XFEM.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#include "XFEM.h"
 
// XFEM includes
#include "XFEMAppTypes.h"
#include "XFEMCutElem2D.h"
#include "XFEMCutElem3D.h"
#include "XFEMFuncs.h"
#include "EFANode.h"
#include "EFAEdge.h"
#include "EFAFace.h"
#include "EFAFragment2D.h"
#include "EFAFragment3D.h"
#include "EFAFuncs.h"
 
// MOOSE includes
#include "AuxiliarySystem.h"
#include "MooseVariable.h"
#include "NonlinearSystem.h"
#include "FEProblem.h"
#include "Assembly.h"
#include "MooseUtils.h"
#include "MaterialPropertyStorage.h"
 
#include "libmesh/mesh_communication.h"
#include "libmesh/partitioner.h"
 
XFEM::XFEM(const InputParameters & params)
  : XFEMInterface(params),
    _state_marked_t_step(0),
    _efa_mesh(Moose::out),
    _debug_output_level(1),
    _min_weight_multiplier(0.0)
{
#ifndef LIBMESH_ENABLE_UNIQUE_ID
  mooseError("MOOSE requires unique ids to be enabled in libmesh (configure with "
             "--enable-unique-id) to use XFEM!");
#endif
  _has_secondary_cut = false;
}
 
XFEM::~XFEM()
{
  for (std::map<unique_id_type, XFEMCutElem *>::iterator cemit = _cut_elem_map.begin();
       cemit != _cut_elem_map.end();
       ++cemit)
    delete cemit->second;
}
 
void
XFEM::addGeometricCut(GeometricCutUserObject * geometric_cut)
{
  _geometric_cuts.push_back(geometric_cut);
 
  geometric_cut->setInterfaceID(_geometric_cuts.size() - 1);
 
  _geom_marker_id_map[geometric_cut] = _geometric_cuts.size() - 1;
}
 
void
XFEM::getCrackTipOrigin(std::map<unsigned int, const Elem *> & elem_id_crack_tip,
                        std::vector<Point> & crack_front_points)
{
  elem_id_crack_tip.clear();
  crack_front_points.clear();
  crack_front_points.resize(_elem_crack_origin_direction_map.size());
 
  unsigned int crack_tip_index = 0;
  // This map is used to sort the order in _elem_crack_origin_direction_map such that every process
  // has same order
  std::map<unsigned int, const Elem *> elem_id_map;
 
  int m = -1;
  for (std::map<const Elem *, std::vector<Point>>::iterator mit1 =
           _elem_crack_origin_direction_map.begin();
       mit1 != _elem_crack_origin_direction_map.end();
       ++mit1)
  {
    unsigned int elem_id = mit1->first->id();
    if (elem_id == std::numeric_limits<unsigned int>::max())
    {
      elem_id_map[m] = mit1->first;
      m--;
    }
    else
      elem_id_map[elem_id] = mit1->first;
  }
 
  for (std::map<unsigned int, const Elem *>::iterator mit1 = elem_id_map.begin();
       mit1 != elem_id_map.end();
       mit1++)
  {
    const Elem * elem = mit1->second;
    std::map<const Elem *, std::vector<Point>>::iterator mit2 =
        _elem_crack_origin_direction_map.find(elem);
    if (mit2 != _elem_crack_origin_direction_map.end())
    {
      elem_id_crack_tip[crack_tip_index] = mit2->first;
      crack_front_points[crack_tip_index] =
          (mit2->second)[0]; // [0] stores origin coordinates and [1] stores direction
      crack_tip_index++;
    }
  }
}
 
void
XFEM::addStateMarkedElem(unsigned int elem_id, RealVectorValue & normal)
{
  Elem * elem = _mesh->elem_ptr(elem_id);
  std::map<const Elem *, RealVectorValue>::iterator mit;
  mit = _state_marked_elems.find(elem);
  if (mit != _state_marked_elems.end())
    mooseError(" ERROR: element ", elem->id(), " already marked for crack growth.");
  _state_marked_elems[elem] = normal;
  _state_marked_t_step = _fe_problem->timeStep();
}
 
void
XFEM::addStateMarkedElem(unsigned int elem_id, RealVectorValue & normal, unsigned int marked_side)
{
  addStateMarkedElem(elem_id, normal);
  Elem * elem = _mesh->elem_ptr(elem_id);
  std::map<const Elem *, unsigned int>::iterator mit;
  mit = _state_marked_elem_sides.find(elem);
  if (mit != _state_marked_elem_sides.end())
    mooseError(" ERROR: side of element ", elem->id(), " already marked for crack initiation.");
 
  _state_marked_elem_sides[elem] = marked_side;
}
 
void
XFEM::addStateMarkedFrag(unsigned int elem_id, RealVectorValue & normal)
{
  addStateMarkedElem(elem_id, normal);
  Elem * elem = _mesh->elem_ptr(elem_id);
  std::set<const Elem *>::iterator mit;
  mit = _state_marked_frags.find(elem);
  if (mit != _state_marked_frags.end())
    mooseError(
        " ERROR: element ", elem->id(), " already marked for fragment-secondary crack initiation.");
 
  _state_marked_frags.insert(elem);
}
 
void
XFEM::clearStateMarkedElems()
{
  _state_marked_elems.clear();
  _state_marked_frags.clear();
  _state_marked_elem_sides.clear();
}
 
void
XFEM::addGeomMarkedElem2D(const unsigned int elem_id,
                          const Xfem::GeomMarkedElemInfo2D geom_info,
                          const unsigned int interface_id)
{
  Elem * elem = _mesh->elem_ptr(elem_id);
  _geom_marked_elems_2d[elem].push_back(geom_info);
  _geom_marker_id_elems[interface_id].insert(elem_id);
}
 
void
XFEM::addGeomMarkedElem3D(const unsigned int elem_id,
                          const Xfem::GeomMarkedElemInfo3D geom_info,
                          const unsigned int interface_id)
{
  Elem * elem = _mesh->elem_ptr(elem_id);
  _geom_marked_elems_3d[elem].push_back(geom_info);
  _geom_marker_id_elems[interface_id].insert(elem_id);
}
 
void
XFEM::clearGeomMarkedElems()
{
  _geom_marked_elems_2d.clear();
  _geom_marked_elems_3d.clear();
}
 
void
XFEM::storeCrackTipOriginAndDirection()
{
  _elem_crack_origin_direction_map.clear();
  std::set<EFAElement *> CrackTipElements = _efa_mesh.getCrackTipElements();
  std::set<EFAElement *>::iterator sit;
  for (sit = CrackTipElements.begin(); sit != CrackTipElements.end(); ++sit)
  {
    if (_mesh->mesh_dimension() == 2)
    {
      EFAElement2D * CEMElem = dynamic_cast<EFAElement2D *>(*sit);
      EFANode * tip_node = CEMElem->getTipEmbeddedNode();
      unsigned int cts_id = CEMElem->getCrackTipSplitElementID();
 
      Point origin(0, 0, 0);
      Point direction(0, 0, 0);
 
      std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
      it = _cut_elem_map.find(_mesh->elem_ptr(cts_id)->unique_id());
      if (it != _cut_elem_map.end())
      {
        const XFEMCutElem * xfce = it->second;
        const EFAElement * EFAelem = xfce->getEFAElement();
        if (EFAelem->isPartial()) // exclude the full crack tip elements
        {
          xfce->getCrackTipOriginAndDirection(tip_node->id(), origin, direction);
        }
      }
 
      std::vector<Point> tip_data;
      tip_data.push_back(origin);
      tip_data.push_back(direction);
      const Elem * elem = _mesh->elem_ptr((*sit)->id());
      _elem_crack_origin_direction_map.insert(
          std::pair<const Elem *, std::vector<Point>>(elem, tip_data));
    }
  }
}
 
bool
XFEM::updateHeal()
{
  bool mesh_changed = false;
 
  mesh_changed = healMesh();
 
  if (mesh_changed)
    buildEFAMesh();
 
  if (mesh_changed)
  {
    _mesh->update_parallel_id_counts();
    libMesh::MeshCommunication().make_elems_parallel_consistent(*_mesh);
    libMesh::MeshCommunication().make_nodes_parallel_consistent(*_mesh);
    //    _mesh->find_neighbors();
    //    _mesh->contract();
    _mesh->allow_renumbering(false);
    _mesh->skip_partitioning(true);
    _mesh->prepare_for_use();
 
    if (_displaced_mesh)
    {
      _displaced_mesh->update_parallel_id_counts();
      libMesh::MeshCommunication().make_elems_parallel_consistent(*_displaced_mesh);
      libMesh::MeshCommunication().make_nodes_parallel_consistent(*_displaced_mesh);
      _displaced_mesh->allow_renumbering(false);
      _displaced_mesh->skip_partitioning(true);
      _displaced_mesh->prepare_for_use();
    }
  }
 
  _geom_marker_id_elems.clear();
 
  return mesh_changed;
}
 
bool
XFEM::update(Real time,
             const std::vector<std::shared_ptr<NonlinearSystemBase>> & nl,
             AuxiliarySystem & aux)
{
  if (_moose_mesh->isDistributedMesh())
    mooseError("Use of XFEM with distributed mesh is not yet supported");
 
  for (const auto & elem : _mesh->active_element_ptr_range())
    if (elem->level() > 0)
      mooseError("XFEM does not currently support mesh adaptivity or adaptively refined meshes");
 
  bool mesh_changed = false;
 
  if (!_state_marked_elems.empty() && _state_marked_t_step == _fe_problem->timeStep())
    clearStateMarkedElems();
 
  buildEFAMesh();
 
  _fe_problem->execute(EXEC_XFEM_MARK);
 
  storeCrackTipOriginAndDirection();
 
  if (markCuts(time))
    mesh_changed = cutMeshWithEFA(nl, aux);
 
  if (mesh_changed)
  {
    buildEFAMesh();
    storeCrackTipOriginAndDirection();
  }
 
  if (mesh_changed)
  {
    _mesh->allow_renumbering(false);
    _mesh->skip_partitioning(true);
    _mesh->prepare_for_use();
 
    if (_displaced_mesh)
    {
      _displaced_mesh->allow_renumbering(false);
      _displaced_mesh->skip_partitioning(true);
      _displaced_mesh->prepare_for_use();
    }
  }
 
  clearStateMarkedElems();
  clearGeomMarkedElems();
 
  return mesh_changed;
}
 
void
XFEM::initSolution(const std::vector<std::shared_ptr<NonlinearSystemBase>> & nls,
                   AuxiliarySystem & aux)
{
  if (nls.size() != 1)
    mooseError("XFEM does not currently support multiple nonlinear systems");
 
  nls[0]->serializeSolution();
  aux.serializeSolution();
  NumericVector<Number> & current_solution = *nls[0]->system().current_local_solution;
  NumericVector<Number> & old_solution = nls[0]->solutionOld();
  NumericVector<Number> & older_solution = nls[0]->solutionOlder();
  NumericVector<Number> & current_aux_solution = *aux.system().current_local_solution;
  NumericVector<Number> & old_aux_solution = aux.solutionOld();
  NumericVector<Number> & older_aux_solution = aux.solutionOlder();
 
  setSolution(*nls[0], _cached_solution, current_solution, old_solution, older_solution);
  setSolution(
      aux, _cached_aux_solution, current_aux_solution, old_aux_solution, older_aux_solution);
 
  current_solution.close();
  old_solution.close();
  older_solution.close();
  current_aux_solution.close();
  old_aux_solution.close();
  older_aux_solution.close();
 
