
            }
            last_edge_idx=edges.size();
            edges.resize(last_edge_idx+1);
            edg = &( edges.back() );
            edg->n_sides = 0;
            edg->side_ = new struct SideIter[ intersection_list.size() ];
 
            // common boundary object
            unsigned int bdr_idx=boundary_.size();
            boundary_.resize(bdr_idx+1);
            BoundaryData &bdr=boundary_.back();
            bdr.bc_ele_idx_ = i;
            bdr.edge_idx_ = last_edge_idx;
            bdr.mesh_=this;
 
            // for 1d boundaries there can be more then one 1d elements connected to the boundary element
            // we do not detect this case later in the main search over bulk elements
            for( vector<unsigned int>::iterator isect = intersection_list.begin(); isect!=intersection_list.end(); ++isect)  {
                ElementAccessor<3> elem = this->element_accessor(*isect);
                for (unsigned int ecs=0; ecs<elem->n_sides(); ecs++) {
                    SideIter si = elem.side(ecs);
                    if ( same_sides( si, side_nodes) ) {
                        if (elem->edge_idx(ecs) != undef_idx) {
                            ASSERT_PTR(elem->boundary_idx_).error("Null boundary idx array.\n");
                            int last_bc_ele_idx=this->boundary_[elem->boundary_idx_[ecs]].bc_ele_idx_;
                            int new_bc_ele_idx=i;
                            THROW( ExcDuplicateBoundary()
                                    << EI_ElemLast(bc_mesh_->find_elem_id(last_bc_ele_idx))
                                    << EI_RegLast(bc_mesh_->element_accessor(last_bc_ele_idx).region().label())
                                    << EI_ElemNew(bc_mesh_->find_elem_id(new_bc_ele_idx))
                                    << EI_RegNew(bc_mesh_->element_accessor(new_bc_ele_idx).region().label())
                                    );
                        }
                        element_vec_[*isect].edge_idx_[ecs] = last_edge_idx;
                        edg->side_[ edg->n_sides++ ] = si;
 
                        if (elem->boundary_idx_ == NULL) {
                            Element *el = &(element_vec_[*isect]);
                            el->boundary_idx_ = new unsigned int [ el->n_sides() ];
                            std::fill( el->boundary_idx_, el->boundary_idx_ + el->n_sides(), undef_idx);
                        }
                        elem->boundary_idx_[ecs] = bdr_idx;
                        break; // next element in intersection list
                    }
                }
            }
        }
 
    }
    // Now we go through all element sides and create edges and neighbours
    unsigned int new_bc_elem_idx = bc_mesh_->n_elements();  //Mesh_idx of new boundary element generated in following block
    for (auto e : this->elements_range()) {
        for (unsigned int s=0; s<e->n_sides(); s++)
        {
            // skip sides that were already found
            if (e->edge_idx(s) != undef_idx) continue;
 
 
            // Find all elements that share this side.
            side_nodes.resize(e.side(s)->n_nodes());
            for (unsigned n=0; n<e.side(s)->n_nodes(); n++) side_nodes[n] = e.side(s)->node(n).idx();
            intersect_element_lists(side_nodes, intersection_list);
 
            bool is_neighbour = find_lower_dim_element(intersection_list, e->dim(), ngh_element_idx);
 
            if (is_neighbour) { // edge connects elements of different dimensions
                // Initialize for the neighbour case.
                neighbour.elem_idx_ = ngh_element_idx;
            } else { // edge connects only elements of the same dimension
                // Initialize for the edge case.
                last_edge_idx=edges.size();
                edges.resize(last_edge_idx+1);
                edg = &( edges.back() );
                edg->n_sides = 0;
                edg->side_ = new struct SideIter[ intersection_list.size() ];
                if (intersection_list.size() > max_edge_sides_[e->dim()-1])
                    max_edge_sides_[e->dim()-1] = intersection_list.size();
 
                if (intersection_list.size() == 1) {
                    // outer edge, create boundary object as well
                    Element &elm = element_vec_[e.idx()];
                    edg->n_sides=1;
                    edg->side_[0] = e.side(s);
                    element_vec_[e.idx()].edge_idx_[s] = last_edge_idx;
 
