OpenMC/include/openmc/mesh.h

//! \file mesh.h
//! \brief Mesh types used for tallies, Shannon entropy, CMFD, etc.

#ifndef OPENMC_MESH_H
#define OPENMC_MESH_H

#include <set>
#include <unordered_map>

#include "hdf5.h"
#include "openmc/tensor.h"
#include "pugixml.hpp"

#include "openmc/bounding_box.h"
#include "openmc/error.h"
#include "openmc/memory.h" // for unique_ptr
#include "openmc/particle.h"
#include "openmc/position.h"
#include "openmc/span.h"
#include "openmc/vector.h"
#include "openmc/xml_interface.h"

#ifdef OPENMC_DAGMC_ENABLED
#include "moab/AdaptiveKDTree.hpp"
#include "moab/Core.hpp"
#include "moab/GeomUtil.hpp"
#include "moab/Matrix3.hpp"
#endif

#ifdef OPENMC_LIBMESH_ENABLED
#include "libmesh/bounding_box.h"
#include "libmesh/dof_map.h"
#include "libmesh/elem.h"
#include "libmesh/equation_systems.h"
#include "libmesh/exodusII_io.h"
#include "libmesh/explicit_system.h"
#include "libmesh/libmesh.h"
#include "libmesh/mesh.h"
#include "libmesh/point.h"
#endif

namespace openmc {

//==============================================================================
// Constants
//==============================================================================

enum class ElementType { UNSUPPORTED = -1, LINEAR_TET, LINEAR_HEX };

//==============================================================================
// Global variables
//==============================================================================

extern "C" const bool LIBMESH_ENABLED;

class Mesh;

namespace model {

extern std::unordered_map<int32_t, int32_t> mesh_map;
extern vector<unique_ptr<Mesh>> meshes;

} // namespace model

#ifdef OPENMC_LIBMESH_ENABLED
namespace settings {
// used when creating new libMesh::MeshBase instances
extern unique_ptr<libMesh::LibMeshInit> libmesh_init;
extern const libMesh::Parallel::Communicator* libmesh_comm;
} // namespace settings
#endif

//==============================================================================
//! Helper class for keeping track of volume for each material in a mesh element
//
//! This class is used in Mesh::material_volumes to manage for each mesh element
//! a list of (material, volume) pairs. The openmc.lib.Mesh class allocates two
//! 2D arrays, one for materials and one for volumes. Because we don't know a
//! priori how many materials there are in each element but at the same time we
//! can't dynamically size an array at runtime for performance reasons, we
//! assume a maximum number of materials per element. For each element, the set
//! of material indices are stored in a hash table with twice as many slots as
//! the assumed maximum number of materials per element. Collision resolution is
//! handled by open addressing with linear probing.
//==============================================================================

namespace detail {

class MaterialVolumes {
public:
  MaterialVolumes(int32_t* mats, double* vols, double* bboxes, int table_size)
    : materials_(mats), volumes_(vols), bboxes_(bboxes), table_size_(table_size)
  {}

  MaterialVolumes(int32_t* mats, double* vols, int table_size)
    : MaterialVolumes(mats, vols, nullptr, table_size)
  {}

  //! Add volume for a given material in a mesh element
  //
  //! \param[in] index_elem Index of the mesh element
  //! \param[in] index_material Index of the material within the model
  //! \param[in] volume Volume to add
  //! \param[in] bbox Bounding box to union into the result (optional)
  void add_volume(int index_elem, int index_material, double volume,
    const BoundingBox* bbox = nullptr);
  void add_volume_unsafe(int index_elem, int index_material, double volume,
    const BoundingBox* bbox = nullptr);

  // Accessors
  int32_t& materials(int i, int j) { return materials_[i * table_size_ + j]; }
  const int32_t& materials(int i, int j) const
  {
    return materials_[i * table_size_ + j];
  }

  double& volumes(int i, int j) { return volumes_[i * table_size_ + j]; }
  const double& volumes(int i, int j) const
  {
    return volumes_[i * table_size_ + j];
  }

  double& bboxes(int i, int j, int k)
  {
    return bboxes_[(i * table_size_ + j) * 6 + k];
  }
  const double& bboxes(int i, int j, int k) const
  {
    return bboxes_[(i * table_size_ + j) * 6 + k];
  }

  bool has_bboxes() const { return bboxes_ != nullptr; }

  bool table_full() const { return table_full_; }

private:
  int32_t* materials_;      //!< material index (bins, table_size)
  double* volumes_;         //!< volume in [cm^3] (bins, table_size)
  double* bboxes_;          //!< bounding boxes (bins, table_size, 6)
  int table_size_;          //!< Size of hash table for each mesh element
  bool table_full_ {false}; //!< Whether the hash table is full
};