  _cached_solution.clear();
  _cached_aux_solution.clear();
}
 
void
XFEM::buildEFAMesh()
{
  _efa_mesh.reset();
 
  // Load all existing elements in to EFA mesh
  for (auto & elem : _mesh->element_ptr_range())
  {
    std::vector<unsigned int> quad;
    for (unsigned int i = 0; i < elem->n_nodes(); ++i)
      quad.push_back(elem->node_id(i));
 
    if (_mesh->mesh_dimension() == 2)
      _efa_mesh.add2DElement(quad, elem->id());
    else if (_mesh->mesh_dimension() == 3)
      _efa_mesh.add3DElement(quad, elem->id());
    else
      mooseError("XFEM only works for 2D and 3D");
  }
 
  // Restore fragment information for elements that have been previously cut
  for (auto & elem : _mesh->element_ptr_range())
  {
    std::map<unique_id_type, XFEMCutElem *>::iterator cemit = _cut_elem_map.find(elem->unique_id());
    if (cemit != _cut_elem_map.end())
    {
      XFEMCutElem * xfce = cemit->second;
      EFAElement * CEMElem = _efa_mesh.getElemByID(elem->id());
      _efa_mesh.restoreFragmentInfo(CEMElem, xfce->getEFAElement());
    }
  }
 
  // Must update edge neighbors before restore edge intersections. Otherwise, when we
  // add edge intersections, we do not have neighbor information to use.
  // Correction: no need to use neighbor info now
  _efa_mesh.updateEdgeNeighbors();
  _efa_mesh.initCrackTipTopology();
}
 
bool
XFEM::markCuts(Real time)
{
  bool marked_sides = false;
  if (_mesh->mesh_dimension() == 2)
  {
    marked_sides = markCutEdgesByGeometry();
    marked_sides |= markCutEdgesByState(time);
  }
  else if (_mesh->mesh_dimension() == 3)
  {
    marked_sides = markCutFacesByGeometry();
    marked_sides |= markCutFacesByState();
  }
  return marked_sides;
}
 
bool
XFEM::markCutEdgesByGeometry()
{
  bool marked_edges = false;
  bool marked_nodes = false;
 
  for (const auto & gme : _geom_marked_elems_2d)
  {
    for (const auto & gmei : gme.second)
    {
      EFAElement2D * EFAElem = getEFAElem2D(gme.first);
 
      for (unsigned int i = 0; i < gmei._elem_cut_edges.size(); ++i) // mark element edges
      {
        if (!EFAElem->isEdgePhantom(
                gmei._elem_cut_edges[i]._host_side_id)) // must not be phantom edge
        {
          _efa_mesh.addElemEdgeIntersection(gme.first->id(),
                                            gmei._elem_cut_edges[i]._host_side_id,
                                            gmei._elem_cut_edges[i]._distance);
          marked_edges = true;
        }
      }
 
      for (unsigned int i = 0; i < gmei._elem_cut_nodes.size(); ++i) // mark element edges
      {
        _efa_mesh.addElemNodeIntersection(gme.first->id(), gmei._elem_cut_nodes[i]._host_id);
        marked_nodes = true;
      }
 
      for (unsigned int i = 0; i < gmei._frag_cut_edges.size();
           ++i) // MUST DO THIS AFTER MARKING ELEMENT EDGES
      {
        if (!EFAElem->getFragment(0)->isSecondaryInteriorEdge(
                gmei._frag_cut_edges[i]._host_side_id))
        {
          if (_efa_mesh.addFragEdgeIntersection(gme.first->id(),
                                                gmei._frag_cut_edges[i]._host_side_id,
                                                gmei._frag_cut_edges[i]._distance))
          {
            marked_edges = true;
            if (!isElemAtCrackTip(gme.first))
              _has_secondary_cut = true;
          }
        }
      }
    }
  }
 
  return marked_edges || marked_nodes;
}
 
void
XFEM::correctCrackExtensionDirection(const Elem * elem,
                                     EFAElement2D * CEMElem,
                                     EFAEdge * orig_edge,
                                     Point normal,
                                     Point crack_tip_origin,
                                     Point crack_tip_direction,
                                     Real & distance_keep,
                                     unsigned int & edge_id_keep,
                                     Point & normal_keep)
{
  std::vector<Point> edge_ends(2, Point(0.0, 0.0, 0.0));
  Point edge1(0.0, 0.0, 0.0);
  Point edge2(0.0, 0.0, 0.0);
  Point left_angle(0.0, 0.0, 0.0);
  Point right_angle(0.0, 0.0, 0.0);
  Point left_angle_normal(0.0, 0.0, 0.0);
  Point right_angle_normal(0.0, 0.0, 0.0);
  Point crack_direction_normal(0.0, 0.0, 0.0);
  Point edge1_to_tip(0.0, 0.0, 0.0);
  Point edge2_to_tip(0.0, 0.0, 0.0);
  Point edge1_to_tip_normal(0.0, 0.0, 0.0);
  Point edge2_to_tip_normal(0.0, 0.0, 0.0);
 
  Real cos_45 = std::cos(45.0 / 180.0 * 3.14159);
  Real sin_45 = std::sin(45.0 / 180.0 * 3.14159);
 
  left_angle(0) = cos_45 * crack_tip_direction(0) - sin_45 * crack_tip_direction(1);
  left_angle(1) = sin_45 * crack_tip_direction(0) + cos_45 * crack_tip_direction(1);
 
  right_angle(0) = cos_45 * crack_tip_direction(0) + sin_45 * crack_tip_direction(1);
  right_angle(1) = -sin_45 * crack_tip_direction(0) + cos_45 * crack_tip_direction(1);
 
  left_angle_normal(0) = -left_angle(1);
  left_angle_normal(1) = left_angle(0);
 
  right_angle_normal(0) = -right_angle(1);
  right_angle_normal(1) = right_angle(0);
 
  crack_direction_normal(0) = -crack_tip_direction(1);
  crack_direction_normal(1) = crack_tip_direction(0);
 
  Real angle_min = 0.0;
  Real distance = 0.0;
  unsigned int nsides = CEMElem->numEdges();
 
  for (unsigned int i = 0; i < nsides; ++i)
  {
    if (!orig_edge->isPartialOverlap(*CEMElem->getEdge(i)))
    {
      edge_ends[0] = getEFANodeCoords(CEMElem->getEdge(i)->getNode(0), CEMElem, elem);
      edge_ends[1] = getEFANodeCoords(CEMElem->getEdge(i)->getNode(1), CEMElem, elem);
 
      edge1_to_tip = (edge_ends[0] * 0.95 + edge_ends[1] * 0.05) - crack_tip_origin;
      edge2_to_tip = (edge_ends[0] * 0.05 + edge_ends[1] * 0.95) - crack_tip_origin;
 
      edge1_to_tip /= pow(edge1_to_tip.norm_sq(), 0.5);
      edge2_to_tip /= pow(edge2_to_tip.norm_sq(), 0.5);
 
      edge1_to_tip_normal(0) = -edge1_to_tip(1);
      edge1_to_tip_normal(1) = edge1_to_tip(0);
 
      edge2_to_tip_normal(0) = -edge2_to_tip(1);
      edge2_to_tip_normal(1) = edge2_to_tip(0);
 
      Real angle_edge1_normal = edge1_to_tip_normal * normal;
      Real angle_edge2_normal = edge2_to_tip_normal * normal;
 
      if (std::abs(angle_edge1_normal) > std::abs(angle_min) &&
          (edge1_to_tip * crack_tip_direction) > std::cos(45.0 / 180.0 * 3.14159))
      {
        edge_id_keep = i;
        distance_keep = 0.05;
        normal_keep = edge1_to_tip_normal;
        angle_min = angle_edge1_normal;
      }
      else if (std::abs(angle_edge2_normal) > std::abs(angle_min) &&
               (edge2_to_tip * crack_tip_direction) > std::cos(45.0 / 180.0 * 3.14159))
      {
        edge_id_keep = i;
        distance_keep = 0.95;
        normal_keep = edge2_to_tip_normal;
        angle_min = angle_edge2_normal;
      }
 
      if (initCutIntersectionEdge(
              crack_tip_origin, left_angle_normal, edge_ends[0], edge_ends[1], distance) &&
          (!CEMElem->isEdgePhantom(i)))
      {
        if (std::abs(left_angle_normal * normal) > std::abs(angle_min) &&
            (edge1_to_tip * crack_tip_direction) > std::cos(45.0 / 180.0 * 3.14159))
        {
          edge_id_keep = i;
          distance_keep = distance;
          normal_keep = left_angle_normal;
          angle_min = left_angle_normal * normal;
        }
      }
      else if (initCutIntersectionEdge(
                   crack_tip_origin, right_angle_normal, edge_ends[0], edge_ends[1], distance) &&
               (!CEMElem->isEdgePhantom(i)))
      {
        if (std::abs(right_angle_normal * normal) > std::abs(angle_min) &&
            (edge2_to_tip * crack_tip_direction) > std::cos(45.0 / 180.0 * 3.14159))
        {
          edge_id_keep = i;
          distance_keep = distance;
          normal_keep = right_angle_normal;
          angle_min = right_angle_normal * normal;
        }
      }
      else if (initCutIntersectionEdge(crack_tip_origin,
                                       crack_direction_normal,
                                       edge_ends[0],
                                       edge_ends[1],
                                       distance) &&
               (!CEMElem->isEdgePhantom(i)))
      {
        if (std::abs(crack_direction_normal * normal) > std::abs(angle_min) &&
            (crack_tip_direction * crack_tip_direction) > std::cos(45.0 / 180.0 * 3.14159))
        {
          edge_id_keep = i;
          distance_keep = distance;
          normal_keep = crack_direction_normal;
          angle_min = crack_direction_normal * normal;
        }
      }
    }
  }
 
  // avoid small volume fraction cut
  if ((distance_keep - 0.05) < 0.0)
  {
    distance_keep = 0.05;
  }
  else if ((distance_keep - 0.95) > 0.0)
  {
    distance_keep = 0.95;
  }
}
 
bool
XFEM::markCutEdgesByState(Real time)
{
  bool marked_edges = false;
  for (std::map<const Elem *, RealVectorValue>::iterator pmeit = _state_marked_elems.begin();
       pmeit != _state_marked_elems.end();
       ++pmeit)
  {
    const Elem * elem = pmeit->first;
    RealVectorValue normal = pmeit->second;
    EFAElement2D * CEMElem = getEFAElem2D(elem);
 