                    if (e->boundary_idx_ == NULL) {
                        elm.boundary_idx_ = new unsigned int [ e->n_sides() ];
                        std::fill( elm.boundary_idx_, elm.boundary_idx_ + e->n_sides(), undef_idx);
                    }
 
                    unsigned int bdr_idx=boundary_.size()+1; // need for VTK mesh that has no boundary elements
                                                             // and bulk elements are indexed from 0
                    boundary_.resize(bdr_idx+1);
                    BoundaryData &bdr=boundary_.back();
                    elm.boundary_idx_[s] = bdr_idx;
 
                    // fill boundary element
                    Element * bc_ele = add_element_to_vector(-bdr_idx, true);
                    bc_ele->init(e->dim()-1, region_db_->implicit_boundary_region() );
                    region_db_->mark_used_region( bc_ele->region_idx_.idx() );
                    for(unsigned int ni = 0; ni< side_nodes.size(); ni++) bc_ele->nodes_[ni] = side_nodes[ni];
 
                    // fill Boundary object
                    bdr.edge_idx_ = last_edge_idx;
                    bdr.bc_ele_idx_ = new_bc_elem_idx; //bc_mesh()->elem_index(-bdr_idx);
                    bdr.mesh_=this;
                    new_bc_elem_idx++;
 
                    continue; // next side of element e
                }
            }
 
            // go through the elements connected to the edge or neighbour
            // setup neigbour or edge
            for( vector<unsigned int>::iterator isect = intersection_list.begin(); isect!=intersection_list.end(); ++isect) {
                ElementAccessor<3> elem = this->element_accessor(*isect);
                for (unsigned int ecs=0; ecs<elem->n_sides(); ecs++) {
                    if (elem->edge_idx(ecs) != undef_idx) continue; // ??? This should not happen.
                    SideIter si = elem.side(ecs);
                    if ( same_sides( si, side_nodes) ) {
                        if (is_neighbour) {
                            // create a new edge and neighbour for this side, and element to the edge
                            last_edge_idx=edges.size();
                            edges.resize(last_edge_idx+1);
                            edg = &( edges.back() );
                            edg->n_sides = 1;
                            edg->side_ = new struct SideIter[1];
                            edg->side_[0] = si;
                            element_vec_[elem.idx()].edge_idx_[ecs] = last_edge_idx;
 
                            neighbour.edge_idx_ = last_edge_idx;
 
                            vb_neighbours_.push_back(neighbour); // copy neighbour with this edge setting
                        } else {
                            // connect the side to the edge, and side to the edge
                            ASSERT_PTR(edg);
                            edg->side_[ edg->n_sides++ ] = si;
                            ASSERT(last_edge_idx != undef_idx);
                            element_vec_[elem.idx()].edge_idx_[ecs] = last_edge_idx;
                        }
                        break; // next element from intersection list
                    }
                } // search for side of other connected element
            } // connected elements
 
            if (! is_neighbour)
                ASSERT_EQ( (unsigned int) edg->n_sides, intersection_list.size())(e.input_id())(s).error("Missing edge sides.");
        } // for element sides
    }   // for elements
 
    MessageOut().fmt( "Created {} edges and {} neighbours.\n", edges.size(), vb_neighbours_.size() );
}
 
 
 
//=============================================================================
//
//=============================================================================
void Mesh::element_to_neigh_vb()
{
 
    //MessageOut() << "Element to neighbours of vb2 type... "/*orig verb 5*/;
 
    for (auto ele : elements_range())
        ele->n_neighs_vb_ =0;
 
    // count vb neighs per element
    for (auto & ngh : this->vb_neighbours_)  ngh.element()->n_neighs_vb_++;
 
    // Allocation of the array per element
    for (vector<Element>::iterator ele = element_vec_.begin(); ele!= element_vec_.end(); ++ele)
        if( ele->n_neighs_vb() > 0 ) {
            ele->neigh_vb = new struct Neighbour* [ele->n_neighs_vb()];
            ele->n_neighs_vb_=0;
        }
 