} // namespace detail

//==============================================================================
//! Base mesh class
//==============================================================================

class Mesh {
public:
  // Constructors and destructor
  Mesh() = default;
  Mesh(pugi::xml_node node);
  Mesh(hid_t group);
  virtual ~Mesh() = default;

  // Factory method for creating meshes from either an XML node or HDF5 group
  template<typename T>
  static const std::unique_ptr<Mesh>& create(
    T dataset, const std::string& mesh_type, const std::string& mesh_library);

  // Methods
  //! Perform any preparation needed to support point location within the mesh
  virtual void prepare_for_point_location() {};

  //! Return a position in the local coordinates of the mesh
  virtual Position local_coords(const Position& r) const { return r; };

  //! Sample a position within a mesh element
  //
  //! \param[in] bin Bin value of the mesh element sampled
  //! \param[inout] seed Seed to use for random sampling
  //! \return sampled position within mesh element
  virtual Position sample_element(int32_t bin, uint64_t* seed) const = 0;

  //! Determine which bins were crossed by a particle
  //
  //! \param[in] r0 Previous position of the particle
  //! \param[in] r1 Current position of the particle
  //! \param[in] u Particle direction
  //! \param[out] bins Bins that were crossed
  //! \param[out] lengths Fraction of tracklength in each bin
  virtual void bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins, vector<double>& lengths) const = 0;

  //! Determine which surface bins were crossed by a particle
  //
  //! \param[in] r0 Previous position of the particle
  //! \param[in] r1 Current position of the particle
  //! \param[in] u Particle direction
  //! \param[out] bins Surface bins that were crossed
  virtual void surface_bins_crossed(
    Position r0, Position r1, const Direction& u, vector<int>& bins) const = 0;

  //! Get bin at a given position in space
  //
  //! \param[in] r Position to get bin for
  //! \return Mesh bin
  virtual int get_bin(Position r) const = 0;

  //! Get the number of mesh cells.
  virtual int n_bins() const = 0;

  //! Get the number of mesh cell surfaces.
  virtual int n_surface_bins() const = 0;

  int32_t id() const { return id_; }

  const std::string& name() const { return name_; }

  //! Set the mesh ID
  void set_id(int32_t id = -1);

  //! Write the mesh data to an HDF5 group
  void to_hdf5(hid_t group) const;

  //! Write mesh data to an HDF5 group
  //
  //! \param[in] group HDF5 group
  virtual void to_hdf5_inner(hid_t group) const = 0;

  //! Find the mesh lines that intersect an axis-aligned slice plot
  //
  //! \param[in] plot_ll The lower-left coordinates of the slice plot.
  //! \param[in] plot_ur The upper-right coordinates of the slice plot.
  //! \return A pair of vectors indicating where the mesh lines lie along each
  //!   of the plot's axes.  For example an xy-slice plot will get back a vector
  //!   of x-coordinates and another of y-coordinates.  These vectors may be
  //!   empty for low-dimensional meshes.
  virtual std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const = 0;

  //! Return a string representation of the mesh bin
  //
  //! \param[in] bin Mesh bin to generate a label for
  virtual std::string bin_label(int bin) const = 0;

  //! Axis names (per dimension) used when labeling surface tally bins
  virtual std::array<const char*, 3> axis_labels() const;

  //! Build the surface component of a mesh surface tally bin label
  std::string surface_bin_label(int surf_index) const;

  //! Get the volume of a mesh bin
  //
  //! \param[in] bin Bin to return the volume for
  //! \return Volume of the bin
  virtual double volume(int bin) const = 0;

  //! Volumes of all elements in the mesh in bin ordering
  vector<double> volumes() const;

  virtual std::string get_mesh_type() const = 0;

  //! Determine volume of materials within each mesh element
  //
  //! \param[in] nx Number of samples in x direction
  //! \param[in] ny Number of samples in y direction
  //! \param[in] nz Number of samples in z direction
  //! \param[in] max_materials Maximum number of materials in a single mesh
  //!                          element
  //! \param[inout] materials Array storing material indices
  //! \param[inout] volumes Array storing volumes
  void material_volumes(int nx, int ny, int nz, int max_materials,
    int32_t* materials, double* volumes) const;