    Real volfrac_elem = getPhysicalVolumeFraction(elem);
    if (volfrac_elem < 0.25)
      continue;
 
    // continue if elem is already cut twice - IMPORTANT
    if (CEMElem->isFinalCut())
      continue;
 
    // find the first cut edge
    unsigned int nsides = CEMElem->numEdges();
    unsigned int orig_cut_side_id = std::numeric_limits<unsigned int>::max();
    Real orig_cut_distance = -1.0;
    EFANode * orig_node = nullptr;
    EFAEdge * orig_edge = nullptr;
 
    // crack tip origin coordinates and direction
    Point crack_tip_origin(0, 0, 0);
    Point crack_tip_direction(0, 0, 0);
 
    if (isElemAtCrackTip(elem)) // crack tip element's crack intiation
    {
      orig_cut_side_id = CEMElem->getTipEdgeID();
      if (orig_cut_side_id < nsides) // valid crack-tip edge found
      {
        orig_edge = CEMElem->getEdge(orig_cut_side_id);
        orig_node = CEMElem->getTipEmbeddedNode();
      }
      else
        mooseError("element ", elem->id(), " has no valid crack-tip edge");
 
      // obtain the crack tip origin coordinates and direction.
      std::map<const Elem *, std::vector<Point>>::iterator ecodm =
          _elem_crack_origin_direction_map.find(elem);
      if (ecodm != _elem_crack_origin_direction_map.end())
      {
        crack_tip_origin = (ecodm->second)[0];
        crack_tip_direction = (ecodm->second)[1];
      }
      else
        mooseError("element ", elem->id(), " cannot find its crack tip origin and direction.");
    }
    else
    {
      std::map<const Elem *, unsigned int>::iterator mit1;
      mit1 = _state_marked_elem_sides.find(elem);
      std::set<const Elem *>::iterator mit2;
      mit2 = _state_marked_frags.find(elem);
 
      if (mit1 != _state_marked_elem_sides.end()) // specified boundary crack initiation
      {
        orig_cut_side_id = mit1->second;
        if (!CEMElem->isEdgePhantom(orig_cut_side_id) &&
            !CEMElem->getEdge(orig_cut_side_id)->hasIntersection())
        {
          orig_cut_distance = 0.5;
          _efa_mesh.addElemEdgeIntersection(elem->id(), orig_cut_side_id, orig_cut_distance);
          orig_edge = CEMElem->getEdge(orig_cut_side_id);
          orig_node = orig_edge->getEmbeddedNode(0);
          // get a virtual crack tip direction
          Point elem_center(0.0, 0.0, 0.0);
          Point edge_center;
          for (unsigned int i = 0; i < nsides; ++i)
          {
            elem_center += getEFANodeCoords(CEMElem->getEdge(i)->getNode(0), CEMElem, elem);
            elem_center += getEFANodeCoords(CEMElem->getEdge(i)->getNode(1), CEMElem, elem);
          }
          elem_center /= nsides * 2.0;
          edge_center = getEFANodeCoords(orig_edge->getNode(0), CEMElem, elem) +
                        getEFANodeCoords(orig_edge->getNode(1), CEMElem, elem);
          edge_center /= 2.0;
          crack_tip_origin = edge_center;
          crack_tip_direction = elem_center - edge_center;
          crack_tip_direction /= pow(crack_tip_direction.norm_sq(), 0.5);
        }
        else
          continue; // skip this elem if specified boundary edge is phantom
      }
      else if (mit2 != _state_marked_frags.end()) // cut-surface secondary crack initiation
      {
        if (CEMElem->numFragments() != 1)
          mooseError("element ",
                     elem->id(),
                     " flagged for a secondary crack, but has ",
                     CEMElem->numFragments(),
                     " fragments");
        std::vector<unsigned int> interior_edge_id = CEMElem->getFragment(0)->getInteriorEdgeID();
        if (interior_edge_id.size() == 1)
          orig_cut_side_id = interior_edge_id[0];
        else
          continue; // skip this elem if more than one interior edges found (i.e. elem's been cut
                    // twice)
        orig_cut_distance = 0.5;
        _efa_mesh.addFragEdgeIntersection(elem->id(), orig_cut_side_id, orig_cut_distance);
        orig_edge = CEMElem->getFragmentEdge(0, orig_cut_side_id);
        orig_node = orig_edge->getEmbeddedNode(0); // must be an interior embedded node
        Point elem_center(0.0, 0.0, 0.0);
        Point edge_center;
        unsigned int nsides_frag = CEMElem->getFragment(0)->numEdges();
        for (unsigned int i = 0; i < nsides_frag; ++i)
        {
          elem_center +=
              getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(0), CEMElem, elem);
          elem_center +=
              getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(1), CEMElem, elem);
        }
        elem_center /= nsides_frag * 2.0;
        edge_center = getEFANodeCoords(orig_edge->getNode(0), CEMElem, elem) +
                      getEFANodeCoords(orig_edge->getNode(1), CEMElem, elem);
        edge_center /= 2.0;
        crack_tip_origin = edge_center;
        crack_tip_direction = elem_center - edge_center;
        crack_tip_direction /= pow(crack_tip_direction.norm_sq(), 0.5);
      }
      else
        mooseError("element ",
                   elem->id(),
                   " flagged for state-based growth, but has no edge intersections");
    }
 
    Point cut_origin(0.0, 0.0, 0.0);
    if (orig_node)
      cut_origin = getEFANodeCoords(orig_node, CEMElem, elem); // cutting plane origin's coords
    else
      mooseError("element ", elem->id(), " does not have valid orig_node");
 
    // loop through element edges to add possible second cut points
    std::vector<Point> edge_ends(2, Point(0.0, 0.0, 0.0));
    Point edge1(0.0, 0.0, 0.0);
    Point edge2(0.0, 0.0, 0.0);
    Point cut_edge_point(0.0, 0.0, 0.0);
    bool find_compatible_direction = false;
    unsigned int edge_id_keep = 0;
    Real distance_keep = 0.0;
    Point normal_keep(0.0, 0.0, 0.0);
    Real distance = 0.0;
    bool edge_cut = false;
 
    for (unsigned int i = 0; i < nsides; ++i)
    {
      if (!orig_edge->isPartialOverlap(*CEMElem->getEdge(i)))
      {
        edge_ends[0] = getEFANodeCoords(CEMElem->getEdge(i)->getNode(0), CEMElem, elem);
        edge_ends[1] = getEFANodeCoords(CEMElem->getEdge(i)->getNode(1), CEMElem, elem);
        if ((initCutIntersectionEdge(
                 crack_tip_origin, normal, edge_ends[0], edge_ends[1], distance) &&
             (!CEMElem->isEdgePhantom(i))))
        {
          cut_edge_point = distance * edge_ends[1] + (1.0 - distance) * edge_ends[0];
          distance_keep = distance;
          edge_id_keep = i;
          normal_keep = normal;
          edge_cut = true;
          break;
        }
      }
    }
 
    Point between_two_cuts = (cut_edge_point - crack_tip_origin);
    between_two_cuts /= pow(between_two_cuts.norm_sq(), 0.5);
    Real angle_between_two_cuts = between_two_cuts * crack_tip_direction;
 
    if (angle_between_two_cuts > std::cos(45.0 / 180.0 * 3.14159)) // original cut direction is good
      find_compatible_direction = true;
 
    if (!find_compatible_direction && edge_cut)
      correctCrackExtensionDirection(elem,
                                     CEMElem,
                                     orig_edge,
                                     normal,
                                     crack_tip_origin,
                                     crack_tip_direction,
                                     distance_keep,
                                     edge_id_keep,
                                     normal_keep);
 
    if (edge_cut)
    {
      if (!_use_crack_growth_increment)
        _efa_mesh.addElemEdgeIntersection(elem->id(), edge_id_keep, distance_keep);
      else
      {
        Point growth_direction(0.0, 0.0, 0.0);
 
        growth_direction(0) = -normal_keep(1);
        growth_direction(1) = normal_keep(0);
 
        if (growth_direction * crack_tip_direction < 1.0e-10)
          growth_direction *= (-1.0);
 
        Real x0 = crack_tip_origin(0);
        Real y0 = crack_tip_origin(1);
        Real x1 = x0 + _crack_growth_increment * growth_direction(0);
        Real y1 = y0 + _crack_growth_increment * growth_direction(1);
 
        XFEMCrackGrowthIncrement2DCut geometric_cut(x0, y0, x1, y1, time * 0.9, time * 0.9);
 
        for (const auto & elem : _mesh->element_ptr_range())
        {
          std::vector<CutEdgeForCrackGrowthIncr> elem_cut_edges;
          EFAElement2D * CEMElem = getEFAElem2D(elem);
 
          // continue if elem has been already cut twice - IMPORTANT
          if (CEMElem->isFinalCut())
            continue;
 
          // mark cut edges for the element and its fragment
          geometric_cut.cutElementByCrackGrowthIncrement(elem, elem_cut_edges, time);
 
          for (unsigned int i = 0; i < elem_cut_edges.size(); ++i) // mark element edges
          {
            if (!CEMElem->isEdgePhantom(
                    elem_cut_edges[i]._host_side_id)) // must not be phantom edge
            {
              _efa_mesh.addElemEdgeIntersection(
                  elem->id(), elem_cut_edges[i]._host_side_id, elem_cut_edges[i]._distance);
            }
          }
        }
      }
    }
    // loop though framgent boundary edges to add possible second cut points
    // N.B. must do this after marking element edges
    if (CEMElem->numFragments() > 0 && !edge_cut)
    {
      for (unsigned int i = 0; i < CEMElem->getFragment(0)->numEdges(); ++i)
      {
        if (!orig_edge->isPartialOverlap(*CEMElem->getFragmentEdge(0, i)))
        {
          edge_ends[0] =
              getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(0), CEMElem, elem);
          edge_ends[1] =
              getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(1), CEMElem, elem);
          if (initCutIntersectionEdge(
                  crack_tip_origin, normal, edge_ends[0], edge_ends[1], distance) &&
              (!CEMElem->getFragment(0)->isSecondaryInteriorEdge(i)))
          {
            if (_efa_mesh.addFragEdgeIntersection(elem->id(), edge_id_keep, distance_keep))
              if (!isElemAtCrackTip(elem))
                _has_secondary_cut = true;
            break;
          }
        }
      }
    }
 
    marked_edges = true;
 