    // fill
    ElementAccessor<3> ele;
    for (auto & ngh : this->vb_neighbours_) {
        ele = ngh.element();
        ele->neigh_vb[ ele->n_neighs_vb_++ ] = &ngh;
    }
 
    //MessageOut() << "... O.K.\n"/*orig verb 6*/;
}
 
 
 
 
 
 
MixedMeshIntersections & Mesh::mixed_intersections() {
    /* Algorithm:
     *
     * 1) create BIH tree
     * 2) for every 1D, find list of candidates
     * 3) compute intersections for 1d, store it to master_elements
     *
     */
    if (! intersections) {
        intersections = std::make_shared<MixedMeshIntersections>(this);
        intersections->compute_intersections();
    }
    return *intersections;
}
 
 
 
ElementAccessor<3> MeshBase::element_accessor(unsigned int idx) const {
    return ElementAccessor<3>(this, idx);
}
 
 
 
NodeAccessor<3> MeshBase::node(unsigned int idx) const {
    return NodeAccessor<3>(this, idx);
}
 
 
 
void Mesh::elements_id_maps( vector<LongIdx> & bulk_elements_id, vector<LongIdx> & boundary_elements_id) const
{
    if (bulk_elements_id.size() ==0) {
        std::vector<LongIdx>::iterator map_it;
 
        bulk_elements_id.resize(n_elements());
        map_it = bulk_elements_id.begin();
        for(unsigned int idx=0; idx < n_elements(); idx++, ++map_it) {
            LongIdx id = this->find_elem_id(idx);
            *map_it = id;
        }
        std::sort(bulk_elements_id.begin(), bulk_elements_id.end());
 
        boundary_elements_id.resize(bc_mesh_->n_elements());
        map_it = boundary_elements_id.begin();
        for(unsigned int idx=0; idx<bc_mesh_->n_elements(); idx++, ++map_it) {
            LongIdx id = bc_mesh_->find_elem_id(idx);
            // We set ID for boundary elements created by the mesh itself to "-1"
            // this force gmsh reader to skip all remaining entries in boundary_elements_id
            // and thus report error for any remaining data lines
            if (id < 0) *map_it=-1;
            else *map_it = id;
        }
    }
}
 
 
bool compare_points(const arma::vec3 &p1, const arma::vec3 &p2) {
    static const double point_tolerance = 1E-10;
    return fabs(p1[0]-p2[0]) < point_tolerance
        && fabs(p1[1]-p2[1]) < point_tolerance
        && fabs(p1[2]-p2[2]) < point_tolerance;
}
 
 
std::shared_ptr<EquivalentMeshMap> Mesh::check_compatible_mesh(Mesh & input_mesh)
{
    // Assumptions:
    // - target (computational) mesh is continous
    // - source mesh can be both continous (unique nodes) and discontinous (duplicit nodes)
    // - at least one compatible element must be found (each mesh can be only subdomain of the other one)
 
    std::vector<unsigned int> node_ids; // indices map: nodes from source mesh to nodes of target mesh
    std::shared_ptr<EquivalentMeshMap> map_ptr = 
        std::make_shared<EquivalentMeshMap>(n_elements(), bc_mesh()->n_elements(), (LongIdx)undef_idx);
    // indices map: nodes from source mesh to nodes of target mesh
 
    {
        // create map `node_ids` from node indices of source mesh to node indices of target mesh
        // - to each node of source mesh there must be one node in target mesh at maximum
        // - to each node of target mesh there can be more than one node in source mesh
        // - iterate over nodes of source mesh, use BIH tree of target mesh to find candidate nodes
        // - check equality of nodes by their L1 distance with tolerance
        std::vector<unsigned int> searched_elements; // for BIH tree
        unsigned int i_node, i_elm_node;
        const BIHTree &bih_tree=this->get_bih_tree();
 