  //! Determine volume and bounding boxes of materials within each mesh element
  //
  //! \param[in] nx Number of samples in x direction
  //! \param[in] ny Number of samples in y direction
  //! \param[in] nz Number of samples in z direction
  //! \param[in] max_materials Maximum number of materials in a single mesh
  //!                          element
  //! \param[inout] materials Array storing material indices
  //! \param[inout] volumes Array storing volumes
  //! \param[inout] bboxes Array storing bounding boxes (n_elems, table_size, 6)
  void material_volumes(int nx, int ny, int nz, int max_materials,
    int32_t* materials, double* volumes, double* bboxes) const;

  //! Determine bounding box of mesh
  //
  //! \return Bounding box of mesh
  BoundingBox bounding_box() const
  {
    return {this->lower_left(), this->upper_right()};
  }

  virtual Position lower_left() const = 0;
  virtual Position upper_right() const = 0;

  // Data members
  tensor::Tensor<double> lower_left_;  //!< Lower-left coordinates of mesh
  tensor::Tensor<double> upper_right_; //!< Upper-right coordinates of mesh
  int id_ {-1};                        //!< Mesh ID
  std::string name_;                   //!< User-specified name
  int n_dimension_ {-1};               //!< Number of dimensions
};

class StructuredMesh : public Mesh {
public:
  StructuredMesh() = default;
  StructuredMesh(pugi::xml_node node) : Mesh {node} {};
  StructuredMesh(hid_t group) : Mesh {group} {};
  virtual ~StructuredMesh() = default;

  using MeshIndex = std::array<int, 3>;

  struct MeshDistance {
    MeshDistance() = default;
    MeshDistance(int _index, bool _max_surface, double _distance)
      : next_index {_index}, max_surface {_max_surface}, distance {_distance}
    {}
    int next_index {-1};
    bool max_surface {true};
    double distance {INFTY};
    bool operator<(const MeshDistance& o) const
    {
      return distance < o.distance;
    }
  };

  Position sample_element(int32_t bin, uint64_t* seed) const override
  {
    return sample_element(get_indices_from_bin(bin), seed);
  };

  virtual Position sample_element(const MeshIndex& ijk, uint64_t* seed) const;

  int get_bin(Position r) const override;

  int n_bins() const override;

  int n_surface_bins() const override;

  void bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins, vector<double>& lengths) const override;

  void surface_bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins) const override;

  //! Determine which cell or surface bins were crossed by a particle
  //
  //! \param[in] r0 Previous position of the particle
  //! \param[in] r1 Current position of the particle
  //! \param[in] u Particle direction
  //! \param[in] tally Functor that eventually stores the tally data
  template<class T>
  void raytrace_mesh(
    Position r0, Position r1, const Direction& u, T tally) const;

  //! Count number of bank sites in each mesh bin / energy bin
  //
  //! \param[in] Pointer to bank sites
  //! \param[in] Number of bank sites
  //! \param[out] Whether any bank sites are outside the mesh
  tensor::Tensor<double> count_sites(
    const SourceSite* bank, int64_t length, bool* outside) const;

  //! Get bin given mesh indices
  //
  //! \param[in] Array of mesh indices
  //! \return Mesh bin
  virtual int get_bin_from_indices(const MeshIndex& ijk) const;

  //! Get mesh indices given a position
  //
  //! \param[in] r Position to get indices for
  //! \param[out] in_mesh Whether position is in mesh
  //! \return Array of mesh indices
  virtual MeshIndex get_indices(Position r, bool& in_mesh) const;

  //! Get mesh indices corresponding to a mesh bin
  //
  //! \param[in] bin Mesh bin
  //! \return ijk Mesh indices
  virtual MeshIndex get_indices_from_bin(int bin) const;

  //! Get mesh index in a particular direction
  //!
  //! \param[in] r Coordinate to get index for
  //! \param[in] i Direction index
  virtual int get_index_in_direction(double r, int i) const = 0;

  //! Get the coordinate for the mesh grid boundary in the positive direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  virtual double positive_grid_boundary(const MeshIndex& ijk, int i) const
  {
    auto msg =
      fmt::format("Attempting to call positive_grid_boundary on a {} mesh.",
        get_mesh_type());
    fatal_error(msg);
  };

  //! Get the coordinate for the mesh grid boundary in the negative direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  virtual double negative_grid_boundary(const MeshIndex& ijk, int i) const
  {
    auto msg =
      fmt::format("Attempting to call negative_grid_boundary on a {} mesh.",
        get_mesh_type());
    fatal_error(msg);
  };