  } // loop over all state_marked_elems
 
  return marked_edges;
}
 
bool
XFEM::markCutFacesByGeometry()
{
  bool marked_faces = false;
 
  for (const auto & gme : _geom_marked_elems_3d)
  {
    for (const auto & gmei : gme.second)
    {
      EFAElement3D * EFAElem = getEFAElem3D(gme.first);
 
      for (unsigned int i = 0; i < gmei._elem_cut_faces.size(); ++i) // mark element faces
      {
        if (!EFAElem->isFacePhantom(gmei._elem_cut_faces[i]._face_id)) // must not be phantom face
        {
          _efa_mesh.addElemFaceIntersection(gme.first->id(),
                                            gmei._elem_cut_faces[i]._face_id,
                                            gmei._elem_cut_faces[i]._face_edge,
                                            gmei._elem_cut_faces[i]._position);
          marked_faces = true;
        }
      }
 
      for (unsigned int i = 0; i < gmei._frag_cut_faces.size();
           ++i) // MUST DO THIS AFTER MARKING ELEMENT EDGES
      {
        if (!EFAElem->getFragment(0)->isThirdInteriorFace(gmei._frag_cut_faces[i]._face_id))
        {
          _efa_mesh.addFragFaceIntersection(gme.first->id(),
                                            gmei._frag_cut_faces[i]._face_id,
                                            gmei._frag_cut_faces[i]._face_edge,
                                            gmei._frag_cut_faces[i]._position);
          marked_faces = true;
        }
      }
    }
  }
 
  return marked_faces;
}
 
bool
XFEM::markCutFacesByState()
{
  bool marked_faces = false;
  // TODO: need to finish this for 3D problems
  return marked_faces;
}
 
bool
XFEM::initCutIntersectionEdge(
    Point cut_origin, RealVectorValue cut_normal, Point & edge_p1, Point & edge_p2, Real & dist)
{
  dist = 0.0;
  bool does_intersect = false;
  Point origin2p1 = edge_p1 - cut_origin;
  Real plane2p1 = cut_normal(0) * origin2p1(0) + cut_normal(1) * origin2p1(1);
  Point origin2p2 = edge_p2 - cut_origin;
  Real plane2p2 = cut_normal(0) * origin2p2(0) + cut_normal(1) * origin2p2(1);
 
  if (plane2p1 * plane2p2 < 0.0)
  {
    dist = -plane2p1 / (plane2p2 - plane2p1);
    does_intersect = true;
  }
  return does_intersect;
}
 
bool
XFEM::healMesh()
{
  bool mesh_changed = false;
 
  std::set<Node *> nodes_to_delete;
  std::set<Node *> nodes_to_delete_displaced;
  std::set<unsigned int> cutelems_to_delete;
  unsigned int deleted_elem_count = 0;
  std::vector<std::string> healed_geometric_cuts;
 
  for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
  {
    if (_geometric_cuts[i]->shouldHealMesh())
    {
      healed_geometric_cuts.push_back(_geometric_cuts[i]->name());
      for (auto & it : _sibling_elems[_geometric_cuts[i]->getInterfaceID()])
      {
        Elem * elem1 = const_cast<Elem *>(it.first);
        Elem * elem2 = const_cast<Elem *>(it.second);
 
        std::map<unique_id_type, XFEMCutElem *>::iterator cemit =
            _cut_elem_map.find(elem1->unique_id());
        if (cemit != _cut_elem_map.end())
        {
          const XFEMCutElem * xfce = cemit->second;
 
          cutelems_to_delete.insert(elem1->unique_id());
 
          for (unsigned int in = 0; in < elem1->n_nodes(); ++in)
          {
            Node * e1node = elem1->node_ptr(in);
            Node * e2node = elem2->node_ptr(in);
            if (!xfce->isPointPhysical(*e1node) &&
                e1node != e2node) // This would happen at the crack tip
            {
              elem1->set_node(in, e2node);
              nodes_to_delete.insert(e1node);
            }
            else if (e1node != e2node)
              nodes_to_delete.insert(e2node);
          }
        }
        else
          mooseError("Could not find XFEMCutElem for element to be kept in healing");
 
        // Store the material properties of the elements to be healed. So that if the element is
        // immediately re-cut, we can restore the material properties (especially those stateful
        // ones).
        std::vector<const Elem *> healed_elems = {elem1, elem2};
 
        if (_geometric_cuts[i]->shouldHealMesh())
          // If the parent element will not be re-cut, then all of its nodes must have the same
          // CutSubdomainID. Therefore, just query the first node in this parent element to
          // get its CutSubdomainID.
          for (auto e : healed_elems)
            if (elem1->processor_id() == _mesh->processor_id() &&
                e->processor_id() == _mesh->processor_id())
            {
              storeMaterialPropertiesForElement(/*parent_elem = */ elem1, /*child_elem = */ e);
              // In case the healed element is not re-cut, copy the corresponding material
              // properties to the parent element now than later.
              CutSubdomainID parent_gcsid =
                  _geometric_cuts[i]->getCutSubdomainID(elem1->node_ptr(0));
              CutSubdomainID gcsid = _geom_cut_elems[e]._cut_subdomain_id;
              if (parent_gcsid == gcsid)
                loadMaterialPropertiesForElement(elem1, e, _geom_cut_elems);
            }
 
        if (_displaced_mesh)
        {
          Elem * elem1_displaced = _displaced_mesh->elem_ptr(it.first->id());
          Elem * elem2_displaced = _displaced_mesh->elem_ptr(it.second->id());
 
          std::map<unique_id_type, XFEMCutElem *>::iterator cemit =
              _cut_elem_map.find(elem1_displaced->unique_id());
          if (cemit != _cut_elem_map.end())
          {
            const XFEMCutElem * xfce = cemit->second;
 
            for (unsigned int in = 0; in < elem1_displaced->n_nodes(); ++in)
            {
              Node * e1node_displaced = elem1_displaced->node_ptr(in);
              Node * e2node_displaced = elem2_displaced->node_ptr(in);
              if (!xfce->isPointPhysical(*elem1->node_ptr(in)) &&
                  e1node_displaced != e2node_displaced)
              {
                elem1_displaced->set_node(in, e2node_displaced);
                nodes_to_delete_displaced.insert(e1node_displaced);
              }
              else if (e1node_displaced != e2node_displaced)
                nodes_to_delete_displaced.insert(e2node_displaced);
            }
          }
          else
            mooseError("Could not find XFEMCutElem for element to be kept in healing");
 
          elem2_displaced->nullify_neighbors();
          _displaced_mesh->get_boundary_info().remove(elem2_displaced);
          _displaced_mesh->delete_elem(elem2_displaced);
        }
 
        // remove the property storage of deleted element/side
        _material_data[0]->eraseProperty(elem2);
        _bnd_material_data[0]->eraseProperty(elem2);
 
        cutelems_to_delete.insert(elem2->unique_id());
        elem2->nullify_neighbors();
        _mesh->get_boundary_info().remove(elem2);
        unsigned int deleted_elem_id = elem2->id();
        _mesh->delete_elem(elem2);
        if (_debug_output_level > 1)
        {
          if (deleted_elem_count == 0)
            _console << "\n";
          _console << "XFEM healing deleted element: " << deleted_elem_id << std::endl;
        }
        ++deleted_elem_count;
        mesh_changed = true;
      }
    }
  }
 
  for (auto & sit : nodes_to_delete)
  {
    Node * node_to_delete = sit;
    dof_id_type deleted_node_id = node_to_delete->id();
    _mesh->get_boundary_info().remove(node_to_delete);
    _mesh->delete_node(node_to_delete);
    if (_debug_output_level > 1)
      _console << "XFEM healing deleted node: " << deleted_node_id << std::endl;
  }
 
  if (_displaced_mesh)
  {
    for (auto & sit : nodes_to_delete_displaced)
    {
      Node * node_to_delete_displaced = sit;
      _displaced_mesh->get_boundary_info().remove(node_to_delete_displaced);
      _displaced_mesh->delete_node(node_to_delete_displaced);
    }
  }
 
  for (auto & ced : cutelems_to_delete)
    if (_cut_elem_map.find(ced) != _cut_elem_map.end())
    {
      delete _cut_elem_map.find(ced)->second;
      _cut_elem_map.erase(ced);
    }
 
  for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
    if (_geometric_cuts[i]->shouldHealMesh())
      _sibling_elems[_geometric_cuts[i]->getInterfaceID()].clear();
 
  if (_displaced_mesh)
  {
    for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
      if (_geometric_cuts[i]->shouldHealMesh())
        _sibling_displaced_elems[_geometric_cuts[i]->getInterfaceID()].clear();
  }
 
  for (auto & ceh : _crack_tip_elems_to_be_healed)
  {
    _crack_tip_elems.erase(ceh);
    _elem_crack_origin_direction_map.erase(ceh);
    delete _cut_elem_map.find(ceh->unique_id())->second;
    _cut_elem_map.erase(ceh->unique_id());
  }
 
  if (!healed_geometric_cuts.empty() && _debug_output_level > 0)
  {
    _console << "\nXFEM mesh healing complete\n";
    _console << "Names of healed geometric cut objects: ";
    for (auto geomcut : healed_geometric_cuts)
      _console << geomcut << " ";
    _console << "\n";
    _console << "# deleted nodes:    " << nodes_to_delete.size() << "\n";
    _console << "# deleted elements: " << deleted_elem_count << "\n";
    _console << std::flush;
  }
 
  return mesh_changed;
}
 
bool
XFEM::cutMeshWithEFA(const std::vector<std::shared_ptr<NonlinearSystemBase>> & nls,
                     AuxiliarySystem & aux)
{
  if (nls.size() != 1)
    mooseError("XFEM does not currently support multiple nonlinear systems");
 
  std::map<unsigned int, Node *> efa_id_to_new_node;
  std::map<unsigned int, Node *> efa_id_to_new_node2;
  std::map<unsigned int, Elem *> efa_id_to_new_elem;
  _cached_solution.clear();
  _cached_aux_solution.clear();
 
  // Copy the current geometric cut element info (from last time) into the
  // _old_geom_cut_elems.
  _old_geom_cut_elems.swap(_geom_cut_elems);
  _geom_cut_elems.clear();
 
  _efa_mesh.updatePhysicalLinksAndFragments();
 
  if (_debug_output_level > 2)
  {
    _console << "\nXFEM Element fragment algorithm mesh prior to cutting:\n";
    _console << std::flush;
    _efa_mesh.printMesh();
  }
 
  _efa_mesh.updateTopology();
 
  if (_debug_output_level > 2)
  {
    _console << "\nXFEM Element fragment algorithm mesh after cutting:\n";
    _console << std::flush;
    _efa_mesh.printMesh();
  }
 
  const std::vector<EFANode *> new_nodes = _efa_mesh.getNewNodes();
  const std::vector<EFAElement *> new_elements = _efa_mesh.getChildElements();
  const std::vector<EFAElement *> delete_elements = _efa_mesh.getParentElements();
 
  bool mesh_changed = (new_nodes.size() + new_elements.size() + delete_elements.size() > 0);
 
  // Prepare to cache solution on DOFs modified by XFEM
  if (mesh_changed)
  {
    nls[0]->serializeSolution();
    aux.serializeSolution();
    if (_debug_output_level > 1)
      _console << "\n";
  }
  NumericVector<Number> & current_solution = *nls[0]->system().current_local_solution;
  NumericVector<Number> & old_solution = nls[0]->solutionOld();
  NumericVector<Number> & older_solution = nls[0]->solutionOlder();
  NumericVector<Number> & current_aux_solution = *aux.system().current_local_solution;
  NumericVector<Number> & old_aux_solution = aux.solutionOld();
  NumericVector<Number> & older_aux_solution = aux.solutionOlder();
 
  std::map<Node *, Node *> new_nodes_to_parents;
 