        // create nodes of mesh
        node_ids.resize( input_mesh.n_nodes(), undef_idx );
        for (auto nod : input_mesh.node_range()) {
            uint found_i_node = undef_idx;
            bih_tree.find_point(*nod, searched_elements);
 
            for (std::vector<unsigned int>::iterator it = searched_elements.begin(); it!=searched_elements.end(); it++) {
                ElementAccessor<3> ele = this->element_accessor( *it );
                for (i_node=0; i_node<ele->n_nodes(); i_node++)
                {
                    static const double point_tolerance = 1E-10;
                    if ( arma::norm(*ele.node(i_node) - *nod, 1) < point_tolerance) {
                        i_elm_node = ele.node(i_node).idx();
                        if (found_i_node == undef_idx)
                            found_i_node = i_elm_node;
                        else if (found_i_node != i_elm_node) {
                            // duplicate nodes in target mesh - not compatible
                            return std::make_shared<EquivalentMeshMap>();
                        }
                    }
                }
            }
 
            if (found_i_node!=undef_idx)
                node_ids[nod.idx()] = found_i_node;
            
            searched_elements.clear();
        }
    }
 
    unsigned int n_found = 0; // number of found equivalent elements
    // create map for bulk elements
    n_found += check_compatible_elements(&input_mesh, this, node_ids, map_ptr->bulk);
    // create map for boundary elements
    n_found += check_compatible_elements(input_mesh.bc_mesh(), this->bc_mesh(), node_ids, map_ptr->boundary);
 
    // no equivalent element found => mesh is not compatible
    if (n_found==0)
        return std::make_shared<EquivalentMeshMap>();
    else
        return map_ptr;
}
 
unsigned int Mesh::check_compatible_elements(MeshBase* source_mesh, MeshBase* target_mesh,
                                             const std::vector<unsigned int>& node_ids,
                                             std::vector<LongIdx>& map)
{
    // create map `element_ids_map` from ele indices of source mesh to ele indices of target mesh
    // - iterate over elements of source mesh
    // - get adjacent nodes of target mesh using `node_ids` map
    // - find adjacent element of target mesh using the found nodes
 
    std::vector<unsigned int> result_list; // list of elements with same dimension as vtk element
    std::vector<unsigned int> node_list; // auxiliary vector of node indices of a single element
    std::vector<unsigned int> candidate_list; // auxiliary output vector for intersect_element_lists function
    bool valid_nodes;
 
    unsigned int n_found = 0; // number of found equivalent elements
    
    for (auto elm : source_mesh->elements_range()) {
        valid_nodes = true;
        for (unsigned int j=0; j<elm->n_nodes(); j++) { // iterate trough all nodes of any element
            if (node_ids[ elm->node_idx(j) ] == undef_idx)
                valid_nodes = false;
            node_list.push_back( node_ids[ elm->node_idx(j) ] );
        }
 
        if (valid_nodes) {
            target_mesh->intersect_element_lists(node_list, candidate_list);
            for (auto i_elm : candidate_list) {
                if ( target_mesh->element_accessor(i_elm)->dim() == elm.dim() )
                    result_list.push_back(i_elm);
            }
        }
 
        if (result_list.size() == 1) {
            map[result_list[0]] = elm.idx();
            n_found++;
        }
 
        node_list.clear();
        result_list.clear();
    }
    return n_found;
}
 
 
void Mesh::read_regions_from_input(Input::Array region_list)
{
    for (Input::Iterator<Input::AbstractRecord> it = region_list.begin<Input::AbstractRecord>();
                it != region_list.end();
                ++it) {
        // constructor has side effect in the mesh - create new region or set and store them to Mesh::region_db_
        (*it).factory< RegionSetBase, const Input::Record &, Mesh * >(*it, this);
    }
}
 
void Mesh::check_and_finish()
{
    modify_element_ids(region_db_->el_to_reg_map_);
    region_db_->el_to_reg_map_.clear();
    region_db_->close();
    region_db_->check_regions();
 
    if ( in_record_.val<bool>("print_regions") ) {
        stringstream ss;
        region_db_->print_region_table(ss);
        MessageOut() << ss.str();
    }
}
 
 
std::vector<BoundingBox> Mesh::get_element_boxes() {
    START_TIMER("Mesh::compute_element_boxes");
    std::vector<BoundingBox> boxes;
 