  //! Get the closest distance from the coordinate r to the grid surface
  //! in i direction  that bounds mesh cell ijk and that is larger than l
  //! The coordinate r does not have to be inside the mesh cell ijk. In
  //! curved coordinates, multiple crossings of the same surface can happen,
  //! these are selected by the parameter l
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i direction index of grid surface
  //! \param[in] r0 position, from where to calculate the distance
  //! \param[in] u direction of flight. actual position is r0 + l * u
  //! \param[in] l actual chord length
  //! \return MeshDistance struct with closest distance, next cell index in
  //! i-direction and min/max surface indicator
  virtual MeshDistance distance_to_grid_boundary(const MeshIndex& ijk, int i,
    const Position& r0, const Direction& u, double l) const = 0;

  //! Get a label for the mesh bin
  std::string bin_label(int bin) const override;

  //! Get mesh dimensions as a tensor
  tensor::Tensor<int> get_shape_tensor() const;

  double volume(int bin) const override
  {
    return this->volume(get_indices_from_bin(bin));
  }

  Position lower_left() const override
  {
    int n = lower_left_.size();
    Position ll {lower_left_[0], 0.0, 0.0};
    ll.y = (n >= 2) ? lower_left_[1] : -INFTY;
    ll.z = (n == 3) ? lower_left_[2] : -INFTY;
    return ll;
  };

  Position upper_right() const override
  {
    int n = upper_right_.size();
    Position ur {upper_right_[0], 0.0, 0.0};
    ur.y = (n >= 2) ? upper_right_[1] : INFTY;
    ur.z = (n == 3) ? upper_right_[2] : INFTY;
    return ur;
  };

  //! Get the volume of a specified element
  //! \param[in] ijk Mesh index to return the volume for
  //! \return Volume of the bin
  virtual double volume(const MeshIndex& ijk) const = 0;

  // Data members
  std::array<int, 3> shape_; //!< Number of mesh elements in each dimension

protected:
};

class PeriodicStructuredMesh : public StructuredMesh {

public:
  PeriodicStructuredMesh() = default;
  PeriodicStructuredMesh(pugi::xml_node node) : StructuredMesh {node} {};
  PeriodicStructuredMesh(hid_t group) : StructuredMesh {group} {};

  Position local_coords(const Position& r) const override
  {
    return r - origin_;
  };

  // Data members
  Position origin_ {0.0, 0.0, 0.0}; //!< Origin of the mesh
};

//==============================================================================
//! Tessellation of n-dimensional Euclidean space by congruent squares or cubes
//==============================================================================

class RegularMesh : public StructuredMesh {
public:
  // Constructors
  RegularMesh() = default;
  RegularMesh(pugi::xml_node node);
  RegularMesh(hid_t group);

  // Overridden methods
  int get_index_in_direction(double r, int i) const override;

  virtual std::string get_mesh_type() const override;

  static const std::string mesh_type;

  MeshDistance distance_to_grid_boundary(const MeshIndex& ijk, int i,
    const Position& r0, const Direction& u, double l) const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  void to_hdf5_inner(hid_t group) const override;

  //! Get the coordinate for the mesh grid boundary in the positive direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  double positive_grid_boundary(const MeshIndex& ijk, int i) const override;

  //! Get the coordinate for the mesh grid boundary in the negative direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  double negative_grid_boundary(const MeshIndex& ijk, int i) const override;

  //! Count number of bank sites in each mesh bin / energy bin
  //
  //! \param[in] bank Array of bank sites
  //! \param[out] Whether any bank sites are outside the mesh
  //! \return Array indicating number of sites in each mesh/energy bin
  tensor::Tensor<double> count_sites(
    const SourceSite* bank, int64_t length, bool* outside) const;

  //! Return the volume for a given mesh index
  double volume(const MeshIndex& ijk) const override;

  int set_grid();

  // Data members
  double volume_frac_;           //!< Volume fraction of each mesh element
  double element_volume_;        //!< Volume of each mesh element
  tensor::Tensor<double> width_; //!< Width of each mesh element
};

class RectilinearMesh : public StructuredMesh {
public:
  // Constructors
  RectilinearMesh() = default;
  RectilinearMesh(pugi::xml_node node);
  RectilinearMesh(hid_t group);

  // Overridden methods
  int get_index_in_direction(double r, int i) const override;

  virtual std::string get_mesh_type() const override;

  static const std::string mesh_type;