  // Add new nodes
  for (unsigned int i = 0; i < new_nodes.size(); ++i)
  {
    unsigned int new_node_id = new_nodes[i]->id();
    unsigned int parent_id = new_nodes[i]->parent()->id();
 
    Node * parent_node = _mesh->node_ptr(parent_id);
    Node * new_node = Node::build(*parent_node, _mesh->max_node_id()).release();
    _mesh->add_node(new_node);
 
    new_nodes_to_parents[new_node] = parent_node;
 
    new_node->set_n_systems(parent_node->n_systems());
    efa_id_to_new_node.insert(std::make_pair(new_node_id, new_node));
    if (_debug_output_level > 1)
      _console << "XFEM added new node: " << new_node->id() << std::endl;
    if (_displaced_mesh)
    {
      const Node * parent_node2 = _displaced_mesh->node_ptr(parent_id);
      Node * new_node2 = Node::build(*parent_node2, _displaced_mesh->max_node_id()).release();
      _displaced_mesh->add_node(new_node2);
 
      new_node2->set_n_systems(parent_node2->n_systems());
      efa_id_to_new_node2.insert(std::make_pair(new_node_id, new_node2));
    }
  }
 
  // Add new elements
  std::map<unsigned int, std::vector<const Elem *>> temporary_parent_children_map;
 
  std::vector<boundary_id_type> parent_boundary_ids;
 
  for (unsigned int i = 0; i < new_elements.size(); ++i)
  {
    unsigned int parent_id = new_elements[i]->getParent()->id();
    unsigned int efa_child_id = new_elements[i]->id();
 
    Elem * parent_elem = _mesh->elem_ptr(parent_id);
    Elem * libmesh_elem = Elem::build(parent_elem->type()).release();
 
    for (unsigned int m = 0; m < _geometric_cuts.size(); ++m)
    {
      for (auto & it : _sibling_elems[_geometric_cuts[m]->getInterfaceID()])
      {
        if (parent_elem == it.first)
          it.first = libmesh_elem;
        else if (parent_elem == it.second)
          it.second = libmesh_elem;
      }
    }
 
    // parent has at least two children
    if (new_elements[i]->getParent()->numChildren() > 1)
      temporary_parent_children_map[parent_elem->id()].push_back(libmesh_elem);
 
    Elem * parent_elem2 = nullptr;
    Elem * libmesh_elem2 = nullptr;
    if (_displaced_mesh)
    {
      parent_elem2 = _displaced_mesh->elem_ptr(parent_id);
      libmesh_elem2 = Elem::build(parent_elem2->type()).release();
 
      for (unsigned int m = 0; m < _geometric_cuts.size(); ++m)
      {
        for (auto & it : _sibling_displaced_elems[_geometric_cuts[m]->getInterfaceID()])
        {
          if (parent_elem2 == it.first)
            it.first = libmesh_elem2;
          else if (parent_elem2 == it.second)
            it.second = libmesh_elem2;
        }
      }
    }
 
    for (unsigned int j = 0; j < new_elements[i]->numNodes(); ++j)
    {
      unsigned int node_id = new_elements[i]->getNode(j)->id();
      Node * libmesh_node;
 
      std::map<unsigned int, Node *>::iterator nit = efa_id_to_new_node.find(node_id);
      if (nit != efa_id_to_new_node.end())
        libmesh_node = nit->second;
      else
        libmesh_node = _mesh->node_ptr(node_id);
 
      if (libmesh_node->processor_id() == DofObject::invalid_processor_id)
        libmesh_node->processor_id() = parent_elem->processor_id();
 
      libmesh_elem->set_node(j, libmesh_node);
 
      // Store solution for all nodes affected by XFEM (even existing nodes)
      if (parent_elem->is_semilocal(_mesh->processor_id()))
      {
        Node * solution_node = libmesh_node; // Node from which to store solution
        if (new_nodes_to_parents.find(libmesh_node) != new_nodes_to_parents.end())
          solution_node = new_nodes_to_parents[libmesh_node];
 
        if ((_moose_mesh->isSemiLocal(solution_node)) ||
            (libmesh_node->processor_id() == _mesh->processor_id()))
        {
          storeSolutionForNode(libmesh_node,
                               solution_node,
                               *nls[0],
                               _cached_solution,
                               current_solution,
                               old_solution,
                               older_solution);
          storeSolutionForNode(libmesh_node,
                               solution_node,
                               aux,
                               _cached_aux_solution,
                               current_aux_solution,
                               old_aux_solution,
                               older_aux_solution);
        }
      }
 
      Node * parent_node = parent_elem->node_ptr(j);
      _mesh->get_boundary_info().boundary_ids(parent_node, parent_boundary_ids);
      _mesh->get_boundary_info().add_node(libmesh_node, parent_boundary_ids);
 
      if (_displaced_mesh)
      {
        std::map<unsigned int, Node *>::iterator nit2 = efa_id_to_new_node2.find(node_id);
        if (nit2 != efa_id_to_new_node2.end())
          libmesh_node = nit2->second;
        else
          libmesh_node = _displaced_mesh->node_ptr(node_id);
 
        if (libmesh_node->processor_id() == DofObject::invalid_processor_id)
          libmesh_node->processor_id() = parent_elem2->processor_id();
 
        libmesh_elem2->set_node(j, libmesh_node);
 
        parent_node = parent_elem2->node_ptr(j);
        _displaced_mesh->get_boundary_info().boundary_ids(parent_node, parent_boundary_ids);
        _displaced_mesh->get_boundary_info().add_node(libmesh_node, parent_boundary_ids);
      }
    }
 
    libmesh_elem->set_p_level(parent_elem->p_level());
    libmesh_elem->set_p_refinement_flag(parent_elem->p_refinement_flag());
    _mesh->add_elem(libmesh_elem);
    libmesh_elem->set_n_systems(parent_elem->n_systems());
    libmesh_elem->subdomain_id() = parent_elem->subdomain_id();
    libmesh_elem->processor_id() = parent_elem->processor_id();
 
    // The crack tip origin map is stored before cut, thus the elem should be updated with new
    // element.
    std::map<const Elem *, std::vector<Point>>::iterator mit =
        _elem_crack_origin_direction_map.find(parent_elem);
    if (mit != _elem_crack_origin_direction_map.end())
    {
      std::vector<Point> crack_data = _elem_crack_origin_direction_map[parent_elem];
      _elem_crack_origin_direction_map.erase(mit);
      _elem_crack_origin_direction_map[libmesh_elem] = crack_data;
    }
 
    if (_debug_output_level > 1)
      _console << "XFEM added new element: " << libmesh_elem->id() << std::endl;
 
    XFEMCutElem * xfce = nullptr;
    if (_mesh->mesh_dimension() == 2)
    {
      EFAElement2D * new_efa_elem2d = dynamic_cast<EFAElement2D *>(new_elements[i]);
      if (!new_efa_elem2d)
        mooseError("EFAelem is not of EFAelement2D type");
      xfce = new XFEMCutElem2D(libmesh_elem,
                               new_efa_elem2d,
                               _fe_problem->assembly(0, /*nl_sys_num=*/0).qRule()->n_points(),
                               libmesh_elem->n_sides());
    }
    else if (_mesh->mesh_dimension() == 3)
    {
      EFAElement3D * new_efa_elem3d = dynamic_cast<EFAElement3D *>(new_elements[i]);
      if (!new_efa_elem3d)
        mooseError("EFAelem is not of EFAelement3D type");
      xfce = new XFEMCutElem3D(libmesh_elem,
                               new_efa_elem3d,
                               _fe_problem->assembly(0, /*nl_sys_num=*/0).qRule()->n_points(),
                               libmesh_elem->n_sides());
    }
    _cut_elem_map.insert(std::pair<unique_id_type, XFEMCutElem *>(libmesh_elem->unique_id(), xfce));
    efa_id_to_new_elem.insert(std::make_pair(efa_child_id, libmesh_elem));
 
    if (_displaced_mesh)
    {
      libmesh_elem2->set_p_level(parent_elem2->p_level());
      libmesh_elem2->set_p_refinement_flag(parent_elem2->p_refinement_flag());
      _displaced_mesh->add_elem(libmesh_elem2);
      libmesh_elem2->set_n_systems(parent_elem2->n_systems());
      libmesh_elem2->subdomain_id() = parent_elem2->subdomain_id();
      libmesh_elem2->processor_id() = parent_elem2->processor_id();
    }
 
    unsigned int n_sides = parent_elem->n_sides();
    for (unsigned int side = 0; side < n_sides; ++side)
    {
      _mesh->get_boundary_info().boundary_ids(parent_elem, side, parent_boundary_ids);
      _mesh->get_boundary_info().add_side(libmesh_elem, side, parent_boundary_ids);
    }
    if (_displaced_mesh)
    {
      n_sides = parent_elem2->n_sides();
      for (unsigned int side = 0; side < n_sides; ++side)
      {
        _displaced_mesh->get_boundary_info().boundary_ids(parent_elem2, side, parent_boundary_ids);
        _displaced_mesh->get_boundary_info().add_side(libmesh_elem2, side, parent_boundary_ids);
      }
    }
 
    unsigned int n_edges = parent_elem->n_edges();
    for (unsigned int edge = 0; edge < n_edges; ++edge)
    {
      _mesh->get_boundary_info().edge_boundary_ids(parent_elem, edge, parent_boundary_ids);
      _mesh->get_boundary_info().add_edge(libmesh_elem, edge, parent_boundary_ids);
    }
    if (_displaced_mesh)
    {
      n_edges = parent_elem2->n_edges();
      for (unsigned int edge = 0; edge < n_edges; ++edge)
      {
        _displaced_mesh->get_boundary_info().edge_boundary_ids(
            parent_elem2, edge, parent_boundary_ids);
        _displaced_mesh->get_boundary_info().add_edge(libmesh_elem2, edge, parent_boundary_ids);
      }
    }
 
    // TODO: Also need to copy neighbor material data
    if (parent_elem->processor_id() == _mesh->processor_id())
    {
      if (_material_data[0]->getMaterialPropertyStorage().hasStatefulProperties())
        _material_data[0]->copy(*libmesh_elem, *parent_elem, 0);
 
      if (_bnd_material_data[0]->getMaterialPropertyStorage().hasStatefulProperties())
        for (unsigned int side = 0; side < parent_elem->n_sides(); ++side)
        {
          _mesh->get_boundary_info().boundary_ids(parent_elem, side, parent_boundary_ids);
          std::vector<boundary_id_type>::iterator it_bd = parent_boundary_ids.begin();
          for (; it_bd != parent_boundary_ids.end(); ++it_bd)
          {
            if (_fe_problem->needBoundaryMaterialOnSide(*it_bd, 0))
              _bnd_material_data[0]->copy(*libmesh_elem, *parent_elem, side);
          }
        }
 
      // Store the current information about the geometrically cut element, and load cached material
      // properties into the new child element, if any.
      const GeometricCutUserObject * gcuo = getGeometricCutForElem(parent_elem);
      if (gcuo && gcuo->shouldHealMesh())
      {
        CutSubdomainID gcsid = getCutSubdomainID(gcuo, libmesh_elem, parent_elem);
        Xfem::CutElemInfo cei(parent_elem, gcuo, gcsid);
        _geom_cut_elems.emplace(libmesh_elem, cei);
        // Find the element to copy data from.
        // Iterate through the old geometrically cut elements, if its parent element AND the
        // geometric cut user object AND the cut subdomain ID are the same as the
        // current element, then that must be it.
        for (auto old_cei : _old_geom_cut_elems)
          if (cei.match(old_cei.second))
          {
            loadMaterialPropertiesForElement(libmesh_elem, old_cei.first, _old_geom_cut_elems);
            if (_debug_output_level > 1)
              _console << "XFEM set material properties for element: " << libmesh_elem->id()
                       << "\n";
            break;
          }
      }
 
      // Store solution for all elements affected by XFEM
      storeSolutionForElement(libmesh_elem,
                              parent_elem,
                              *nls[0],
                              _cached_solution,
                              current_solution,
                              old_solution,
                              older_solution);
      storeSolutionForElement(libmesh_elem,
                              parent_elem,
                              aux,
                              _cached_aux_solution,
                              current_aux_solution,
                              old_aux_solution,
                              older_aux_solution);
    }
  }
 
  // delete elements
  for (std::size_t i = 0; i < delete_elements.size(); ++i)
  {
    Elem * elem_to_delete = _mesh->elem_ptr(delete_elements[i]->id());
 
    // delete the XFEMCutElem object for any elements that are to be deleted
    std::map<unique_id_type, XFEMCutElem *>::iterator cemit =
        _cut_elem_map.find(elem_to_delete->unique_id());
    if (cemit != _cut_elem_map.end())
    {
      delete cemit->second;
      _cut_elem_map.erase(cemit);
    }
 
    // remove the property storage of deleted element/side
    _material_data[0]->eraseProperty(elem_to_delete);
    _bnd_material_data[0]->eraseProperty(elem_to_delete);
 
    elem_to_delete->nullify_neighbors();
    _mesh->get_boundary_info().remove(elem_to_delete);
    unsigned int deleted_elem_id = elem_to_delete->id();
    _mesh->delete_elem(elem_to_delete);
    if (_debug_output_level > 1)
      _console << "XFEM deleted element: " << deleted_elem_id << std::endl;
 
    if (_displaced_mesh)
    {
      Elem * elem_to_delete2 = _displaced_mesh->elem_ptr(delete_elements[i]->id());
      elem_to_delete2->nullify_neighbors();
      _displaced_mesh->get_boundary_info().remove(elem_to_delete2);
      _displaced_mesh->delete_elem(elem_to_delete2);
    }
  }
 
  for (std::map<unsigned int, std::vector<const Elem *>>::iterator it =
           temporary_parent_children_map.begin();
       it != temporary_parent_children_map.end();
       ++it)
  {
    std::vector<const Elem *> & sibling_elem_vec = it->second;
    // TODO: for cut-node case, how to find the sibling elements?
    // if (sibling_elem_vec.size() != 2)
    // mooseError("Must have exactly 2 sibling elements");
 
    for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
      for (auto const & elem_id : _geom_marker_id_elems[_geometric_cuts[i]->getInterfaceID()])
        if (it->first == elem_id)
          _sibling_elems[_geometric_cuts[i]->getInterfaceID()].push_back(
              std::make_pair(sibling_elem_vec[0], sibling_elem_vec[1]));
  }
 
  // add sibling elems on displaced mesh
  if (_displaced_mesh)
  {
    for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
    {
      for (auto & se : _sibling_elems[_geometric_cuts[i]->getInterfaceID()])
      {
        Elem * elem = _displaced_mesh->elem_ptr(se.first->id());
        Elem * elem_pair = _displaced_mesh->elem_ptr(se.second->id());
        _sibling_displaced_elems[_geometric_cuts[i]->getInterfaceID()].push_back(
            std::make_pair(elem, elem_pair));
      }
    }
  }
 
  // clear the temporary map
  temporary_parent_children_map.clear();
 
  // Store information about crack tip elements
  if (mesh_changed)
  {
    _crack_tip_elems.clear();
    _crack_tip_elems_to_be_healed.clear();
    const std::set<EFAElement *> CrackTipElements = _efa_mesh.getCrackTipElements();
    std::set<EFAElement *>::const_iterator sit;
    for (sit = CrackTipElements.begin(); sit != CrackTipElements.end(); ++sit)
    {
      unsigned int eid = (*sit)->id();
      Elem * crack_tip_elem;
      std::map<unsigned int, Elem *>::iterator eit = efa_id_to_new_elem.find(eid);
      if (eit != efa_id_to_new_elem.end())
        crack_tip_elem = eit->second;
      else
        crack_tip_elem = _mesh->elem_ptr(eid);
      _crack_tip_elems.insert(crack_tip_elem);
 
      // Store the crack tip elements which are going to be healed
      for (unsigned int i = 0; i < _geometric_cuts.size(); ++i)
      {
        if (_geometric_cuts[i]->shouldHealMesh())
        {
          for (auto const & mie : _geom_marker_id_elems[_geometric_cuts[i]->getInterfaceID()])
            if ((*sit)->getParent() != nullptr)
            {
              if (_mesh->mesh_dimension() == 2)
              {
                EFAElement2D * efa_elem2d = dynamic_cast<EFAElement2D *>((*sit)->getParent());
                if (!efa_elem2d)
                  mooseError("EFAelem is not of EFAelement2D type");
 
                for (unsigned int edge_id = 0; edge_id < efa_elem2d->numEdges(); ++edge_id)
                {
                  for (unsigned int en_iter = 0; en_iter < efa_elem2d->numEdgeNeighbors(edge_id);
                       ++en_iter)
                  {
                    EFAElement2D * edge_neighbor = efa_elem2d->getEdgeNeighbor(edge_id, en_iter);
                    if (edge_neighbor != nullptr && edge_neighbor->id() == mie)
                      _crack_tip_elems_to_be_healed.insert(crack_tip_elem);
                  }
                }
              }
              else if (_mesh->mesh_dimension() == 3)
              {
                EFAElement3D * efa_elem3d = dynamic_cast<EFAElement3D *>((*sit)->getParent());
                if (!efa_elem3d)
                  mooseError("EFAelem is not of EFAelement3D type");
 
                for (unsigned int face_id = 0; face_id < efa_elem3d->numFaces(); ++face_id)
                {
                  for (unsigned int fn_iter = 0; fn_iter < efa_elem3d->numFaceNeighbors(face_id);
                       ++fn_iter)
                  {
                    EFAElement3D * face_neighbor = efa_elem3d->getFaceNeighbor(face_id, fn_iter);
                    if (face_neighbor != nullptr && face_neighbor->id() == mie)
                      _crack_tip_elems_to_be_healed.insert(crack_tip_elem);
                  }
                }
              }
            }
        }
      }
    }
  }
 
  if (_debug_output_level > 0)
  {
    _console << "\nXFEM mesh cutting with element fragment algorithm complete\n";
    _console << "# new nodes:        " << new_nodes.size() << "\n";
    _console << "# new elements:     " << new_elements.size() << "\n";
    _console << "# deleted elements: " << delete_elements.size() << "\n";
    _console << std::flush;
  }
 
  // store virtual nodes
  // store cut edge info
  return mesh_changed;
}
 
Point
XFEM::getEFANodeCoords(EFANode * CEMnode,
                       EFAElement * CEMElem,
                       const Elem * elem,
                       MeshBase * displaced_mesh) const
{
  Point node_coor(0.0, 0.0, 0.0);
  std::vector<EFANode *> master_nodes;
  std::vector<Point> master_points;
  std::vector<double> master_weights;
 
  CEMElem->getMasterInfo(CEMnode, master_nodes, master_weights);
  for (std::size_t i = 0; i < master_nodes.size(); ++i)
  {
    if (master_nodes[i]->category() == EFANode::N_CATEGORY_PERMANENT)
    {
      unsigned int local_node_id = CEMElem->getLocalNodeIndex(master_nodes[i]);
      const Node * node = elem->node_ptr(local_node_id);
      if (displaced_mesh)
        node = displaced_mesh->node_ptr(node->id());
      Point node_p((*node)(0), (*node)(1), (*node)(2));
      master_points.push_back(node_p);
    }
    else
      mooseError("master nodes must be permanent");
  }
  for (std::size_t i = 0; i < master_nodes.size(); ++i)
    node_coor += master_weights[i] * master_points[i];
 
  return node_coor;
}
 
Real
XFEM::getPhysicalVolumeFraction(const Elem * elem) const
{
  Real phys_volfrac = 1.0;
  std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
  it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    XFEMCutElem * xfce = it->second;
    const EFAElement * EFAelem = xfce->getEFAElement();
    if (EFAelem->isPartial())
    { // exclude the full crack tip elements
      xfce->computePhysicalVolumeFraction();
      phys_volfrac = xfce->getPhysicalVolumeFraction();
    }
  }
 
  return phys_volfrac;
}
 
bool
XFEM::isPointInsidePhysicalDomain(const Elem * elem, const Point & point) const
{
  std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
  it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    XFEMCutElem * xfce = it->second;
 
    if (xfce->isPointPhysical(point))
      return true;
  }
  else
    return true;
 
  return false;
}
 
Real
XFEM::getCutPlane(const Elem * elem,
                  const Xfem::XFEM_CUTPLANE_QUANTITY quantity,
                  unsigned int plane_id) const
{
  Real comp = 0.0;
  Point planedata(0.0, 0.0, 0.0);
  std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
  it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    const XFEMCutElem * xfce = it->second;
    const EFAElement * EFAelem = xfce->getEFAElement();
    if (EFAelem->isPartial()) // exclude the full crack tip elements
    {
      if ((unsigned int)quantity < 3)
      {
        unsigned int index = (unsigned int)quantity;
        planedata = xfce->getCutPlaneOrigin(plane_id, _displaced_mesh);
        comp = planedata(index);
      }
      else if ((unsigned int)quantity < 6)
      {
        unsigned int index = (unsigned int)quantity - 3;
        planedata = xfce->getCutPlaneNormal(plane_id, _displaced_mesh);
        comp = planedata(index);
      }
      else
        mooseError("In get_cut_plane index out of range");
    }
  }
  return comp;
}
 
bool
XFEM::isElemAtCrackTip(const Elem * elem) const
{
  return (_crack_tip_elems.find(elem) != _crack_tip_elems.end());
}
 
bool
XFEM::isElemCut(const Elem * elem, XFEMCutElem *& xfce) const
{
  const auto it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    xfce = it->second;
    const EFAElement * EFAelem = xfce->getEFAElement();
    if (EFAelem->isPartial()) // exclude the full crack tip elements
      return true;
  }
 
  xfce = nullptr;
  return false;
}
 
bool
XFEM::isElemCut(const Elem * elem) const
{
  XFEMCutElem * xfce;
  return isElemCut(elem, xfce);
}
 
void
XFEM::getFragmentFaces(const Elem * elem,
                       std::vector<std::vector<Point>> & frag_faces,
                       bool displaced_mesh) const
{
  std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
  it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    const XFEMCutElem * xfce = it->second;
    if (displaced_mesh)
      xfce->getFragmentFaces(frag_faces, _displaced_mesh);
    else
      xfce->getFragmentFaces(frag_faces);
  }
}
 
EFAElement2D *
XFEM::getEFAElem2D(const Elem * elem)
{
  EFAElement * EFAelem = _efa_mesh.getElemByID(elem->id());
  EFAElement2D * EFAelem2D = dynamic_cast<EFAElement2D *>(EFAelem);
 
  if (!EFAelem2D)
    mooseError("EFAelem is not of EFAelement2D type");
 
  return EFAelem2D;
}
 
EFAElement3D *
XFEM::getEFAElem3D(const Elem * elem)
{
  EFAElement * EFAelem = _efa_mesh.getElemByID(elem->id());
  EFAElement3D * EFAelem3D = dynamic_cast<EFAElement3D *>(EFAelem);
 
  if (!EFAelem3D)
    mooseError("EFAelem is not of EFAelement3D type");
 
  return EFAelem3D;
}
 
void
XFEM::getFragmentEdges(const Elem * elem,
                       EFAElement2D * CEMElem,
                       std::vector<std::vector<Point>> & frag_edges) const
{
  // N.B. CEMElem here has global EFAnode
  frag_edges.clear();
  if (CEMElem->numFragments() > 0)
  {
    if (CEMElem->numFragments() > 1)
      mooseError("element ", elem->id(), " has more than one fragment at this point");
    for (unsigned int i = 0; i < CEMElem->getFragment(0)->numEdges(); ++i)
    {
      std::vector<Point> p_line(2, Point(0.0, 0.0, 0.0));
      p_line[0] = getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(0), CEMElem, elem);
      p_line[1] = getEFANodeCoords(CEMElem->getFragmentEdge(0, i)->getNode(1), CEMElem, elem);
      frag_edges.push_back(p_line);
    }
  }
}
 
void
XFEM::getFragmentFaces(const Elem * elem,
                       EFAElement3D * CEMElem,
                       std::vector<std::vector<Point>> & frag_faces) const
{
  // N.B. CEMElem here has global EFAnode
  frag_faces.clear();
  if (CEMElem->numFragments() > 0)
  {
    if (CEMElem->numFragments() > 1)
      mooseError("element ", elem->id(), " has more than one fragment at this point");
    for (unsigned int i = 0; i < CEMElem->getFragment(0)->numFaces(); ++i)
    {
      unsigned int num_face_nodes = CEMElem->getFragmentFace(0, i)->numNodes();
      std::vector<Point> p_line(num_face_nodes, Point(0.0, 0.0, 0.0));
      for (unsigned int j = 0; j < num_face_nodes; ++j)
        p_line[j] = getEFANodeCoords(CEMElem->getFragmentFace(0, i)->getNode(j), CEMElem, elem);
      frag_faces.push_back(p_line);
    }
  }
}
 
Xfem::XFEM_QRULE &
XFEM::getXFEMQRule()
{
  return _XFEM_qrule;
}
 
void
XFEM::setXFEMQRule(std::string & xfem_qrule)
{
  if (xfem_qrule == "volfrac")
    _XFEM_qrule = Xfem::VOLFRAC;
  else if (xfem_qrule == "moment_fitting")
    _XFEM_qrule = Xfem::MOMENT_FITTING;
  else if (xfem_qrule == "direct")
    _XFEM_qrule = Xfem::DIRECT;
}
 
void
XFEM::setCrackGrowthMethod(bool use_crack_growth_increment, Real crack_growth_increment)
{
  _use_crack_growth_increment = use_crack_growth_increment;
  _crack_growth_increment = crack_growth_increment;
}
 
void
XFEM::setDebugOutputLevel(unsigned int debug_output_level)
{
  _debug_output_level = debug_output_level;
}
 
void
XFEM::setMinWeightMultiplier(Real min_weight_multiplier)
{
  _min_weight_multiplier = min_weight_multiplier;
}
 
bool
XFEM::getXFEMWeights(MooseArray<Real> & weights,
                     const Elem * elem,
                     QBase * qrule,
                     const MooseArray<Point> & q_points)
{
  bool have_weights = false;
  XFEMCutElem * xfce = nullptr;
  if (isElemCut(elem, xfce))
  {
    mooseAssert(xfce != nullptr, "Must have valid XFEMCutElem object here");
    xfce->getWeightMultipliers(weights, qrule, getXFEMQRule(), q_points);
    have_weights = true;
 
    Real ave_weight_multiplier = 0;
    for (unsigned int i = 0; i < weights.size(); ++i)
      ave_weight_multiplier += weights[i];
    ave_weight_multiplier /= weights.size();
 
    if (ave_weight_multiplier < _min_weight_multiplier)
    {
      const Real amount_to_add = _min_weight_multiplier - ave_weight_multiplier;
      for (unsigned int i = 0; i < weights.size(); ++i)
        weights[i] += amount_to_add;
    }
  }
  return have_weights;
}
 
bool
XFEM::getXFEMFaceWeights(MooseArray<Real> & weights,
                         const Elem * elem,
                         QBase * qrule,
                         const MooseArray<Point> & q_points,
                         unsigned int side)
{
  bool have_weights = false;
  XFEMCutElem * xfce = nullptr;
  if (isElemCut(elem, xfce))
  {
    mooseAssert(xfce != nullptr, "Must have valid XFEMCutElem object here");
    xfce->getFaceWeightMultipliers(weights, qrule, getXFEMQRule(), q_points, side);
    have_weights = true;
  }
  return have_weights;
}
 
void
XFEM::getXFEMIntersectionInfo(const Elem * elem,
                              unsigned int plane_id,
                              Point & normal,
                              std::vector<Point> & intersectionPoints,
                              bool displaced_mesh) const
{
  std::map<unique_id_type, XFEMCutElem *>::const_iterator it;
  it = _cut_elem_map.find(elem->unique_id());
  if (it != _cut_elem_map.end())
  {
    const XFEMCutElem * xfce = it->second;
    if (displaced_mesh)
      xfce->getIntersectionInfo(plane_id, normal, intersectionPoints, _displaced_mesh);
    else
      xfce->getIntersectionInfo(plane_id, normal, intersectionPoints);
  }
}
 
void
XFEM::getXFEMqRuleOnLine(std::vector<Point> & intersection_points,
                         std::vector<Point> & quad_pts,
                         std::vector<Real> & quad_wts) const
{
  Point p1 = intersection_points[0];
  Point p2 = intersection_points[1];
 
  // number of quadrature points
  std::size_t num_qpoints = 2;
 
  // quadrature coordinates
  Real xi0 = -std::sqrt(1.0 / 3.0);
  Real xi1 = std::sqrt(1.0 / 3.0);
 
  quad_wts.resize(num_qpoints);
  quad_pts.resize(num_qpoints);
 
  Real integ_jacobian = pow((p1 - p2).norm_sq(), 0.5) * 0.5;
 
  quad_wts[0] = 1.0 * integ_jacobian;
  quad_wts[1] = 1.0 * integ_jacobian;
 
  quad_pts[0] = (1.0 - xi0) / 2.0 * p1 + (1.0 + xi0) / 2.0 * p2;
  quad_pts[1] = (1.0 - xi1) / 2.0 * p1 + (1.0 + xi1) / 2.0 * p2;
}
 
void
XFEM::getXFEMqRuleOnSurface(std::vector<Point> & intersection_points,
                            std::vector<Point> & quad_pts,
                            std::vector<Real> & quad_wts) const
{
  std::size_t nnd_pe = intersection_points.size();
  Point xcrd(0.0, 0.0, 0.0);
  for (std::size_t i = 0; i < nnd_pe; ++i)
    xcrd += intersection_points[i];
  xcrd /= nnd_pe;
 
  quad_pts.resize(nnd_pe);
  quad_wts.resize(nnd_pe);
 
  Real jac = 0.0;
 
  for (std::size_t j = 0; j < nnd_pe; ++j) // loop all sub-tris
  {
    std::vector<std::vector<Real>> shape(3, std::vector<Real>(3, 0.0));
    std::vector<Point> subtrig_points(3, Point(0.0, 0.0, 0.0)); // sub-trig nodal coords
 
    int jplus1 = j < nnd_pe - 1 ? j + 1 : 0;
    subtrig_points[0] = xcrd;
    subtrig_points[1] = intersection_points[j];
    subtrig_points[2] = intersection_points[jplus1];
 
    std::vector<std::vector<Real>> sg2;
    Xfem::stdQuadr2D(3, 1, sg2);                 // get sg2
    for (std::size_t l = 0; l < sg2.size(); ++l) // loop all int pts on a sub-trig
    {
      Xfem::shapeFunc2D(3, sg2[l], subtrig_points, shape, jac, true); // Get shape
      std::vector<Real> tsg_line(3, 0.0);
      for (std::size_t k = 0; k < 3; ++k) // loop sub-trig nodes
      {
        tsg_line[0] += shape[k][2] * subtrig_points[k](0);
        tsg_line[1] += shape[k][2] * subtrig_points[k](1);
        tsg_line[2] += shape[k][2] * subtrig_points[k](2);
      }
      quad_pts[j + l] = Point(tsg_line[0], tsg_line[1], tsg_line[2]);
      quad_wts[j + l] = sg2[l][3] * jac;
    }
  }
}
 
void
XFEM::storeSolutionForNode(const Node * node_to_store_to,
                           const Node * node_to_store_from,
                           SystemBase & sys,
                           std::map<unique_id_type, std::vector<Real>> & stored_solution,
                           const NumericVector<Number> & current_solution,
                           const NumericVector<Number> & old_solution,
                           const NumericVector<Number> & older_solution)
{
  std::vector<dof_id_type> stored_solution_dofs = getNodeSolutionDofs(node_to_store_from, sys);
  std::vector<Real> stored_solution_scratch;
  // Size for current solution, as well as for old, and older solution only for transient case
  std::size_t stored_solution_size =
      (_fe_problem->isTransient() ? stored_solution_dofs.size() * 3 : stored_solution_dofs.size());
  stored_solution_scratch.reserve(stored_solution_size);
 
  // Store in the order defined in stored_solution_dofs first for the current, then for old and
  // older if applicable
  for (auto dof : stored_solution_dofs)
    stored_solution_scratch.push_back(current_solution(dof));
 
  if (_fe_problem->isTransient())
  {
    for (auto dof : stored_solution_dofs)
      stored_solution_scratch.push_back(old_solution(dof));
 
    for (auto dof : stored_solution_dofs)
      stored_solution_scratch.push_back(older_solution(dof));
  }
 
  if (stored_solution_scratch.size() > 0)
    stored_solution[node_to_store_to->unique_id()] = stored_solution_scratch;
}
 
void
XFEM::storeSolutionForElement(const Elem * elem_to_store_to,
                              const Elem * elem_to_store_from,
                              SystemBase & sys,
                              std::map<unique_id_type, std::vector<Real>> & stored_solution,
                              const NumericVector<Number> & current_solution,
                              const NumericVector<Number> & old_solution,
                              const NumericVector<Number> & older_solution)
{
  std::vector<dof_id_type> stored_solution_dofs = getElementSolutionDofs(elem_to_store_from, sys);
  std::vector<Real> stored_solution_scratch;
  // Size for current solution, as well as for old, and older solution only for transient case
  std::size_t stored_solution_size =
      (_fe_problem->isTransient() ? stored_solution_dofs.size() * 3 : stored_solution_dofs.size());
  stored_solution_scratch.reserve(stored_solution_size);
 
  // Store in the order defined in stored_solution_dofs first for the current, then for old and
  // older if applicable
  for (auto dof : stored_solution_dofs)
    stored_solution_scratch.push_back(current_solution(dof));
 
  if (_fe_problem->isTransient())
  {
    for (auto dof : stored_solution_dofs)
      stored_solution_scratch.push_back(old_solution(dof));
 
    for (auto dof : stored_solution_dofs)
      stored_solution_scratch.push_back(older_solution(dof));
  }
 
  if (stored_solution_scratch.size() > 0)
    stored_solution[elem_to_store_to->unique_id()] = stored_solution_scratch;
}
 
void
XFEM::setSolution(SystemBase & sys,
                  const std::map<unique_id_type, std::vector<Real>> & stored_solution,
                  NumericVector<Number> & current_solution,
                  NumericVector<Number> & old_solution,
                  NumericVector<Number> & older_solution)
{
  for (auto & node : _mesh->local_node_ptr_range())
  {
    auto mit = stored_solution.find(node->unique_id());
    if (mit != stored_solution.end())
    {
      const std::vector<Real> & stored_node_solution = mit->second;
      std::vector<dof_id_type> stored_solution_dofs = getNodeSolutionDofs(node, sys);
      setSolutionForDOFs(stored_node_solution,
                         stored_solution_dofs,
                         current_solution,
                         old_solution,
                         older_solution);
    }
  }
 
  for (auto & elem : as_range(_mesh->local_elements_begin(), _mesh->local_elements_end()))
  {
    auto mit = stored_solution.find(elem->unique_id());
    if (mit != stored_solution.end())
    {
      const std::vector<Real> & stored_elem_solution = mit->second;
      std::vector<dof_id_type> stored_solution_dofs = getElementSolutionDofs(elem, sys);
      setSolutionForDOFs(stored_elem_solution,
                         stored_solution_dofs,
                         current_solution,
                         old_solution,
                         older_solution);
    }
  }
}
 
void
XFEM::setSolutionForDOFs(const std::vector<Real> & stored_solution,
                         const std::vector<dof_id_type> & stored_solution_dofs,
                         NumericVector<Number> & current_solution,
                         NumericVector<Number> & old_solution,
                         NumericVector<Number> & older_solution)
{
  // Solution vector is stored first for current, then old and older solutions.
  // These are the offsets to the beginning of the old and older solutions in the vector.
  const auto old_solution_offset = stored_solution_dofs.size();
  const auto older_solution_offset = old_solution_offset * 2;
 
  for (std::size_t i = 0; i < stored_solution_dofs.size(); ++i)
  {
    current_solution.set(stored_solution_dofs[i], stored_solution[i]);
    if (_fe_problem->isTransient())
    {
      old_solution.set(stored_solution_dofs[i], stored_solution[old_solution_offset + i]);
      older_solution.set(stored_solution_dofs[i], stored_solution[older_solution_offset + i]);
    }
  }
}
 
std::vector<dof_id_type>
XFEM::getElementSolutionDofs(const Elem * elem, SystemBase & sys) const
{
  SubdomainID sid = elem->subdomain_id();
  const std::vector<MooseVariableFEBase *> & vars = sys.getVariables(0);
  std::vector<dof_id_type> solution_dofs;
  solution_dofs.reserve(vars.size()); // just an approximation
  for (auto var : vars)
  {
    if (!var->isNodal())
    {
      const std::set<SubdomainID> & var_subdomains = sys.getSubdomainsForVar(var->number());
      if (var_subdomains.empty() || var_subdomains.find(sid) != var_subdomains.end())
      {
        unsigned int n_comp = elem->n_comp(sys.number(), var->number());
        for (unsigned int icomp = 0; icomp < n_comp; ++icomp)
        {
          dof_id_type elem_dof = elem->dof_number(sys.number(), var->number(), icomp);
          solution_dofs.push_back(elem_dof);
        }
      }
    }
  }
  return solution_dofs;
}
 
std::vector<dof_id_type>
XFEM::getNodeSolutionDofs(const Node * node, SystemBase & sys) const
{
  const std::set<SubdomainID> & sids = _moose_mesh->getNodeBlockIds(*node);
  const std::vector<MooseVariableFEBase *> & vars = sys.getVariables(0);
  std::vector<dof_id_type> solution_dofs;
  solution_dofs.reserve(vars.size()); // just an approximation
  for (auto var : vars)
  {
    if (var->isNodal())
    {
      const std::set<SubdomainID> & var_subdomains = sys.getSubdomainsForVar(var->number());
      std::set<SubdomainID> intersect;
      set_intersection(var_subdomains.begin(),
                       var_subdomains.end(),
                       sids.begin(),
                       sids.end(),
                       std::inserter(intersect, intersect.begin()));
      if (var_subdomains.empty() || !intersect.empty())
      {
        unsigned int n_comp = node->n_comp(sys.number(), var->number());
        for (unsigned int icomp = 0; icomp < n_comp; ++icomp)
        {
          dof_id_type node_dof = node->dof_number(sys.number(), var->number(), icomp);
          solution_dofs.push_back(node_dof);
        }
      }
    }
  }
  return solution_dofs;
}
 
const GeometricCutUserObject *
XFEM::getGeometricCutForElem(const Elem * elem) const
{
  for (auto gcmit : _geom_marker_id_elems)
  {
    std::set<unsigned int> elems = gcmit.second;
    if (elems.find(elem->id()) != elems.end())
      return _geometric_cuts[gcmit.first];
  }
  return nullptr;
}
 
void
XFEM::storeMaterialPropertiesForElementHelper(const Elem * elem, MaterialPropertyStorage & storage)
{
  for (const auto state : storage.statefulIndexRange())
  {
    const auto & elem_props = storage.props(state).at(elem);
    auto & serialized_props = _geom_cut_elems[elem]._elem_material_properties[state - 1];
    serialized_props.clear();
    for (const auto & side_props_pair : elem_props)
    {
      const auto side = side_props_pair.first;
      std::ostringstream oss;
      dataStore(oss, storage.setProps(elem, side, state), nullptr);
      serialized_props[side].assign(oss.str());
    }
  }
}
 
void
XFEM::storeMaterialPropertiesForElement(const Elem * parent_elem, const Elem * child_elem)
{
  // Set the parent element so that it is consistent post-healing
  _geom_cut_elems[child_elem]._parent_elem = parent_elem;
 
  // Locally store the element material properties
  storeMaterialPropertiesForElementHelper(child_elem,
                                          _material_data[0]->getMaterialPropertyStorageForXFEM({}));
 
  // Locally store the boundary material properties
  // First check if any of the side need material properties
  bool need_boundary_materials = false;
  for (unsigned int side = 0; side < child_elem->n_sides(); ++side)
  {
    std::vector<boundary_id_type> elem_boundary_ids;
    _mesh->get_boundary_info().boundary_ids(child_elem, side, elem_boundary_ids);
    for (auto bdid : elem_boundary_ids)
      if (_fe_problem->needBoundaryMaterialOnSide(bdid, 0))
        need_boundary_materials = true;
  }
 
  // If boundary material properties are needed for this element, then store them.
  if (need_boundary_materials)
    storeMaterialPropertiesForElementHelper(
        child_elem, _bnd_material_data[0]->getMaterialPropertyStorageForXFEM({}));
}
 
void
XFEM::loadMaterialPropertiesForElementHelper(const Elem * elem,
                                             const Xfem::CachedMaterialProperties & cached_props,
                                             MaterialPropertyStorage & storage) const
{
  if (!storage.hasStatefulProperties())
    return;
 
  for (const auto state : storage.statefulIndexRange())
  {
    const auto & serialized_props = cached_props[state - 1];
    for (const auto & [side, serialized_side_props] : serialized_props)
    {
      std::istringstream iss;
      iss.str(serialized_side_props);
      iss.clear();
 
      // This is very dirty. We should not write to MOOSE's stateful properties.
      // Please remove me :(
      dataLoad(iss, storage.setProps(elem, side, state), nullptr);
    }
  }
}
 
void
XFEM::loadMaterialPropertiesForElement(
    const Elem * elem,
    const Elem * elem_from,
    std::unordered_map<const Elem *, Xfem::CutElemInfo> & cached_cei) const
{
  // Restore the element material properties
  mooseAssert(cached_cei.count(elem_from) > 0, "XFEM: Unable to find cached material properties.");
  Xfem::CutElemInfo & cei = cached_cei[elem_from];
 
  // Load element material properties from cached properties
  loadMaterialPropertiesForElementHelper(elem,
                                         cei._elem_material_properties,
                                         _material_data[0]->getMaterialPropertyStorageForXFEM({}));
 
  // Check if any of the element side need material properties
  bool need_boundary_materials = false;
  for (unsigned int side = 0; side < elem->n_sides(); ++side)
  {
    std::vector<boundary_id_type> elem_boundary_ids;
    _mesh->get_boundary_info().boundary_ids(elem, side, elem_boundary_ids);
    for (auto bdid : elem_boundary_ids)
      if (_fe_problem->needBoundaryMaterialOnSide(bdid, 0))
        need_boundary_materials = true;
  }
 
  // Load boundary material properties from cached properties
  if (need_boundary_materials)
    loadMaterialPropertiesForElementHelper(
        elem,
        cei._bnd_material_properties,
        _bnd_material_data[0]->getMaterialPropertyStorageForXFEM({}));
}
 
CutSubdomainID
XFEM::getCutSubdomainID(const GeometricCutUserObject * gcuo,
                        const Elem * cut_elem,
                        const Elem * parent_elem) const
{
  if (!parent_elem)
    parent_elem = cut_elem;
  // Pick any node from the parent element that is inside the physical domain and return its
  // CutSubdomainID.
  const Node * node = pickFirstPhysicalNode(cut_elem, parent_elem);
  return gcuo->getCutSubdomainID(node);
}
 
const Node *
XFEM::pickFirstPhysicalNode(const Elem * e, const Elem * e0) const
{
  for (auto i : e0->node_index_range())
    if (isPointInsidePhysicalDomain(e, e0->node_ref(i)))
      return e0->node_ptr(i);
  mooseError("cannot find a physical node in the current element");
  return nullptr;
}