    // make element boxes
    unsigned int i=0;
    boxes.resize(this->n_elements());
    for (auto element : this->elements_range()) {
        boxes[i] = element.bounding_box();
        i++;
    }
 
    return boxes;
}
 
const BIHTree &Mesh::get_bih_tree() {
    if (! this->bih_tree_) {
        bih_tree_ = std::make_shared<BIHTree>();
        bih_tree_->add_boxes( this->get_element_boxes() );
        bih_tree_->construct();
    }
    return *bih_tree_;
}
 
double Mesh::global_snap_radius() const {
    return in_record_.val<double>("global_snap_radius");
}
 
void Mesh::add_physical_name(unsigned int dim, unsigned int id, std::string name) {
    region_db_->add_region(id, name, dim, "$PhysicalNames");
}
 
 
void Mesh::add_node(unsigned int node_id, arma::vec3 coords) {
 
    nodes_->append(coords);
    node_ids_->add_item(node_id);
    node_permutation_.push_back(node_permutation_.size());
}
 
 
void Mesh::add_element(unsigned int elm_id, unsigned int dim, unsigned int region_id, unsigned int partition_id,
        std::vector<unsigned int> node_ids) {
    RegionIdx region_idx = region_db_->get_region( region_id, dim );
    if ( !region_idx.is_valid() ) {
        region_idx = region_db_->add_region( region_id, region_db_->create_label_from_id(region_id), dim, "$Element" );
    }
    region_db_->mark_used_region(region_idx.idx());
 
    if (!region_idx.is_boundary() && dim == 0) {
        WarningOut().fmt("Bulk elements of zero size(dim=0) are not supported. Element ID: {}.\n", elm_id);
    } else {
        Element *ele = add_element_to_vector(elm_id, region_idx.is_boundary());
        this->init_element(ele, elm_id, dim, region_idx, partition_id, node_ids);
    }
}
 
 
void Mesh::init_element(Element *ele, unsigned int elm_id, unsigned int dim, RegionIdx region_idx, unsigned int partition_id,
        std::vector<unsigned int> node_ids) {
    ele->init(dim, region_idx);
    ele->pid_ = partition_id;
 
    unsigned int ni=0;
    for (; ni<ele->n_nodes(); ni++) {
        ele->nodes_[ni] = this->node_index(node_ids[ni]);
    }
    for( ;ni < 4; ni++) ele->nodes_[ni] = undef_idx;
 
    // check that tetrahedron element is numbered correctly and is not degenerated
    if(ele->dim() == 3)
    {
        ElementAccessor<3> ea = this->element_accessor( this->elem_index(elm_id) );
        double jac = ea.jacobian_S3();
        if( ! (jac > 0) ) {
            WarningOut().fmt("Tetrahedron element with id {} has wrong numbering or is degenerated (Jacobian = {}).",elm_id, jac);
        }
    }
}
 
 
vector<vector<unsigned int> > const & MeshBase::node_elements() {
    if (node_elements_.size() == 0) {
        this->create_node_element_lists();
    }
    return node_elements_;
}
 
 
void MeshBase::init_element_vector(unsigned int size) {
    element_vec_.clear();
    element_ids_.clear();
    elem_permutation_.clear();
    element_vec_.reserve(size);
    element_ids_.reserve(size);
    elem_permutation_.reserve(size);
}
 
 
void MeshBase::init_node_vector(unsigned int size) {
    nodes_->reinit(size);
    node_ids_->clear();
    node_ids_->reserve(size);
    node_permutation_.clear();
    node_permutation_.reserve(size);
}
 
 
Element * MeshBase::add_element_to_vector(int id, bool is_boundary) {
    Element * elem;
    if (is_boundary) {
        elem = bc_mesh()->add_element_to_vector(id, false);
    } else {
        element_vec_.push_back( Element() );
        elem = &element_vec_.back(); //[element_vec_.size()-1];
        element_ids_.add_item((unsigned int)(id));
        elem_permutation_.push_back(elem_permutation_.size());
    }
    return elem;
}
 
Range<ElementAccessor<3>> MeshBase::elements_range() const {
    auto bgn_it = make_iter<ElementAccessor<3>>( ElementAccessor<3>(this, 0) );
    auto end_it = make_iter<ElementAccessor<3>>( ElementAccessor<3>(this, element_vec_.size()) );
    return Range<ElementAccessor<3>>(bgn_it, end_it);
}
 