  MeshDistance distance_to_grid_boundary(const MeshIndex& ijk, int i,
    const Position& r0, const Direction& u, double l) const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  void to_hdf5_inner(hid_t group) const override;

  //! Get the coordinate for the mesh grid boundary in the positive direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  double positive_grid_boundary(const MeshIndex& ijk, int i) const override;

  //! Get the coordinate for the mesh grid boundary in the negative direction
  //!
  //! \param[in] ijk Array of mesh indices
  //! \param[in] i Direction index
  double negative_grid_boundary(const MeshIndex& ijk, int i) const override;

  //! Return the volume for a given mesh index
  double volume(const MeshIndex& ijk) const override;

  int set_grid();

  // Data members
  array<vector<double>, 3> grid_;
};

class CylindricalMesh : public PeriodicStructuredMesh {
public:
  // Constructors
  CylindricalMesh() = default;
  CylindricalMesh(pugi::xml_node node);
  CylindricalMesh(hid_t group);

  // Overridden methods
  virtual MeshIndex get_indices(Position r, bool& in_mesh) const override;

  int get_index_in_direction(double r, int i) const override;

  virtual std::string get_mesh_type() const override;

  static const std::string mesh_type;

  std::array<const char*, 3> axis_labels() const override;

  Position sample_element(const MeshIndex& ijk, uint64_t* seed) const override;

  MeshDistance distance_to_grid_boundary(const MeshIndex& ijk, int i,
    const Position& r0, const Direction& u, double l) const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  void to_hdf5_inner(hid_t group) const override;

  double volume(const MeshIndex& ijk) const override;

  // grid accessors
  double r(int i) const { return grid_[0][i]; }
  double phi(int i) const { return grid_[1][i]; }
  double z(int i) const { return grid_[2][i]; }

  int set_grid();

  // Data members
  array<vector<double>, 3> grid_;

private:
  double find_r_crossing(
    const Position& r, const Direction& u, double l, int shell) const;
  double find_phi_crossing(
    const Position& r, const Direction& u, double l, int shell) const;
  StructuredMesh::MeshDistance find_z_crossing(
    const Position& r, const Direction& u, double l, int shell) const;

  bool full_phi_ {false};

  inline int sanitize_angular_index(int idx, bool full, int N) const
  {
    if ((idx > 0) and (idx <= N)) {
      return idx;
    } else if (full) {
      return (idx + N - 1) % N + 1;
    } else {
      return 0;
    }
  }

  inline int sanitize_phi(int idx) const
  {
    return sanitize_angular_index(idx, full_phi_, shape_[1]);
  }
};

class SphericalMesh : public PeriodicStructuredMesh {
public:
  // Constructors
  SphericalMesh() = default;
  SphericalMesh(pugi::xml_node node);
  SphericalMesh(hid_t group);

  // Overridden methods
  virtual MeshIndex get_indices(Position r, bool& in_mesh) const override;

  int get_index_in_direction(double r, int i) const override;

  virtual std::string get_mesh_type() const override;

  static const std::string mesh_type;

  std::array<const char*, 3> axis_labels() const override;

  Position sample_element(const MeshIndex& ijk, uint64_t* seed) const override;

  MeshDistance distance_to_grid_boundary(const MeshIndex& ijk, int i,
    const Position& r0, const Direction& u, double l) const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  void to_hdf5_inner(hid_t group) const override;

  double r(int i) const { return grid_[0][i]; }
  double theta(int i) const { return grid_[1][i]; }
  double phi(int i) const { return grid_[2][i]; }

  int set_grid();

  // Data members
  array<vector<double>, 3> grid_;

private:
  double find_r_crossing(
    const Position& r, const Direction& u, double l, int shell) const;
  double find_theta_crossing(
    const Position& r, const Direction& u, double l, int shell) const;
  double find_phi_crossing(
    const Position& r, const Direction& u, double l, int shell) const;

  bool full_theta_ {false};
  bool full_phi_ {false};

  inline int sanitize_angular_index(int idx, bool full, int N) const
  {
    if ((idx > 0) and (idx <= N)) {
      return idx;
    } else if (full) {
      return (idx + N - 1) % N + 1;
    } else {
      return 0;
    }
  }

  double volume(const MeshIndex& ijk) const override;

  inline int sanitize_theta(int idx) const
  {
    return sanitize_angular_index(idx, full_theta_, shape_[1]);
  }
  inline int sanitize_phi(int idx) const
  {
    return sanitize_angular_index(idx, full_phi_, shape_[2]);
  }
};

// Abstract class for unstructured meshes
class UnstructuredMesh : public Mesh {

public:
  // Constructors
  UnstructuredMesh() { n_dimension_ = 3; };
  UnstructuredMesh(pugi::xml_node node);
  UnstructuredMesh(hid_t group);

  static const std::string mesh_type;
  virtual std::string get_mesh_type() const override;

  // Overridden Methods

  void surface_bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins) const override;

  void to_hdf5_inner(hid_t group) const override;

  std::string bin_label(int bin) const override;

  // Methods

  //! Add a variable to the mesh instance
  virtual void add_score(const std::string& var_name) = 0;

  //! Remove tally data from the instance
  virtual void remove_scores() = 0;

  //! Set the value of a bin for a variable on the internal
  //  mesh instance
  virtual void set_score_data(const std::string& var_name,
    const vector<double>& values, const vector<double>& std_dev) = 0;

  //! Write the unstructured mesh to file
  //
  //! \param[in] filename Base of the file to write
  virtual void write(const std::string& base_filename) const = 0;

  //! Retrieve a centroid for the mesh cell
  //
  //! \param[in] bin Bin to return the centroid for
  //! \return The centroid of the bin
  virtual Position centroid(int bin) const = 0;

  //! Get the number of vertices in the mesh
  //
  //! \return Number of vertices
  virtual int n_vertices() const = 0;

  //! Retrieve a vertex of the mesh
  //
  //! \param[in] vertex ID
  //! \return vertex coordinates
  virtual Position vertex(int id) const = 0;

  //! Retrieve connectivity of a mesh element
  //
  //! \param[in] element ID
  //! \return element connectivity as IDs of the vertices
  virtual std::vector<int> connectivity(int id) const = 0;

  //! Get the library used for this unstructured mesh
  virtual std::string library() const = 0;

  // Data members
  bool output_ {
    true}; //!< Write tallies onto the unstructured mesh at the end of a run
  std::string filename_; //!< Path to unstructured mesh file

  ElementType element_type(int bin) const;

  Position lower_left() const override
  {
    return {lower_left_[0], lower_left_[1], lower_left_[2]};
  }
  Position upper_right() const override
  {
    return {upper_right_[0], upper_right_[1], upper_right_[2]};
  }

protected:
  //! Set the length multiplier to apply to each point in the mesh
  void set_length_multiplier(const double length_multiplier);

  //! Sample barycentric coordinates given a seed and the vertex positions and
  //! return the sampled position
  //
  //! \param[in] coords Coordinates of the tetrahedron
  //! \param[in] seed Random number generation seed
  //! \return Sampled position within the tetrahedron
  Position sample_tet(std::array<Position, 4> coords, uint64_t* seed) const;

  // Data members
  double length_multiplier_ {
    -1.0};              //!< Multiplicative factor applied to mesh coordinates
  std::string options_; //!< Options for search data structures

  //! Determine lower-left and upper-right bounds of mesh
  void determine_bounds();

private:
  //! Setup method for the mesh. Builds data structures,
  //! sets up element mapping, creates bounding boxes, etc.
  virtual void initialize() = 0;
};

#ifdef OPENMC_DAGMC_ENABLED

class MOABMesh : public UnstructuredMesh {
public:
  // Constructors
  MOABMesh() = default;
  MOABMesh(pugi::xml_node);
  MOABMesh(hid_t group);
  MOABMesh(const std::string& filename, double length_multiplier = 1.0);
  MOABMesh(std::shared_ptr<moab::Interface> external_mbi);

  static const std::string mesh_lib_type;

  // Overridden Methods

  //! Perform any preparation needed to support use in mesh filters
  void prepare_for_point_location() override;

  Position sample_element(int32_t bin, uint64_t* seed) const override;

  void bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins, vector<double>& lengths) const override;

  int get_bin(Position r) const override;

  int n_bins() const override;

  int n_surface_bins() const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  std::string library() const override;

  //! Add a score to the mesh instance
  void add_score(const std::string& score) override;

  //! Remove all scores from the mesh instance
  void remove_scores() override;

  //! Set data for a score
  void set_score_data(const std::string& score, const vector<double>& values,
    const vector<double>& std_dev) override;

  //! Write the mesh with any current tally data
  void write(const std::string& base_filename) const override;

  Position centroid(int bin) const override;

  int n_vertices() const override;

  Position vertex(int id) const override;

  std::vector<int> connectivity(int id) const override;

  //! Get the volume of a mesh bin
  //
  //! \param[in] bin Bin to return the volume for
  //! \return Volume of the bin
  double volume(int bin) const override;

private:
  void initialize() override;

  // Methods

  //! Create the MOAB interface pointer
  void create_interface();

  //! Find all intersections with faces of the mesh.
  //
  //! \param[in] start Staring location
  //! \param[in] dir Normalized particle direction
  //! \param[in] track_len length of particle track
  //! \param[out] Mesh intersections
  void intersect_track(const moab::CartVect& start, const moab::CartVect& dir,
    double track_len, vector<double>& hits) const;

  //! Calculate the volume for a given tetrahedron handle.
  //
  // \param[in] tet MOAB EntityHandle of the tetrahedron
  double tet_volume(moab::EntityHandle tet) const;

  //! Find the tetrahedron for the given location if
  //! one exists
  //
  //! \param[in]
  //! \return MOAB EntityHandle of tet
  moab::EntityHandle get_tet(const Position& r) const;

  //! Return the containing tet given a position
  moab::EntityHandle get_tet(const moab::CartVect& r) const
  {
    return get_tet(Position(r[0], r[1], r[2]));
  };

  //! Check for point containment within a tet; uses
  //! pre-computed barycentric data.
  //
  //! \param[in] r Position to check
  //! \param[in] MOAB terahedron to check
  //! \return True if r is inside, False if r is outside
  bool point_in_tet(const moab::CartVect& r, moab::EntityHandle tet) const;

  //! Compute barycentric coordinate data for all tetrahedra
  //! in the mesh.
  //
  //! \param[in] tets MOAB Range of tetrahedral elements
  void compute_barycentric_data(const moab::Range& tets);

  //! Translate a MOAB EntityHandle to its corresponding bin.
  //
  //! \param[in] eh MOAB EntityHandle to translate
  //! \return Mesh bin
  int get_bin_from_ent_handle(moab::EntityHandle eh) const;

  //! Translate a bin to its corresponding MOAB EntityHandle
  //! for the tetrahedron representing that bin.
  //
  //! \param[in] bin Bin value to translate
  //! \return MOAB EntityHandle of tet
  moab::EntityHandle get_ent_handle_from_bin(int bin) const;

  //! Get a vertex index into the global range from a handle
  int get_vert_idx_from_handle(moab::EntityHandle vert) const;

  //! Get the bin for a given mesh cell index
  //
  //! \param[in] idx Index of the mesh cell.
  //! \return Mesh bin
  int get_bin_from_index(int idx) const;

  //! Get the mesh cell index for a given position
  //
  //! \param[in] r Position to get index for
  //! \param[in,out] in_mesh Whether position is in the mesh
  int get_index(const Position& r, bool* in_mesh) const;

  //! Get the mesh cell index from a bin
  //
  //! \param[in] bin Bin to get the index for
  //! \return Index of the bin
  int get_index_from_bin(int bin) const;

  //! Build a KDTree for all tetrahedra in the mesh. All
  //! triangles representing 2D faces of the mesh are
  //! added to the tree as well.
  //
  //! \param[in] all_tets MOAB Range of tetrahedra for the tree
  void build_kdtree(const moab::Range& all_tets);

  //! Get the tags for a score from the mesh instance
  //! or create them if they are not there
  //
  //! \param[in] score Name of the score
  //! \return The MOAB value and error tag handles, respectively
  std::pair<moab::Tag, moab::Tag> get_score_tags(std::string score) const;

  // Data members
  moab::Range ehs_;   //!< Range of tetrahedra EntityHandle's in the mesh
  moab::Range verts_; //!< Range of vertex EntityHandle's in the mesh
  moab::EntityHandle tetset_;      //!< EntitySet containing all tetrahedra
  moab::EntityHandle kdtree_root_; //!< Root of the MOAB KDTree
  std::shared_ptr<moab::Interface> mbi_;    //!< MOAB instance
  unique_ptr<moab::AdaptiveKDTree> kdtree_; //!< MOAB KDTree instance
  vector<moab::Matrix3> baryc_data_;        //!< Barycentric data for tetrahedra
  vector<std::string> tag_names_; //!< Names of score tags added to the mesh
};

#endif

#ifdef OPENMC_LIBMESH_ENABLED

class LibMesh : public UnstructuredMesh {
public:
  // Constructors
  LibMesh(pugi::xml_node node);
  LibMesh(hid_t group);
  LibMesh(const std::string& filename, double length_multiplier = 1.0);
  LibMesh(libMesh::MeshBase& input_mesh, double length_multiplier = 1.0);

  static const std::string mesh_lib_type;

  // Overridden Methods
  void bins_crossed(Position r0, Position r1, const Direction& u,
    vector<int>& bins, vector<double>& lengths) const override;

  Position sample_element(int32_t bin, uint64_t* seed) const override;

  virtual int get_bin(Position r) const override;

  int n_bins() const override;

  int n_surface_bins() const override;

  std::pair<vector<double>, vector<double>> plot(
    Position plot_ll, Position plot_ur) const override;

  std::string library() const override;

  void add_score(const std::string& var_name) override;

  void remove_scores() override;

  void set_score_data(const std::string& var_name, const vector<double>& values,
    const vector<double>& std_dev) override;

  void write(const std::string& base_filename) const override;

  Position centroid(int bin) const override;

  int n_vertices() const override;

  Position vertex(int id) const override;

  std::vector<int> connectivity(int id) const override;

  //! Get the volume of a mesh bin
  //
  //! \param[in] bin Bin to return the volume for
  //! \return Volume of the bin
  double volume(int bin) const override;

  libMesh::MeshBase* mesh_ptr() const { return m_; };

protected:
  // Methods
  //! Translate a bin value to an element reference
  virtual const libMesh::Elem& get_element_from_bin(int bin) const;

  //! Translate an element pointer to a bin index
  virtual int get_bin_from_element(const libMesh::Elem* elem) const;

  // Data members
  libMesh::MeshBase* m_; //!< pointer to libMesh MeshBase instance, always set
                         //!< during intialization
  vector<unique_ptr<libMesh::PointLocatorBase>>
    pl_;                      //!< per-thread point locators
  libMesh::BoundingBox bbox_; //!< bounding box of the mesh

private:
  // Methods
  void initialize() override;
  void set_mesh_pointer_from_filename(const std::string& filename);
  void build_eqn_sys();

  // Data members
  unique_ptr<libMesh::MeshBase> unique_m_ =
    nullptr; //!< pointer to the libMesh MeshBase instance, only used if mesh is
             //!< created inside OpenMC
  unique_ptr<libMesh::EquationSystems>
    equation_systems_; //!< pointer to the libMesh EquationSystems
                       //!< instance
  std::string
    eq_system_name_; //!< name of the equation system holding OpenMC results
  std::unordered_map<std::string, unsigned int>
    variable_map_; //!< mapping of variable names (tally scores) to libMesh
                   //!< variable numbers
  libMesh::dof_id_type
    first_element_id_; //!< id of the first element in the mesh
};

class AdaptiveLibMesh : public LibMesh {
public:
  // Constructor
  AdaptiveLibMesh(libMesh::MeshBase& input_mesh, double length_multiplier = 1.0,
    const std::set<libMesh::subdomain_id_type>& block_ids =
      std::set<libMesh::subdomain_id_type>());

  // Overridden methods
  int n_bins() const override;

  void add_score(const std::string& var_name) override;

  void set_score_data(const std::string& var_name, const vector<double>& values,
    const vector<double>& std_dev) override;

  void write(const std::string& filename) const override;

  int get_bin(Position r) const override;

protected:
  // Overridden methods
  int get_bin_from_element(const libMesh::Elem* elem) const override;

  const libMesh::Elem& get_element_from_bin(int bin) const override;

private:
  // Data members
  const std::set<libMesh::subdomain_id_type>
    block_ids_;               //!< subdomains of the mesh to tally on
  const bool block_restrict_; //!< whether a subset of the mesh is being used
  const libMesh::dof_id_type num_active_; //!< cached number of active elements

  std::vector<libMesh::dof_id_type>
    bin_to_elem_map_; //!< mapping bin indices to dof indices for active
                      //!< elements
  std::vector<int> elem_to_bin_map_; //!< mapping dof indices to bin indices for
                                     //!< active elements
};

#endif

//==============================================================================
// Non-member functions
//==============================================================================

//! Read meshes from either settings/tallies
//
//! \param[in] root XML node
void read_meshes(pugi::xml_node root);

//! Read meshes from an HDF5 file
//
//! \param[in] group HDF5 group ("meshes" group)
void read_meshes(hid_t group);

//! Write mesh data to an HDF5 group
//
//! \param[in] group HDF5 group
void meshes_to_hdf5(hid_t group);

void free_memory_mesh();

} // namespace openmc

#endif // OPENMC_MESH_H