Range<NodeAccessor<3>> MeshBase::node_range() const {
    auto bgn_it = make_iter<NodeAccessor<3>>( NodeAccessor<3>(this, 0) );
    auto end_it = make_iter<NodeAccessor<3>>( NodeAccessor<3>(this, n_nodes()) );
    return Range<NodeAccessor<3>>(bgn_it, end_it);
}
 
 
/*
 * Output of internal flow data.
 */
void Mesh::output_internal_ngh_data()
{
    START_TIMER("Mesh::output_internal_ngh_data");
 
    FilePath raw_output_file_path;
    if (! in_record_.opt_val("raw_ngh_output", raw_output_file_path)) return;
 
    ofstream raw_ngh_output_file;
    int rank;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    if (rank == 0) {
        MessageOut() << "Opening raw ngh output: " << raw_output_file_path << "\n";
        try {
            raw_output_file_path.open_stream(raw_ngh_output_file);
        } INPUT_CATCH(FilePath::ExcFileOpen, FilePath::EI_Address_String, (in_record_))
    }
 
    if (! raw_ngh_output_file.is_open()) return;
    
    // header
    raw_ngh_output_file <<  "// fields:\n//ele_id    n_sides    ns_side_neighbors[n]    neighbors[n*ns]    n_vb_neighbors    vb_neighbors[n_vb]\n";
    raw_ngh_output_file <<  fmt::format("{}\n" , n_elements());
 
    int cit = 0;
    
    // map from higher dim elements to its lower dim neighbors, using gmsh IDs: ele->id()
    unsigned int undefined_ele_id = -1;
    std::map<unsigned int, std::vector<unsigned int>> neigh_vb_map;
    for (auto ele : this->elements_range()) {
        if(ele->n_neighs_vb() > 0){
            for (unsigned int i = 0; i < ele->n_neighs_vb(); i++){
                ElementAccessor<3> higher_ele = ele->neigh_vb[i]->side()->element();
                
                auto search = neigh_vb_map.find(higher_ele.idx());
                if(search != neigh_vb_map.end()){
                    // if found, add id to correct local side idx
                    search->second[ele->neigh_vb[i]->side()->side_idx()] = ele.idx();
                }
                else{
                    // if not found, create new vector, each side can have one vb neighbour
                    std::vector<unsigned int> higher_ele_side_ngh(higher_ele->n_sides(), undefined_ele_id);
                    higher_ele_side_ngh[ele->neigh_vb[i]->side()->side_idx()] = ele.idx();
                    neigh_vb_map[higher_ele.idx()] = higher_ele_side_ngh;
                }
            }
        }
    }
 
    for (unsigned int i_elem=0; i_elem<n_elements(); ++i_elem)
    {
        auto ele = element_accessor(elem_permutation_[i_elem]);
        std::stringstream ss;
        ss << ele.input_id() << " ";
        ss << ele->n_sides() << " ";
 
        // use node permutation to permute sides
        auto &new_to_old_node = ele.orig_nodes_order();
        std::vector<uint> old_to_new_side(ele->n_sides());
        for (unsigned int i = 0; i < ele->n_sides(); i++) {
            // According to RefElement<dim>::opposite_node()
            uint new_opp_node = ele->n_sides() - i - 1;
            uint old_opp_node = new_to_old_node[new_opp_node];
            uint old_iside = ele->n_sides() - old_opp_node - 1;
            old_to_new_side[old_iside] = i;
        }
 
        auto search_neigh = neigh_vb_map.end();
        for (unsigned int i = 0; i < ele->n_sides(); i++) {
            uint new_iside = old_to_new_side[i];
 
            uint n_side_neighs = ele.side(new_iside)->edge().n_sides()-1;  //n_sides - the current one
            // check vb neighbors (lower dimension)
            if(n_side_neighs == 0){
                //update search
                if(search_neigh == neigh_vb_map.end())
                    search_neigh = neigh_vb_map.find(ele.idx());
                
                if(search_neigh != neigh_vb_map.end())
                    if(search_neigh->second[new_iside] != undefined_ele_id)
                        n_side_neighs = 1;
            }
            ss << n_side_neighs << " ";
        }
        
        for (unsigned int i = 0; i < ele->n_sides(); i++) {
            uint new_iside = old_to_new_side[i];
            Edge edge = ele.side(new_iside)->edge();
            if(edge.n_sides() > 1){
                for (uint j = 0; j < edge.n_sides(); j++) {
                    if(edge.side(j) != ele.side(new_iside))
                        ss << edge.side(j)->element().input_id() << " ";
                }
            }
            //check vb neighbour
            else if(search_neigh != neigh_vb_map.end()
                    && search_neigh->second[new_iside] != undefined_ele_id){
                auto neigh_ele = element_accessor(search_neigh->second[new_iside]);
                ss << neigh_ele.input_id() << " ";
            }
        }
        
        // list higher dim neighbours
        ss << ele->n_neighs_vb() << " ";
        for (unsigned int i = 0; i < ele->n_neighs_vb(); i++)
            ss << ele->neigh_vb[i]->side()->element().input_id() << " ";
        
        // remove last white space
        string line = ss.str();
        raw_ngh_output_file << line.substr(0, line.size()-1) << endl;
        cit ++;
    }
    raw_ngh_output_file << "$EndFlowField\n" << endl;
}
 
 
 
 
 
void Mesh::distribute_nodes() {
    ASSERT_PTR(el_4_loc).error("Array 'el_4_loc' is not initialized. Did you call Partitioning::id_maps?\n");
 
    unsigned int i_proc, i_node, i_ghost_node, elm_node;
    unsigned int my_proc = el_ds->myp();
    unsigned int n_proc = el_ds->np();
 
    // distribute nodes between processes, every node is assigned to minimal process of elements that own node
    // fill node_proc vector with same values on all processes
    std::vector<unsigned int> node_proc( this->n_nodes(), n_proc );
    std::vector<bool> local_node_flag( this->n_nodes(), false );
 
    for ( auto elm : this->elements_range() ) {
        i_proc = elm.proc();
        for (elm_node=0; elm_node<elm->n_nodes(); elm_node++) {
            i_node = elm->node_idx(elm_node);
            if (i_proc == my_proc) local_node_flag[i_node] = true;
            if (i_proc < node_proc[i_node]) node_proc[i_node] = i_proc;
        }
    }
 
    unsigned int n_own_nodes=0, n_local_nodes=0; // number of own and ghost nodes
    for(uint loc_flag : local_node_flag) if (loc_flag) n_local_nodes++;
    for(uint i_proc : node_proc) {
        if (i_proc == my_proc)
            n_own_nodes++;
        else if (i_proc == n_proc)
            ASSERT_PERMANENT(0)(find_node_id(n_own_nodes)).error("A node does not belong to any element!");
    }
 
    //DebugOut() << print_var(n_own_nodes) << print_var(n_local_nodes) << this->n_nodes();
    // create and fill node_4_loc_ (mapping local to global indexes)
    node_4_loc_ = new LongIdx [ n_local_nodes ];
    i_node=0;
    i_ghost_node = n_own_nodes;
    for (unsigned int i=0; i<this->n_nodes(); ++i) {
        if (local_node_flag[i]) {
            if (node_proc[i]==my_proc)
                node_4_loc_[i_node++] = i;
            else
                node_4_loc_[i_ghost_node++] = i;
        }
    }
 
    // Construct node distribution object, set number of local nodes (own+ghost)
    node_ds_ = new Distribution(n_own_nodes, PETSC_COMM_WORLD);
    node_ds_->get_lsizes_array(); // need to initialize lsizes data member
    n_local_nodes_ = n_local_nodes;
 
}
 
 
inline int MeshBase::elem_index(int elem_id) const
{
    return element_ids_.get_position(elem_id);
}
 
 
const Neighbour &MeshBase::vb_neighbour(unsigned int nb) const
{ 
    // ASSERT_PERMANENT(nb < vb_neighbours_.size());
    return vb_neighbours_[nb];
}
 
//-----------------------------------------------------------------------------
// vim: set cindent: