LCOV - code coverage report
Current view: top level - src/mesh - mesh_modification.C (source / functions) Hit Total Coverage
Test: libMesh/libmesh: #4519 (472f82) with base e77e8c Lines: 705 1007 70.0 %
Date: 2026-08-07 23:12:05 Functions: 26 30 86.7 %
Legend: Lines: hit not hit

          Line data    Source code
       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
       3             : 
       4             : // This library is free software; you can redistribute it and/or
       5             : // modify it under the terms of the GNU Lesser General Public
       6             : // License as published by the Free Software Foundation; either
       7             : // version 2.1 of the License, or (at your option) any later version.
       8             : 
       9             : // This library is distributed in the hope that it will be useful,
      10             : // but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      12             : // Lesser General Public License for more details.
      13             : 
      14             : // You should have received a copy of the GNU Lesser General Public
      15             : // License along with this library; if not, write to the Free Software
      16             : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      17             : 
      18             : 
      19             : 
      20             : // C++ includes
      21             : #include <cstdlib> // *must* precede <cmath> for proper std:abs() on PGI, Sun Studio CC
      22             : #include <cmath> // for std::acos()
      23             : #include <algorithm>
      24             : #include <limits>
      25             : #include <map>
      26             : #include <array>
      27             : 
      28             : // Local includes
      29             : #include "libmesh/boundary_info.h"
      30             : #include "libmesh/function_base.h"
      31             : #include "libmesh/cell_tet4.h"
      32             : #include "libmesh/cell_tet10.h"
      33             : #include "libmesh/cell_c0polyhedron.h"
      34             : #include "libmesh/cell_polyhedron.h"
      35             : #include "libmesh/elem_range.h"
      36             : #include "libmesh/face_c0polygon.h"
      37             : #include "libmesh/face_polygon.h"
      38             : #include "libmesh/face_tri3.h"
      39             : #include "libmesh/face_tri6.h"
      40             : #include "libmesh/libmesh_logging.h"
      41             : #include "libmesh/mesh_communication.h"
      42             : #include "libmesh/mesh_modification.h"
      43             : #include "libmesh/mesh_tools.h"
      44             : #include "libmesh/parallel.h"
      45             : #include "libmesh/parallel_ghost_sync.h"
      46             : #include "libmesh/remote_elem.h"
      47             : #include "libmesh/surface.h"
      48             : #include "libmesh/enum_to_string.h"
      49             : #include "libmesh/unstructured_mesh.h"
      50             : #include "libmesh/elem_side_builder.h"
      51             : #include "libmesh/tensor_value.h"
      52             : 
      53             : namespace
      54             : {
      55             : using namespace libMesh;
      56             : 
      57        1712 : bool split_first_diagonal(const Elem * elem,
      58             :                           unsigned int diag_1_node_1,
      59             :                           unsigned int diag_1_node_2,
      60             :                           unsigned int diag_2_node_1,
      61             :                           unsigned int diag_2_node_2)
      62             : {
      63         372 :   return ((elem->node_id(diag_1_node_1) > elem->node_id(diag_2_node_1) &&
      64        2044 :            elem->node_id(diag_1_node_1) > elem->node_id(diag_2_node_2)) ||
      65        1712 :           (elem->node_id(diag_1_node_2) > elem->node_id(diag_2_node_1) &&
      66        1768 :            elem->node_id(diag_1_node_2) > elem->node_id(diag_2_node_2)));
      67             : }
      68             : 
      69             : 
      70             : // Return the local index of the vertex on \p elem with the highest
      71             : // node id.
      72       44518 : unsigned int highest_vertex_on(const Elem * elem)
      73             : {
      74        1792 :   unsigned int highest_n = 0;
      75        3584 :   dof_id_type highest_n_id = elem->node_id(0);
      76      356144 :   for (auto n : make_range(1u, elem->n_vertices()))
      77             :     {
      78       25088 :       const dof_id_type n_id = elem->node_id(n);
      79      311626 :       if (n_id > highest_n_id)
      80             :         {
      81        6928 :           highest_n = n;
      82        6928 :           highest_n_id = n_id;
      83             :         }
      84             :     }
      85             : 
      86       44518 :   return highest_n;
      87             : }
      88             : 
      89             : 
      90             : static const std::array<std::array<unsigned int, 3>, 8> opposing_nodes =
      91             : {{ {2,5,7},{3,4,6},{0,5,7},{1,4,6},{1,3,6},{0,2,7},{1,3,4},{0,2,5} }};
      92             : 
      93             : 
      94             : // Find the highest id on these side nodes of this element
      95             : std::pair<unsigned int, unsigned int>
      96      201321 : split_diagonal(const Elem * elem,
      97             :                const std::vector<unsigned int> & nodes_on_side)
      98             : {
      99        6552 :   libmesh_assert_equal_to(elem->type(), HEX8);
     100             : 
     101      201321 :   unsigned int highest_n = nodes_on_side.front();
     102       13104 :   dof_id_type highest_n_id = elem->node_id(nodes_on_side.front());
     103     1006605 :   for (auto n : nodes_on_side)
     104             :     {
     105       26208 :       const dof_id_type n_id = elem->node_id(n);
     106      805284 :       if (n_id > highest_n_id)
     107             :         {
     108       11056 :           highest_n = n;
     109       11056 :           highest_n_id = n_id;
     110             :         }
     111             :     }
     112             : 
     113      409682 :   for (auto n : nodes_on_side)
     114             :     {
     115     1114909 :       for (auto n2 : opposing_nodes[highest_n])
     116      906548 :         if (n2 == n)
     117        6552 :           return std::make_pair(highest_n, n2);
     118             :     }
     119             : 
     120           0 :   libmesh_error();
     121             : 
     122             :   return std::make_pair(libMesh::invalid_uint, libMesh::invalid_uint);
     123             : }
     124             : 
     125             : 
     126             : // Reconstruct a C++20 feature in C++14
     127             : template <typename T>
     128             : struct reversion_wrapper { T& iterable; };
     129             : 
     130             : template <typename T>
     131        4928 : auto begin (reversion_wrapper<T> w) {return std::rbegin(w.iterable);}
     132             : 
     133             : template <typename T>
     134        4928 : auto end (reversion_wrapper<T> w) {return std::rend(w.iterable);}
     135             : 
     136             : template <typename T>
     137        4928 : reversion_wrapper<T> reverse(T&& iterable) {return {iterable};}
     138             : 
     139             : }
     140             : 
     141             : 
     142             : namespace libMesh
     143             : {
     144             : 
     145             : 
     146             : // ------------------------------------------------------------
     147             : // MeshTools::Modification functions for mesh modification
     148         426 : void MeshTools::Modification::distort (MeshBase & mesh,
     149             :                                        const Real factor,
     150             :                                        const bool perturb_boundary)
     151             : {
     152          12 :   libmesh_assert (mesh.n_nodes());
     153          12 :   libmesh_assert (mesh.n_elem());
     154          12 :   libmesh_assert ((factor >= 0.) && (factor <= 1.));
     155             : 
     156          24 :   LOG_SCOPE("distort()", "MeshTools::Modification");
     157             : 
     158             :   // If we are not perturbing boundary nodes, make a
     159             :   // quickly-searchable list of node ids we can check against.
     160          24 :   std::unordered_set<dof_id_type> boundary_node_ids;
     161         426 :   if (!perturb_boundary)
     162         840 :     boundary_node_ids = MeshTools::find_boundary_nodes (mesh);
     163             : 
     164             :   // Now calculate the minimum distance to
     165             :   // neighboring nodes for each node.
     166             :   // hmin holds these distances.
     167         438 :   std::vector<float> hmin (mesh.max_node_id(),
     168         438 :                            std::numeric_limits<float>::max());
     169             : 
     170       13674 :   for (const auto & elem : mesh.active_element_ptr_range())
     171       43425 :     for (auto & n : elem->node_ref_range())
     172       38700 :       hmin[n.id()] = std::min(hmin[n.id()],
     173       48831 :                               static_cast<float>(elem->hmin()));
     174             : 
     175             :   // Now actually move the nodes
     176             :   {
     177          12 :     const unsigned int seed = 123456;
     178             : 
     179             :     // seed the random number generator.
     180             :     // We'll loop from 1 to n_nodes on every processor, even those
     181             :     // that don't have a particular node, so that the pseudorandom
     182             :     // numbers will be the same everywhere.
     183         426 :     std::srand(seed);
     184             : 
     185             :     // If the node is on the boundary or
     186             :     // the node is not used by any element (hmin[n]<1.e20)
     187             :     // then we should not move it.
     188             :     // [Note: Testing for (in)equality might be wrong
     189             :     // (different types, namely float and double)]
     190       10437 :     for (auto n : make_range(mesh.max_node_id()))
     191       11432 :       if ((perturb_boundary || !boundary_node_ids.count(n)) && hmin[n] < 1.e20)
     192             :         {
     193             :           // the direction, random but unit normalized
     194        1207 :           Point dir (static_cast<Real>(std::rand())/static_cast<Real>(RAND_MAX),
     195        2414 :                      (mesh.mesh_dimension() > 1) ? static_cast<Real>(std::rand())/static_cast<Real>(RAND_MAX) : 0.,
     196        4828 :                      ((mesh.mesh_dimension() == 3) ? static_cast<Real>(std::rand())/static_cast<Real>(RAND_MAX) : 0.));
     197             : 
     198        1207 :           dir(0) = (dir(0)-.5)*2.;
     199             : #if LIBMESH_DIM > 1
     200        1207 :           if (mesh.mesh_dimension() > 1)
     201        1207 :             dir(1) = (dir(1)-.5)*2.;
     202             : #endif
     203             : #if LIBMESH_DIM > 2
     204        1207 :           if (mesh.mesh_dimension() == 3)
     205         852 :             dir(2) = (dir(2)-.5)*2.;
     206             : #endif
     207             : 
     208        1207 :           dir = dir.unit();
     209             : 
     210        1207 :           Node * node = mesh.query_node_ptr(n);
     211        1207 :           if (!node)
     212           0 :             continue;
     213             : 
     214        1207 :           (*node)(0) += dir(0)*factor*hmin[n];
     215             : #if LIBMESH_DIM > 1
     216        1207 :           if (mesh.mesh_dimension() > 1)
     217        1241 :             (*node)(1) += dir(1)*factor*hmin[n];
     218             : #endif
     219             : #if LIBMESH_DIM > 2
     220        1207 :           if (mesh.mesh_dimension() == 3)
     221         876 :             (*node)(2) += dir(2)*factor*hmin[n];
     222             : #endif
     223             :         }
     224             :   }
     225             : 
     226             :   // We haven't changed any topology, but just changing geometry could
     227             :   // have invalidated a point locator.
     228         426 :   mesh.clear_point_locator();
     229         426 : }
     230             : 
     231             : 
     232             : 
     233      188526 : void MeshTools::Modification::permute_elements(MeshBase & mesh)
     234             : {
     235       10584 :   LOG_SCOPE("permute_elements()", "MeshTools::Modification");
     236             : 
     237             :   // We don't yet support doing permute() on a parent element, which
     238             :   // would require us to consistently permute all its children and
     239             :   // give them different local child numbers.
     240      188526 :   unsigned int n_levels = MeshTools::n_levels(mesh);
     241      188526 :   if (n_levels > 1)
     242           0 :     libmesh_error();
     243             : 
     244        5292 :   const unsigned int seed = 123456;
     245             : 
     246             :   // seed the random number generator.
     247             :   // We'll loop from 1 to max_elem_id on every processor, even those
     248             :   // that don't have a particular element, so that the pseudorandom
     249             :   // numbers will be the same everywhere.
     250      188526 :   std::srand(seed);
     251             : 
     252             : 
     253     4795231 :   for (auto e_id : make_range(mesh.max_elem_id()))
     254             :     {
     255     4606705 :       int my_rand = std::rand();
     256             : 
     257     4606705 :       Elem * elem = mesh.query_elem_ptr(e_id);
     258             : 
     259     4606705 :       if (!elem)
     260     2770054 :         continue;
     261             : 
     262     1836651 :       const unsigned int max_permutation = elem->n_permutations();
     263     1836651 :       if (!max_permutation)
     264        4627 :         continue;
     265             : 
     266     1831366 :       const unsigned int perm = my_rand % max_permutation;
     267             : 
     268     1831366 :       elem->permute(perm);
     269             :     }
     270      188526 : }
     271             : 
     272             : 
     273        2236 : void MeshTools::Modification::orient_elements(MeshBase & mesh)
     274             : {
     275         152 :   LOG_SCOPE("orient_elements()", "MeshTools::Modification");
     276             : 
     277             :   // We don't yet support doing orient() on a parent element, which
     278             :   // would require us to consistently orient all its children and
     279             :   // give them different local child numbers.
     280        2236 :   unsigned int n_levels = MeshTools::n_levels(mesh);
     281        2236 :   if (n_levels > 1)
     282           0 :     libmesh_not_implemented_msg("orient_elements() does not support refined meshes");
     283             : 
     284          76 :   BoundaryInfo & boundary_info = mesh.get_boundary_info();
     285       92940 :   for (auto elem : mesh.element_ptr_range())
     286       45412 :     elem->orient(&boundary_info);
     287        2236 : }
     288             : 
     289             : 
     290             : 
     291      188505 : void MeshTools::Modification::redistribute (MeshBase & mesh,
     292             :                                             const FunctionBase<Real> & mapfunc)
     293             : {
     294        5310 :   libmesh_assert (mesh.n_nodes());
     295        5310 :   libmesh_assert (mesh.n_elem());
     296             : 
     297       10620 :   LOG_SCOPE("redistribute()", "MeshTools::Modification");
     298             : 
     299      188505 :   DenseVector<Real> output_vec(LIBMESH_DIM);
     300             : 
     301             :   // FIXME - we should thread this later.
     302      193815 :   std::unique_ptr<FunctionBase<Real>> myfunc = mapfunc.clone();
     303             : 
     304     4309130 :   for (auto & node : mesh.node_ptr_range())
     305             :     {
     306     3937430 :       (*myfunc)(*node, output_vec);
     307             : 
     308     3937430 :       (*node)(0) = output_vec(0);
     309             : #if LIBMESH_DIM > 1
     310     3937430 :       (*node)(1) = output_vec(1);
     311             : #endif
     312             : #if LIBMESH_DIM > 2
     313     3937430 :       (*node)(2) = output_vec(2);
     314             : #endif
     315      177885 :     }
     316             : 
     317             :   // If we just moved a mesh in or out out of the X axis or XY plane
     318             :   // then we might have changed its spatial_dimension()
     319        5310 :   mesh.unset_has_cached_elem_data();
     320             : 
     321             :   // We haven't changed any topology, but just changing geometry could
     322             :   // have invalidated a point locator.
     323      188505 :   mesh.clear_point_locator();
     324      366390 : }
     325             : 
     326             : 
     327             : 
     328         217 : void MeshTools::Modification::translate (MeshBase & mesh,
     329             :                                          const Real xt,
     330             :                                          const Real yt,
     331             :                                          const Real zt)
     332             : {
     333           8 :   const Point p(xt, yt, zt);
     334             : 
     335       72646 :   for (auto & node : mesh.node_ptr_range())
     336       37603 :     *node += p;
     337             : 
     338             :   // If we just moved a mesh in or out out of the X axis or XY plane
     339             :   // then we might have changed its spatial_dimension()
     340           8 :   mesh.unset_has_cached_elem_data();
     341             : 
     342             :   // We haven't changed any topology, but just changing geometry could
     343             :   // have invalidated a point locator.
     344         217 :   mesh.clear_point_locator();
     345         217 : }
     346             : 
     347             : 
     348             : // void MeshTools::Modification::rotate2D (MeshBase & mesh,
     349             : //                                         const Real alpha)
     350             : // {
     351             : //   libmesh_assert_not_equal_to (mesh.mesh_dimension(), 1);
     352             : 
     353             : //   const Real pi = std::acos(-1);
     354             : //   const Real  a = alpha/180.*pi;
     355             : //   for (unsigned int n=0; n<mesh.n_nodes(); n++)
     356             : //     {
     357             : //       const Point p = mesh.node_ref(n);
     358             : //       const Real  x = p(0);
     359             : //       const Real  y = p(1);
     360             : //       const Real  z = p(2);
     361             : //       mesh.node_ref(n) = Point(std::cos(a)*x - std::sin(a)*y,
     362             : //                                std::sin(a)*x + std::cos(a)*y,
     363             : //                                z);
     364             : //     }
     365             : 
     366             : // }
     367             : 
     368             : 
     369             : 
     370             : RealTensorValue
     371      164386 : MeshTools::Modification::rotate (MeshBase & mesh,
     372             :                                  const Real phi,
     373             :                                  const Real theta,
     374             :                                  const Real psi)
     375             : {
     376             :   // We won't change any topology, but just changing geometry could
     377             :   // invalidate a point locator.
     378      164386 :   mesh.clear_point_locator();
     379             : 
     380             : #if LIBMESH_DIM == 3
     381      164386 :   const auto R = RealTensorValue::intrinsic_rotation_matrix(phi, theta, psi);
     382             : 
     383     9885150 :   for (auto & node : mesh.node_ptr_range())
     384             :     {
     385     4970613 :       Point & pt = *node;
     386     4970613 :       pt = R * pt;
     387      155162 :     }
     388             : 
     389             :   // If we just moved a mesh in or out out of the X axis or XY plane
     390             :   // then we might have changed its spatial_dimension()
     391        4612 :   mesh.unset_has_cached_elem_data();
     392             : 
     393      164386 :   return R;
     394             : 
     395             : #else
     396             :   libmesh_ignore(mesh, phi, theta, psi);
     397             :   libmesh_error_msg("MeshTools::Modification::rotate() requires libMesh to be compiled with LIBMESH_DIM==3");
     398             :   // We'll never get here
     399             :   return RealTensorValue();
     400             : #endif
     401             : }
     402             : 
     403             : 
     404          71 : void MeshTools::Modification::scale (MeshBase & mesh,
     405             :                                      const Real xs,
     406             :                                      const Real ys,
     407             :                                      const Real zs)
     408             : {
     409           2 :   const Real x_scale = xs;
     410           2 :   Real y_scale       = ys;
     411           2 :   Real z_scale       = zs;
     412             : 
     413          71 :   if (ys == 0.)
     414             :     {
     415           0 :       libmesh_assert_equal_to (zs, 0.);
     416             : 
     417           0 :       y_scale = z_scale = x_scale;
     418             :     }
     419             : 
     420             :   // Scale the x coordinate in all dimensions
     421         495 :   for (auto & node : mesh.node_ptr_range())
     422         422 :     (*node)(0) *= x_scale;
     423             : 
     424             :   // Only scale the y coordinate in 2 and 3D
     425             :   if (LIBMESH_DIM < 2)
     426             :     return;
     427             : 
     428         495 :   for (auto & node : mesh.node_ptr_range())
     429         422 :     (*node)(1) *= y_scale;
     430             : 
     431             :   // Only scale the z coordinate in 3D
     432             :   if (LIBMESH_DIM < 3)
     433             :     return;
     434             : 
     435         495 :   for (auto & node : mesh.node_ptr_range())
     436         422 :     (*node)(2) *= z_scale;
     437             : 
     438             :   // If we just collapsed a manifold onto the X axis or XY plane
     439             :   // then we might have changed its spatial_dimension()
     440           2 :   mesh.unset_has_cached_elem_data();
     441             : 
     442             :   // We haven't changed any topology, but just changing geometry could
     443             :   // have invalidated a point locator.
     444          71 :   mesh.clear_point_locator();
     445             : }
     446             : 
     447             : 
     448             : 
     449        3337 : void MeshTools::Modification::all_tri (MeshBase & mesh)
     450             : {
     451         188 :   LOG_SCOPE("all_tri()", "MeshTools::Modification");
     452             : 
     453        3337 :   if (!mesh.is_replicated() && !mesh.is_prepared())
     454           0 :     mesh.prepare_for_use();
     455             : 
     456             :   // The number of elements in the original mesh before any additions
     457             :   // or deletions.
     458        3337 :   const dof_id_type n_orig_elem = mesh.n_elem();
     459        3337 :   const dof_id_type max_orig_id = mesh.max_elem_id();
     460             : 
     461             :   // We store pointers to the newly created elements in a vector
     462             :   // until they are ready to be added to the mesh.  This is because
     463             :   // adding new elements on the fly can cause reallocation and invalidation
     464             :   // of existing mesh element_iterators.
     465         282 :   std::vector<std::unique_ptr<Elem>> new_elements;
     466             : 
     467        3337 :   unsigned int max_subelems = 1;  // in 1D nothing needs to change
     468        3337 :   if (mesh.mesh_dimension() == 2) // in 2D quads can split into 2 tris
     469        2769 :     max_subelems = 2;
     470        3337 :   if (mesh.mesh_dimension() == 3) // in 3D hexes can split into 6 tets
     471         568 :     max_subelems = 6;
     472             : 
     473             :   // 2D polygons and 3D polyhedra can be split into an arbitrary
     474             :   // number of triangles/tetrahedra depending on their topology, so we
     475             :   // have to scan the mesh to find the largest split we will need.
     476      172566 :   for (const Elem * elem : mesh.element_ptr_range())
     477             :     {
     478       86587 :       if (const Polygon * poly = dynamic_cast<const Polygon *>(elem))
     479         919 :         max_subelems = std::max(max_subelems, poly->n_subtriangles());
     480       85806 :       else if (const Polyhedron * polyhedron = dynamic_cast<const Polyhedron *>(elem))
     481         211 :         max_subelems = std::max(max_subelems, polyhedron->n_subelements());
     482        3149 :     }
     483        3337 :   mesh.comm().max(max_subelems);
     484             : 
     485        3337 :   new_elements.reserve (max_subelems*n_orig_elem);
     486             : 
     487             :   // If the original mesh has *side* boundary data, we carry that over
     488             :   // to the new mesh with triangular elements.  We currently only
     489             :   // support bringing over side-based BCs to the all-tri mesh, but
     490             :   // that could probably be extended to node and edge-based BCs as
     491             :   // well.
     492        3337 :   const bool mesh_has_boundary_data = (mesh.get_boundary_info().n_boundary_conds() > 0);
     493             : 
     494             :   // Temporary vectors to store the new boundary element pointers, side numbers, and boundary ids
     495         188 :   std::vector<Elem *> new_bndry_elements;
     496         188 :   std::vector<unsigned short int> new_bndry_sides;
     497         188 :   std::vector<boundary_id_type> new_bndry_ids;
     498             : 
     499             :   // We may need to add new points if we run into a 1.5th order
     500             :   // element; if we do that on a DistributedMesh in a ghost element then
     501             :   // we will need to fix their ids / unique_ids
     502        3337 :   bool added_new_ghost_point = false;
     503             : 
     504             :   // Iterate over the elements, splitting:
     505             :   // QUADs into pairs of conforming triangles
     506             :   // PYRAMIDs into pairs of conforming tets,
     507             :   // PRISMs into triplets of conforming tets, and
     508             :   // HEXs into quintets or sextets of conforming tets.
     509             :   // We split on the shortest diagonal to give us better
     510             :   // triangle quality in 2D, and we split based on node ids
     511             :   // to guarantee consistency in 3D.
     512             :   // C0POLYGONs into their sub-triangles
     513             :   // C0POLYHEDRA into their sub-elements (currently only tets)
     514             : 
     515             :   // FIXME: This algorithm does not work on refined grids!
     516             :   {
     517             : #ifdef LIBMESH_ENABLE_UNIQUE_ID
     518        3337 :     unique_id_type max_unique_id = mesh.parallel_max_unique_id();
     519             : #endif
     520             : 
     521             :     // For avoiding extraneous allocation when building side elements
     522        3337 :     std::unique_ptr<const Elem> elem_side, subside_elem;
     523             : 
     524      172566 :     for (auto & elem : mesh.element_ptr_range())
     525             :       {
     526       86587 :         const ElemType etype = elem->type();
     527             : 
     528             :         // all_tri currently only works on coarse meshes
     529       90181 :         if (elem->parent())
     530           0 :           libmesh_not_implemented_msg("Cannot convert a refined element into simplices\n");
     531             : 
     532             :         // The new elements we will split the quad into. Reserving for the maximum
     533             :         // number of sub-elements created for each element
     534       89247 :         std::vector<std::unique_ptr<Elem>> subelem(max_subelems);
     535             : 
     536       86587 :         switch (etype)
     537             :           {
     538       12309 :           case QUAD4:
     539             :             {
     540       23518 :               subelem[0] = Elem::build(TRI3);
     541       23518 :               subelem[1] = Elem::build(TRI3);
     542             : 
     543             :               // Check for possible edge swap
     544       12859 :               if ((elem->point(0) - elem->point(2)).norm() <
     545       12309 :                   (elem->point(1) - elem->point(3)).norm())
     546             :                 {
     547        4470 :                   subelem[0]->set_node(0, elem->node_ptr(0));
     548        4470 :                   subelem[0]->set_node(1, elem->node_ptr(1));
     549        4470 :                   subelem[0]->set_node(2, elem->node_ptr(2));
     550             : 
     551        4470 :                   subelem[1]->set_node(0, elem->node_ptr(0));
     552        4470 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     553        4470 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     554             :                 }
     555             : 
     556             :               else
     557             :                 {
     558        8939 :                   subelem[0]->set_node(0, elem->node_ptr(0));
     559        8939 :                   subelem[0]->set_node(1, elem->node_ptr(1));
     560        8939 :                   subelem[0]->set_node(2, elem->node_ptr(3));
     561             : 
     562        8939 :                   subelem[1]->set_node(0, elem->node_ptr(1));
     563        8939 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     564        8939 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     565             :                 }
     566             : 
     567             : 
     568         550 :               break;
     569             :             }
     570             : 
     571         142 :           case QUAD8:
     572             :             {
     573         146 :               if (elem->processor_id() != mesh.processor_id())
     574         118 :                 added_new_ghost_point = true;
     575             : 
     576         276 :               subelem[0] = Elem::build(TRI6);
     577         276 :               subelem[1] = Elem::build(TRI6);
     578             : 
     579             :               // Add a new node at the center (vertex average) of the element.
     580         150 :               Node * new_node = mesh.add_point((mesh.point(elem->node_id(0)) +
     581         150 :                                                 mesh.point(elem->node_id(1)) +
     582         150 :                                                 mesh.point(elem->node_id(2)) +
     583         146 :                                                 mesh.point(elem->node_id(3)))/4,
     584             :                                                DofObject::invalid_id,
     585         142 :                                                elem->processor_id());
     586             : 
     587             :               // Check for possible edge swap
     588         146 :               if ((elem->point(0) - elem->point(2)).norm() <
     589         142 :                   (elem->point(1) - elem->point(3)).norm())
     590             :                 {
     591           0 :                   subelem[0]->set_node(0, elem->node_ptr(0));
     592           0 :                   subelem[0]->set_node(1, elem->node_ptr(1));
     593           0 :                   subelem[0]->set_node(2, elem->node_ptr(2));
     594           0 :                   subelem[0]->set_node(3, elem->node_ptr(4));
     595           0 :                   subelem[0]->set_node(4, elem->node_ptr(5));
     596           0 :                   subelem[0]->set_node(5, new_node);
     597             : 
     598           0 :                   subelem[1]->set_node(0, elem->node_ptr(0));
     599           0 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     600           0 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     601           0 :                   subelem[1]->set_node(3, new_node);
     602           0 :                   subelem[1]->set_node(4, elem->node_ptr(6));
     603           0 :                   subelem[1]->set_node(5, elem->node_ptr(7));
     604             : 
     605             :                 }
     606             : 
     607             :               else
     608             :                 {
     609         150 :                   subelem[0]->set_node(0, elem->node_ptr(3));
     610         150 :                   subelem[0]->set_node(1, elem->node_ptr(0));
     611         150 :                   subelem[0]->set_node(2, elem->node_ptr(1));
     612         150 :                   subelem[0]->set_node(3, elem->node_ptr(7));
     613         150 :                   subelem[0]->set_node(4, elem->node_ptr(4));
     614         146 :                   subelem[0]->set_node(5, new_node);
     615             : 
     616         150 :                   subelem[1]->set_node(0, elem->node_ptr(1));
     617         150 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     618         150 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     619         150 :                   subelem[1]->set_node(3, elem->node_ptr(5));
     620         150 :                   subelem[1]->set_node(4, elem->node_ptr(6));
     621         146 :                   subelem[1]->set_node(5, new_node);
     622             :                 }
     623             : 
     624           4 :               break;
     625             :             }
     626             : 
     627        3964 :           case QUAD9:
     628             :             {
     629        7384 :               subelem[0] = Elem::build(TRI6);
     630        7384 :               subelem[1] = Elem::build(TRI6);
     631             : 
     632             :               // Check for possible edge swap
     633        4236 :               if ((elem->point(0) - elem->point(2)).norm() <
     634        3964 :                   (elem->point(1) - elem->point(3)).norm())
     635             :                 {
     636        1888 :                   subelem[0]->set_node(0, elem->node_ptr(0));
     637        1888 :                   subelem[0]->set_node(1, elem->node_ptr(1));
     638        1888 :                   subelem[0]->set_node(2, elem->node_ptr(2));
     639        1888 :                   subelem[0]->set_node(3, elem->node_ptr(4));
     640        1888 :                   subelem[0]->set_node(4, elem->node_ptr(5));
     641        1888 :                   subelem[0]->set_node(5, elem->node_ptr(8));
     642             : 
     643        1888 :                   subelem[1]->set_node(0, elem->node_ptr(0));
     644        1888 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     645        1888 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     646        1888 :                   subelem[1]->set_node(3, elem->node_ptr(8));
     647        1888 :                   subelem[1]->set_node(4, elem->node_ptr(6));
     648        1888 :                   subelem[1]->set_node(5, elem->node_ptr(7));
     649             :                 }
     650             : 
     651             :               else
     652             :                 {
     653        2620 :                   subelem[0]->set_node(0, elem->node_ptr(0));
     654        2620 :                   subelem[0]->set_node(1, elem->node_ptr(1));
     655        2620 :                   subelem[0]->set_node(2, elem->node_ptr(3));
     656        2620 :                   subelem[0]->set_node(3, elem->node_ptr(4));
     657        2620 :                   subelem[0]->set_node(4, elem->node_ptr(8));
     658        2620 :                   subelem[0]->set_node(5, elem->node_ptr(7));
     659             : 
     660        2620 :                   subelem[1]->set_node(0, elem->node_ptr(1));
     661        2620 :                   subelem[1]->set_node(1, elem->node_ptr(2));
     662        2620 :                   subelem[1]->set_node(2, elem->node_ptr(3));
     663        2620 :                   subelem[1]->set_node(3, elem->node_ptr(5));
     664        2620 :                   subelem[1]->set_node(4, elem->node_ptr(6));
     665        2620 :                   subelem[1]->set_node(5, elem->node_ptr(8));
     666             :                 }
     667             : 
     668         272 :               break;
     669             :             }
     670             : 
     671        1792 :           case HEX8:
     672             :             {
     673        1792 :               BoundaryInfo & boundary_info = mesh.get_boundary_info();
     674             : 
     675             :               // Hexes all split into six tetrahedra
     676       85452 :               subelem[0] = Elem::build(TET4);
     677       85452 :               subelem[1] = Elem::build(TET4);
     678       85452 :               subelem[2] = Elem::build(TET4);
     679       85452 :               subelem[3] = Elem::build(TET4);
     680       85452 :               subelem[4] = Elem::build(TET4);
     681       85452 :               subelem[5] = Elem::build(TET4);
     682             : 
     683             :               // On faces, we choose the node with the highest
     684             :               // global id, and we split on the diagonal which
     685             :               // includes that node.  This ensures that (even in
     686             :               // parallel, even on distributed meshes) the same
     687             :               // diagonal split will be chosen for elements on either
     688             :               // side of the same quad face.
     689       44518 :               const unsigned int highest_n = highest_vertex_on(elem);
     690             : 
     691             :               // opposing_node[n] is the local node number of the node
     692             :               // on the farthest corner of a hex8 from local node n
     693             :               static const std::array<unsigned int, 8> opposing_node =
     694             :                 {6, 7, 4, 5, 2, 3, 0, 1};
     695             : 
     696             :               static const std::vector<std::vector<unsigned int>> sides_opposing_highest =
     697       45153 :                 {{2,3,5},{3,4,5},{1,4,5},{1,2,5},{0,2,3},{0,3,4},{0,1,4},{0,1,2}};
     698             :               static const std::vector<std::vector<unsigned int>> nodes_neighboring_highest =
     699       45153 :                 {{1,3,4},{0,2,5},{1,3,6},{0,2,7},{0,5,7},{1,4,6},{2,5,7},{3,4,6}};
     700             : 
     701             :               // Start by looking in three directions away from the
     702             :               // highest-id node.  In each direction there will be two
     703             :               // different possibilities for the split depending on
     704             :               // how the opposing face nodes are numbered.
     705             :               //
     706             :               // This is tricky enough that I'm not going to worry
     707             :               // about manually keeping tets oriented; we'll just call
     708             :               // orient() on each as we go.
     709             : 
     710        1792 :               unsigned int next_subelem = 0;
     711      179864 :               for (auto side : sides_opposing_highest[highest_n])
     712             :                 {
     713             :                   const std::vector<unsigned int> nodes_on_side =
     714      138930 :                     elem->nodes_on_side(side);
     715             : 
     716      133554 :                   auto [dn, dn2] = split_diagonal(elem, nodes_on_side);
     717             : 
     718        5376 :                   unsigned int split_on_neighbor = false;
     719      341933 :                   for (auto n : nodes_neighboring_highest[highest_n])
     720      302503 :                     if (dn == n || dn2 == n)
     721             :                       {
     722        4928 :                         split_on_neighbor = true;
     723        4928 :                         break;
     724             :                       }
     725             : 
     726             :                   // Add one or two elements for each opposing side,
     727             :                   // depending on whether the diagonal split there
     728             :                   // connects to the neighboring diagonal split or
     729             :                   // not.
     730      133554 :                   if (split_on_neighbor)
     731             :                     {
     732      109356 :                       subelem[next_subelem]->set_node(0, elem->node_ptr(highest_n));
     733      109356 :                       subelem[next_subelem]->set_node(1, elem->node_ptr(dn));
     734      109356 :                       subelem[next_subelem]->set_node(2, elem->node_ptr(dn2));
     735      150520 :                       for (auto n : nodes_on_side)
     736      150520 :                         if (n != dn && n != dn2)
     737             :                           {
     738      109356 :                             subelem[next_subelem]->set_node(3, elem->node_ptr(n));
     739        4928 :                             break;
     740             :                           }
     741       99500 :                       subelem[next_subelem]->orient(&boundary_info);
     742       99500 :                       ++next_subelem;
     743             : 
     744      109356 :                       subelem[next_subelem]->set_node(0, elem->node_ptr(highest_n));
     745      109356 :                       subelem[next_subelem]->set_node(1, elem->node_ptr(dn));
     746      109356 :                       subelem[next_subelem]->set_node(2, elem->node_ptr(dn2));
     747      147980 :                       for (auto n : reverse(nodes_on_side))
     748      147980 :                         if (n != dn && n != dn2)
     749             :                           {
     750      109356 :                             subelem[next_subelem]->set_node(3, elem->node_ptr(n));
     751        4928 :                             break;
     752             :                           }
     753       99500 :                       subelem[next_subelem]->orient(&boundary_info);
     754       99500 :                       ++next_subelem;
     755             :                     }
     756             :                   else
     757             :                     {
     758       34950 :                       subelem[next_subelem]->set_node(0, elem->node_ptr(highest_n));
     759       34950 :                       subelem[next_subelem]->set_node(1, elem->node_ptr(dn));
     760       34950 :                       subelem[next_subelem]->set_node(2, elem->node_ptr(dn2));
     761      101267 :                       for (auto n : nodes_on_side)
     762      337087 :                         for (auto n2 : nodes_neighboring_highest[highest_n])
     763      268406 :                           if (n == n2)
     764             :                             {
     765       34950 :                               subelem[next_subelem]->set_node(3, elem->node_ptr(n));
     766       33606 :                               goto break_both_loops;
     767             :                             }
     768             : 
     769       34054 :                       break_both_loops:
     770       34054 :                       subelem[next_subelem]->orient(&boundary_info);
     771       34054 :                       ++next_subelem;
     772             :                     }
     773             :                 }
     774             : 
     775             :               // At this point we've created between 3 and 6 tets.
     776             :               // What's left to do depends on how many.
     777             : 
     778             :               // If we just chopped off three vertices into three
     779             :               // tets, then the best way to split this hex would be
     780             :               // the symmetric five-split.  Chop off the opposing
     781             :               // vertex too, and then the remaining interior is our
     782             :               // final tet.
     783       44518 :               if (next_subelem == 3)
     784             :                 {
     785        2470 :                   subelem[next_subelem]->set_node(0, elem->node_ptr(opposing_nodes[highest_n][0]));
     786        2470 :                   subelem[next_subelem]->set_node(1, elem->node_ptr(opposing_nodes[highest_n][1]));
     787        2470 :                   subelem[next_subelem]->set_node(2, elem->node_ptr(opposing_nodes[highest_n][2]));
     788        2470 :                   subelem[next_subelem]->set_node(3, elem->node_ptr(opposing_node[highest_n]));
     789        2470 :                   subelem[next_subelem]->orient(&boundary_info);
     790           0 :                   ++next_subelem;
     791             : 
     792        2470 :                   subelem[next_subelem]->set_node(0, elem->node_ptr(opposing_nodes[highest_n][0]));
     793        2470 :                   subelem[next_subelem]->set_node(1, elem->node_ptr(opposing_nodes[highest_n][1]));
     794        2470 :                   subelem[next_subelem]->set_node(2, elem->node_ptr(opposing_nodes[highest_n][2]));
     795        2470 :                   subelem[next_subelem]->set_node(3, elem->node_ptr(highest_n));
     796        2470 :                   subelem[next_subelem]->orient(&boundary_info);
     797           0 :                   ++next_subelem;
     798             : 
     799             :                   // We don't need the 6th tet after all
     800           0 :                   subelem[next_subelem].reset();
     801           0 :                   ++next_subelem;
     802             :                 }
     803             : 
     804             :               // If we just chopped off one (or two) vertices into
     805             :               // tets, then the remaining gap is best (or only) filled
     806             :               // by pairing another tet with each.
     807       44518 :               if (next_subelem == 4 ||
     808             :                   next_subelem == 5)
     809             :                 {
     810       90748 :                   for (auto side : sides_opposing_highest[highest_n])
     811             :                     {
     812             :                       const std::vector<unsigned int> nodes_on_side =
     813       68943 :                         elem->nodes_on_side(side);
     814             : 
     815       67767 :                       auto [dn, dn2] = split_diagonal(elem, nodes_on_side);
     816             : 
     817        1176 :                       unsigned int split_on_neighbor = false;
     818      191339 :                       for (auto n : nodes_neighboring_highest[highest_n])
     819      163519 :                         if (dn == n || dn2 == n)
     820             :                           {
     821         728 :                             split_on_neighbor = true;
     822         728 :                             break;
     823             :                           }
     824             : 
     825             :                       // The two !split_on_neighbor sides are where we
     826             :                       // need the two remaining tets
     827       67767 :                       if (!split_on_neighbor)
     828             :                         {
     829       27540 :                           subelem[next_subelem]->set_node(0, elem->node_ptr(highest_n));
     830       27540 :                           subelem[next_subelem]->set_node(1, elem->node_ptr(dn));
     831       27540 :                           subelem[next_subelem]->set_node(2, elem->node_ptr(dn2));
     832       27540 :                           subelem[next_subelem]->set_node(3, elem->node_ptr(opposing_node[highest_n]));
     833       26644 :                           subelem[next_subelem]->orient(&boundary_info);
     834       26644 :                           ++next_subelem;
     835             :                         }
     836             :                     }
     837             :                 }
     838             : 
     839             :               // Whether we got there by creating six tets from the
     840             :               // first for loop or by patching up the split afterward,
     841             :               // we should have considered six tets (possibly
     842             :               // including one deleted one...) at this point.
     843        1792 :               libmesh_assert(next_subelem == 6);
     844             : 
     845        1792 :               break;
     846             :             }
     847             : 
     848         142 :           case PRISM6:
     849             :             {
     850             :               // Prisms all split into three tetrahedra
     851         276 :               subelem[0] = Elem::build(TET4);
     852         276 :               subelem[1] = Elem::build(TET4);
     853         276 :               subelem[2] = Elem::build(TET4);
     854             : 
     855             :               // Triangular faces are not split.
     856             : 
     857             :               // On quad faces, we choose the node with the highest
     858             :               // global id, and we split on the diagonal which
     859             :               // includes that node.  This ensures that (even in
     860             :               // parallel, even on distributed meshes) the same
     861             :               // diagonal split will be chosen for elements on either
     862             :               // side of the same quad face.  It also ensures that we
     863             :               // always have a mix of "clockwise" and
     864             :               // "counterclockwise" split faces (two of one and one
     865             :               // of the other on each prism; this is useful since the
     866             :               // alternative all-clockwise or all-counterclockwise
     867             :               // face splittings can't be turned into tets without
     868             :               // adding more nodes
     869             : 
     870             :               // Split on 0-4 diagonal
     871         142 :               if (split_first_diagonal(elem, 0,4, 1,3))
     872             :                 {
     873             :                   // Split on 0-5 diagonal
     874         142 :                   if (split_first_diagonal(elem, 0,5, 2,3))
     875             :                     {
     876             :                       // Split on 1-5 diagonal
     877         142 :                       if (split_first_diagonal(elem, 1,5, 2,4))
     878             :                         {
     879          75 :                           subelem[0]->set_node(0, elem->node_ptr(0));
     880          75 :                           subelem[0]->set_node(1, elem->node_ptr(4));
     881          75 :                           subelem[0]->set_node(2, elem->node_ptr(5));
     882          75 :                           subelem[0]->set_node(3, elem->node_ptr(3));
     883             : 
     884          75 :                           subelem[1]->set_node(0, elem->node_ptr(0));
     885          75 :                           subelem[1]->set_node(1, elem->node_ptr(4));
     886          75 :                           subelem[1]->set_node(2, elem->node_ptr(1));
     887          75 :                           subelem[1]->set_node(3, elem->node_ptr(5));
     888             : 
     889          75 :                           subelem[2]->set_node(0, elem->node_ptr(0));
     890          75 :                           subelem[2]->set_node(1, elem->node_ptr(1));
     891          75 :                           subelem[2]->set_node(2, elem->node_ptr(2));
     892          75 :                           subelem[2]->set_node(3, elem->node_ptr(5));
     893             :                         }
     894             :                       else // Split on 2-4 diagonal
     895             :                         {
     896           2 :                           libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
     897             : 
     898          75 :                           subelem[0]->set_node(0, elem->node_ptr(0));
     899          75 :                           subelem[0]->set_node(1, elem->node_ptr(4));
     900          75 :                           subelem[0]->set_node(2, elem->node_ptr(5));
     901          75 :                           subelem[0]->set_node(3, elem->node_ptr(3));
     902             : 
     903          75 :                           subelem[1]->set_node(0, elem->node_ptr(0));
     904          75 :                           subelem[1]->set_node(1, elem->node_ptr(4));
     905          75 :                           subelem[1]->set_node(2, elem->node_ptr(2));
     906          75 :                           subelem[1]->set_node(3, elem->node_ptr(5));
     907             : 
     908          75 :                           subelem[2]->set_node(0, elem->node_ptr(0));
     909          75 :                           subelem[2]->set_node(1, elem->node_ptr(1));
     910          75 :                           subelem[2]->set_node(2, elem->node_ptr(2));
     911          75 :                           subelem[2]->set_node(3, elem->node_ptr(4));
     912             :                         }
     913             :                     }
     914             :                   else // Split on 2-3 diagonal
     915             :                     {
     916           0 :                       libmesh_assert (split_first_diagonal(elem, 2,3, 0,5));
     917             : 
     918             :                       // 0-4 and 2-3 split implies 2-4 split
     919           0 :                       libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
     920             : 
     921           0 :                       subelem[0]->set_node(0, elem->node_ptr(0));
     922           0 :                       subelem[0]->set_node(1, elem->node_ptr(4));
     923           0 :                       subelem[0]->set_node(2, elem->node_ptr(2));
     924           0 :                       subelem[0]->set_node(3, elem->node_ptr(3));
     925             : 
     926           0 :                       subelem[1]->set_node(0, elem->node_ptr(3));
     927           0 :                       subelem[1]->set_node(1, elem->node_ptr(4));
     928           0 :                       subelem[1]->set_node(2, elem->node_ptr(2));
     929           0 :                       subelem[1]->set_node(3, elem->node_ptr(5));
     930             : 
     931           0 :                       subelem[2]->set_node(0, elem->node_ptr(0));
     932           0 :                       subelem[2]->set_node(1, elem->node_ptr(1));
     933           0 :                       subelem[2]->set_node(2, elem->node_ptr(2));
     934           0 :                       subelem[2]->set_node(3, elem->node_ptr(4));
     935             :                     }
     936             :                 }
     937             :               else // Split on 1-3 diagonal
     938             :                 {
     939           0 :                   libmesh_assert (split_first_diagonal(elem, 1,3, 0,4));
     940             : 
     941             :                   // Split on 0-5 diagonal
     942           0 :                   if (split_first_diagonal(elem, 0,5, 2,3))
     943             :                     {
     944             :                       // 1-3 and 0-5 split implies 1-5 split
     945           0 :                       libmesh_assert (split_first_diagonal(elem, 1,5, 2,4));
     946             : 
     947           0 :                       subelem[0]->set_node(0, elem->node_ptr(1));
     948           0 :                       subelem[0]->set_node(1, elem->node_ptr(3));
     949           0 :                       subelem[0]->set_node(2, elem->node_ptr(4));
     950           0 :                       subelem[0]->set_node(3, elem->node_ptr(5));
     951             : 
     952           0 :                       subelem[1]->set_node(0, elem->node_ptr(1));
     953           0 :                       subelem[1]->set_node(1, elem->node_ptr(0));
     954           0 :                       subelem[1]->set_node(2, elem->node_ptr(3));
     955           0 :                       subelem[1]->set_node(3, elem->node_ptr(5));
     956             : 
     957           0 :                       subelem[2]->set_node(0, elem->node_ptr(0));
     958           0 :                       subelem[2]->set_node(1, elem->node_ptr(1));
     959           0 :                       subelem[2]->set_node(2, elem->node_ptr(2));
     960           0 :                       subelem[2]->set_node(3, elem->node_ptr(5));
     961             :                     }
     962             :                   else // Split on 2-3 diagonal
     963             :                     {
     964           0 :                       libmesh_assert (split_first_diagonal(elem, 2,3, 0,5));
     965             : 
     966             :                       // Split on 1-5 diagonal
     967           0 :                       if (split_first_diagonal(elem, 1,5, 2,4))
     968             :                         {
     969           0 :                           subelem[0]->set_node(0, elem->node_ptr(0));
     970           0 :                           subelem[0]->set_node(1, elem->node_ptr(1));
     971           0 :                           subelem[0]->set_node(2, elem->node_ptr(2));
     972           0 :                           subelem[0]->set_node(3, elem->node_ptr(3));
     973             : 
     974           0 :                           subelem[1]->set_node(0, elem->node_ptr(3));
     975           0 :                           subelem[1]->set_node(1, elem->node_ptr(1));
     976           0 :                           subelem[1]->set_node(2, elem->node_ptr(2));
     977           0 :                           subelem[1]->set_node(3, elem->node_ptr(5));
     978             : 
     979           0 :                           subelem[2]->set_node(0, elem->node_ptr(1));
     980           0 :                           subelem[2]->set_node(1, elem->node_ptr(3));
     981           0 :                           subelem[2]->set_node(2, elem->node_ptr(4));
     982           0 :                           subelem[2]->set_node(3, elem->node_ptr(5));
     983             :                         }
     984             :                       else // Split on 2-4 diagonal
     985             :                         {
     986           0 :                           libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
     987             : 
     988           0 :                           subelem[0]->set_node(0, elem->node_ptr(0));
     989           0 :                           subelem[0]->set_node(1, elem->node_ptr(1));
     990           0 :                           subelem[0]->set_node(2, elem->node_ptr(2));
     991           0 :                           subelem[0]->set_node(3, elem->node_ptr(3));
     992             : 
     993           0 :                           subelem[1]->set_node(0, elem->node_ptr(2));
     994           0 :                           subelem[1]->set_node(1, elem->node_ptr(3));
     995           0 :                           subelem[1]->set_node(2, elem->node_ptr(4));
     996           0 :                           subelem[1]->set_node(3, elem->node_ptr(5));
     997             : 
     998           0 :                           subelem[2]->set_node(0, elem->node_ptr(3));
     999           0 :                           subelem[2]->set_node(1, elem->node_ptr(1));
    1000           0 :                           subelem[2]->set_node(2, elem->node_ptr(2));
    1001           0 :                           subelem[2]->set_node(3, elem->node_ptr(4));
    1002             :                         }
    1003             :                     }
    1004             :                 }
    1005             : 
    1006           4 :               break;
    1007             :             }
    1008             : 
    1009         426 :           case PRISM20:
    1010             :           case PRISM21:
    1011             :             libmesh_experimental(); // We should upgrade this to TET14...
    1012             :             libmesh_fallthrough();
    1013             :           case PRISM18:
    1014             :             {
    1015         828 :               subelem[0] = Elem::build(TET10);
    1016         828 :               subelem[1] = Elem::build(TET10);
    1017         828 :               subelem[2] = Elem::build(TET10);
    1018             : 
    1019             :               // Split on 0-4 diagonal
    1020         426 :               if (split_first_diagonal(elem, 0,4, 1,3))
    1021             :                 {
    1022             :                   // Split on 0-5 diagonal
    1023         426 :                   if (split_first_diagonal(elem, 0,5, 2,3))
    1024             :                     {
    1025             :                       // Split on 1-5 diagonal
    1026         426 :                       if (split_first_diagonal(elem, 1,5, 2,4))
    1027             :                         {
    1028         225 :                           subelem[0]->set_node(0, elem->node_ptr(0));
    1029         225 :                           subelem[0]->set_node(1, elem->node_ptr(4));
    1030         225 :                           subelem[0]->set_node(2, elem->node_ptr(5));
    1031         225 :                           subelem[0]->set_node(3, elem->node_ptr(3));
    1032             : 
    1033         225 :                           subelem[0]->set_node(4, elem->node_ptr(15));
    1034         225 :                           subelem[0]->set_node(5, elem->node_ptr(13));
    1035         225 :                           subelem[0]->set_node(6, elem->node_ptr(17));
    1036         225 :                           subelem[0]->set_node(7, elem->node_ptr(9));
    1037         225 :                           subelem[0]->set_node(8, elem->node_ptr(12));
    1038         225 :                           subelem[0]->set_node(9, elem->node_ptr(14));
    1039             : 
    1040         225 :                           subelem[1]->set_node(0, elem->node_ptr(0));
    1041         225 :                           subelem[1]->set_node(1, elem->node_ptr(4));
    1042         225 :                           subelem[1]->set_node(2, elem->node_ptr(1));
    1043         225 :                           subelem[1]->set_node(3, elem->node_ptr(5));
    1044             : 
    1045         225 :                           subelem[1]->set_node(4, elem->node_ptr(15));
    1046         225 :                           subelem[1]->set_node(5, elem->node_ptr(10));
    1047         225 :                           subelem[1]->set_node(6, elem->node_ptr(6));
    1048         225 :                           subelem[1]->set_node(7, elem->node_ptr(17));
    1049         225 :                           subelem[1]->set_node(8, elem->node_ptr(13));
    1050         225 :                           subelem[1]->set_node(9, elem->node_ptr(16));
    1051             : 
    1052         225 :                           subelem[2]->set_node(0, elem->node_ptr(0));
    1053         225 :                           subelem[2]->set_node(1, elem->node_ptr(1));
    1054         225 :                           subelem[2]->set_node(2, elem->node_ptr(2));
    1055         225 :                           subelem[2]->set_node(3, elem->node_ptr(5));
    1056             : 
    1057         225 :                           subelem[2]->set_node(4, elem->node_ptr(6));
    1058         225 :                           subelem[2]->set_node(5, elem->node_ptr(7));
    1059         225 :                           subelem[2]->set_node(6, elem->node_ptr(8));
    1060         225 :                           subelem[2]->set_node(7, elem->node_ptr(17));
    1061         225 :                           subelem[2]->set_node(8, elem->node_ptr(16));
    1062         225 :                           subelem[2]->set_node(9, elem->node_ptr(11));
    1063             :                         }
    1064             :                       else // Split on 2-4 diagonal
    1065             :                         {
    1066           6 :                           libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
    1067             : 
    1068         225 :                           subelem[0]->set_node(0, elem->node_ptr(0));
    1069         225 :                           subelem[0]->set_node(1, elem->node_ptr(4));
    1070         225 :                           subelem[0]->set_node(2, elem->node_ptr(5));
    1071         225 :                           subelem[0]->set_node(3, elem->node_ptr(3));
    1072             : 
    1073         225 :                           subelem[0]->set_node(4, elem->node_ptr(15));
    1074         225 :                           subelem[0]->set_node(5, elem->node_ptr(13));
    1075         225 :                           subelem[0]->set_node(6, elem->node_ptr(17));
    1076         225 :                           subelem[0]->set_node(7, elem->node_ptr(9));
    1077         225 :                           subelem[0]->set_node(8, elem->node_ptr(12));
    1078         225 :                           subelem[0]->set_node(9, elem->node_ptr(14));
    1079             : 
    1080         225 :                           subelem[1]->set_node(0, elem->node_ptr(0));
    1081         225 :                           subelem[1]->set_node(1, elem->node_ptr(4));
    1082         225 :                           subelem[1]->set_node(2, elem->node_ptr(2));
    1083         225 :                           subelem[1]->set_node(3, elem->node_ptr(5));
    1084             : 
    1085         225 :                           subelem[1]->set_node(4, elem->node_ptr(15));
    1086         225 :                           subelem[1]->set_node(5, elem->node_ptr(16));
    1087         225 :                           subelem[1]->set_node(6, elem->node_ptr(8));
    1088         225 :                           subelem[1]->set_node(7, elem->node_ptr(17));
    1089         225 :                           subelem[1]->set_node(8, elem->node_ptr(13));
    1090         225 :                           subelem[1]->set_node(9, elem->node_ptr(11));
    1091             : 
    1092         225 :                           subelem[2]->set_node(0, elem->node_ptr(0));
    1093         225 :                           subelem[2]->set_node(1, elem->node_ptr(1));
    1094         225 :                           subelem[2]->set_node(2, elem->node_ptr(2));
    1095         225 :                           subelem[2]->set_node(3, elem->node_ptr(4));
    1096             : 
    1097         225 :                           subelem[2]->set_node(4, elem->node_ptr(6));
    1098         225 :                           subelem[2]->set_node(5, elem->node_ptr(7));
    1099         225 :                           subelem[2]->set_node(6, elem->node_ptr(8));
    1100         225 :                           subelem[2]->set_node(7, elem->node_ptr(15));
    1101         225 :                           subelem[2]->set_node(8, elem->node_ptr(10));
    1102         225 :                           subelem[2]->set_node(9, elem->node_ptr(16));
    1103             :                         }
    1104             :                     }
    1105             :                   else // Split on 2-3 diagonal
    1106             :                     {
    1107           0 :                       libmesh_assert (split_first_diagonal(elem, 2,3, 0,5));
    1108             : 
    1109             :                       // 0-4 and 2-3 split implies 2-4 split
    1110           0 :                       libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
    1111             : 
    1112           0 :                       subelem[0]->set_node(0, elem->node_ptr(0));
    1113           0 :                       subelem[0]->set_node(1, elem->node_ptr(4));
    1114           0 :                       subelem[0]->set_node(2, elem->node_ptr(2));
    1115           0 :                       subelem[0]->set_node(3, elem->node_ptr(3));
    1116             : 
    1117           0 :                       subelem[0]->set_node(4, elem->node_ptr(15));
    1118           0 :                       subelem[0]->set_node(5, elem->node_ptr(16));
    1119           0 :                       subelem[0]->set_node(6, elem->node_ptr(8));
    1120           0 :                       subelem[0]->set_node(7, elem->node_ptr(9));
    1121           0 :                       subelem[0]->set_node(8, elem->node_ptr(12));
    1122           0 :                       subelem[0]->set_node(9, elem->node_ptr(17));
    1123             : 
    1124           0 :                       subelem[1]->set_node(0, elem->node_ptr(3));
    1125           0 :                       subelem[1]->set_node(1, elem->node_ptr(4));
    1126           0 :                       subelem[1]->set_node(2, elem->node_ptr(2));
    1127           0 :                       subelem[1]->set_node(3, elem->node_ptr(5));
    1128             : 
    1129           0 :                       subelem[1]->set_node(4, elem->node_ptr(12));
    1130           0 :                       subelem[1]->set_node(5, elem->node_ptr(16));
    1131           0 :                       subelem[1]->set_node(6, elem->node_ptr(17));
    1132           0 :                       subelem[1]->set_node(7, elem->node_ptr(14));
    1133           0 :                       subelem[1]->set_node(8, elem->node_ptr(13));
    1134           0 :                       subelem[1]->set_node(9, elem->node_ptr(11));
    1135             : 
    1136           0 :                       subelem[2]->set_node(0, elem->node_ptr(0));
    1137           0 :                       subelem[2]->set_node(1, elem->node_ptr(1));
    1138           0 :                       subelem[2]->set_node(2, elem->node_ptr(2));
    1139           0 :                       subelem[2]->set_node(3, elem->node_ptr(4));
    1140             : 
    1141           0 :                       subelem[2]->set_node(4, elem->node_ptr(6));
    1142           0 :                       subelem[2]->set_node(5, elem->node_ptr(7));
    1143           0 :                       subelem[2]->set_node(6, elem->node_ptr(8));
    1144           0 :                       subelem[2]->set_node(7, elem->node_ptr(15));
    1145           0 :                       subelem[2]->set_node(8, elem->node_ptr(10));
    1146           0 :                       subelem[2]->set_node(9, elem->node_ptr(16));
    1147             :                     }
    1148             :                 }
    1149             :               else // Split on 1-3 diagonal
    1150             :                 {
    1151           0 :                   libmesh_assert (split_first_diagonal(elem, 1,3, 0,4));
    1152             : 
    1153             :                   // Split on 0-5 diagonal
    1154           0 :                   if (split_first_diagonal(elem, 0,5, 2,3))
    1155             :                     {
    1156             :                       // 1-3 and 0-5 split implies 1-5 split
    1157           0 :                       libmesh_assert (split_first_diagonal(elem, 1,5, 2,4));
    1158             : 
    1159           0 :                       subelem[0]->set_node(0, elem->node_ptr(1));
    1160           0 :                       subelem[0]->set_node(1, elem->node_ptr(3));
    1161           0 :                       subelem[0]->set_node(2, elem->node_ptr(4));
    1162           0 :                       subelem[0]->set_node(3, elem->node_ptr(5));
    1163             : 
    1164           0 :                       subelem[0]->set_node(4, elem->node_ptr(15));
    1165           0 :                       subelem[0]->set_node(5, elem->node_ptr(12));
    1166           0 :                       subelem[0]->set_node(6, elem->node_ptr(10));
    1167           0 :                       subelem[0]->set_node(7, elem->node_ptr(16));
    1168           0 :                       subelem[0]->set_node(8, elem->node_ptr(14));
    1169           0 :                       subelem[0]->set_node(9, elem->node_ptr(13));
    1170             : 
    1171           0 :                       subelem[1]->set_node(0, elem->node_ptr(1));
    1172           0 :                       subelem[1]->set_node(1, elem->node_ptr(0));
    1173           0 :                       subelem[1]->set_node(2, elem->node_ptr(3));
    1174           0 :                       subelem[1]->set_node(3, elem->node_ptr(5));
    1175             : 
    1176           0 :                       subelem[1]->set_node(4, elem->node_ptr(6));
    1177           0 :                       subelem[1]->set_node(5, elem->node_ptr(9));
    1178           0 :                       subelem[1]->set_node(6, elem->node_ptr(15));
    1179           0 :                       subelem[1]->set_node(7, elem->node_ptr(16));
    1180           0 :                       subelem[1]->set_node(8, elem->node_ptr(17));
    1181           0 :                       subelem[1]->set_node(9, elem->node_ptr(14));
    1182             : 
    1183           0 :                       subelem[2]->set_node(0, elem->node_ptr(0));
    1184           0 :                       subelem[2]->set_node(1, elem->node_ptr(1));
    1185           0 :                       subelem[2]->set_node(2, elem->node_ptr(2));
    1186           0 :                       subelem[2]->set_node(3, elem->node_ptr(5));
    1187             : 
    1188           0 :                       subelem[2]->set_node(4, elem->node_ptr(6));
    1189           0 :                       subelem[2]->set_node(5, elem->node_ptr(7));
    1190           0 :                       subelem[2]->set_node(6, elem->node_ptr(8));
    1191           0 :                       subelem[2]->set_node(7, elem->node_ptr(17));
    1192           0 :                       subelem[2]->set_node(8, elem->node_ptr(16));
    1193           0 :                       subelem[2]->set_node(9, elem->node_ptr(11));
    1194             :                     }
    1195             :                   else // Split on 2-3 diagonal
    1196             :                     {
    1197           0 :                       libmesh_assert (split_first_diagonal(elem, 2,3, 0,5));
    1198             : 
    1199             :                       // Split on 1-5 diagonal
    1200           0 :                       if (split_first_diagonal(elem, 1,5, 2,4))
    1201             :                         {
    1202           0 :                           subelem[0]->set_node(0, elem->node_ptr(0));
    1203           0 :                           subelem[0]->set_node(1, elem->node_ptr(1));
    1204           0 :                           subelem[0]->set_node(2, elem->node_ptr(2));
    1205           0 :                           subelem[0]->set_node(3, elem->node_ptr(3));
    1206             : 
    1207           0 :                           subelem[0]->set_node(4, elem->node_ptr(6));
    1208           0 :                           subelem[0]->set_node(5, elem->node_ptr(7));
    1209           0 :                           subelem[0]->set_node(6, elem->node_ptr(8));
    1210           0 :                           subelem[0]->set_node(7, elem->node_ptr(9));
    1211           0 :                           subelem[0]->set_node(8, elem->node_ptr(15));
    1212           0 :                           subelem[0]->set_node(9, elem->node_ptr(17));
    1213             : 
    1214           0 :                           subelem[1]->set_node(0, elem->node_ptr(3));
    1215           0 :                           subelem[1]->set_node(1, elem->node_ptr(1));
    1216           0 :                           subelem[1]->set_node(2, elem->node_ptr(2));
    1217           0 :                           subelem[1]->set_node(3, elem->node_ptr(5));
    1218             : 
    1219           0 :                           subelem[1]->set_node(4, elem->node_ptr(15));
    1220           0 :                           subelem[1]->set_node(5, elem->node_ptr(7));
    1221           0 :                           subelem[1]->set_node(6, elem->node_ptr(17));
    1222           0 :                           subelem[1]->set_node(7, elem->node_ptr(14));
    1223           0 :                           subelem[1]->set_node(8, elem->node_ptr(16));
    1224           0 :                           subelem[1]->set_node(9, elem->node_ptr(11));
    1225             : 
    1226           0 :                           subelem[2]->set_node(0, elem->node_ptr(1));
    1227           0 :                           subelem[2]->set_node(1, elem->node_ptr(3));
    1228           0 :                           subelem[2]->set_node(2, elem->node_ptr(4));
    1229           0 :                           subelem[2]->set_node(3, elem->node_ptr(5));
    1230             : 
    1231           0 :                           subelem[2]->set_node(4, elem->node_ptr(15));
    1232           0 :                           subelem[2]->set_node(5, elem->node_ptr(12));
    1233           0 :                           subelem[2]->set_node(6, elem->node_ptr(10));
    1234           0 :                           subelem[2]->set_node(7, elem->node_ptr(16));
    1235           0 :                           subelem[2]->set_node(8, elem->node_ptr(14));
    1236           0 :                           subelem[2]->set_node(9, elem->node_ptr(13));
    1237             :                         }
    1238             :                       else // Split on 2-4 diagonal
    1239             :                         {
    1240           0 :                           libmesh_assert (split_first_diagonal(elem, 2,4, 1,5));
    1241             : 
    1242           0 :                           subelem[0]->set_node(0, elem->node_ptr(0));
    1243           0 :                           subelem[0]->set_node(1, elem->node_ptr(1));
    1244           0 :                           subelem[0]->set_node(2, elem->node_ptr(2));
    1245           0 :                           subelem[0]->set_node(3, elem->node_ptr(3));
    1246             : 
    1247           0 :                           subelem[0]->set_node(4, elem->node_ptr(6));
    1248           0 :                           subelem[0]->set_node(5, elem->node_ptr(7));
    1249           0 :                           subelem[0]->set_node(6, elem->node_ptr(8));
    1250           0 :                           subelem[0]->set_node(7, elem->node_ptr(9));
    1251           0 :                           subelem[0]->set_node(8, elem->node_ptr(15));
    1252           0 :                           subelem[0]->set_node(9, elem->node_ptr(17));
    1253             : 
    1254           0 :                           subelem[1]->set_node(0, elem->node_ptr(2));
    1255           0 :                           subelem[1]->set_node(1, elem->node_ptr(3));
    1256           0 :                           subelem[1]->set_node(2, elem->node_ptr(4));
    1257           0 :                           subelem[1]->set_node(3, elem->node_ptr(5));
    1258             : 
    1259           0 :                           subelem[1]->set_node(4, elem->node_ptr(17));
    1260           0 :                           subelem[1]->set_node(5, elem->node_ptr(12));
    1261           0 :                           subelem[1]->set_node(6, elem->node_ptr(16));
    1262           0 :                           subelem[1]->set_node(7, elem->node_ptr(11));
    1263           0 :                           subelem[1]->set_node(8, elem->node_ptr(14));
    1264           0 :                           subelem[1]->set_node(9, elem->node_ptr(13));
    1265             : 
    1266           0 :                           subelem[2]->set_node(0, elem->node_ptr(3));
    1267           0 :                           subelem[2]->set_node(1, elem->node_ptr(1));
    1268           0 :                           subelem[2]->set_node(2, elem->node_ptr(2));
    1269           0 :                           subelem[2]->set_node(3, elem->node_ptr(4));
    1270             : 
    1271           0 :                           subelem[2]->set_node(4, elem->node_ptr(15));
    1272           0 :                           subelem[2]->set_node(5, elem->node_ptr(7));
    1273           0 :                           subelem[2]->set_node(6, elem->node_ptr(17));
    1274           0 :                           subelem[2]->set_node(7, elem->node_ptr(12));
    1275           0 :                           subelem[2]->set_node(8, elem->node_ptr(10));
    1276           0 :                           subelem[2]->set_node(9, elem->node_ptr(16));
    1277             :                         }
    1278             :                     }
    1279             :                 }
    1280             : 
    1281          12 :               break;
    1282             :             }
    1283             : 
    1284         781 :           case C0POLYGON:
    1285             :             {
    1286             :               // Split a C0Polygon into the triangles defined by its
    1287             :               // current triangulation.  This relies on the user having
    1288             :               // a valid triangulation (the constructor sets a default
    1289             :               // one, and the user can refresh it via retriangulate()
    1290             :               // after moving nodes).
    1291         781 :               const C0Polygon * polygon = cast_ptr<const C0Polygon *>(elem);
    1292          22 :               const unsigned int n_subtri = polygon->n_subtriangles();
    1293        2698 :               for (unsigned int t = 0; t != n_subtri; ++t)
    1294             :                 {
    1295        1917 :                   const std::array<int, 3> tri = polygon->subtriangle(t);
    1296        1917 :                   if (tri[0] < 0 || tri[1] < 0 || tri[2] < 0)
    1297           0 :                     libmesh_not_implemented_msg
    1298             :                       ("Cannot convert a C0Polygon whose triangulation\n"
    1299             :                        "introduces special (non-vertex) points");
    1300        1917 :                   subelem[t] = Elem::build(TRI3);
    1301        2025 :                   subelem[t]->set_node(0, elem->node_ptr(tri[0]));
    1302        2025 :                   subelem[t]->set_node(1, elem->node_ptr(tri[1]));
    1303        2025 :                   subelem[t]->set_node(2, elem->node_ptr(tri[2]));
    1304             :                 }
    1305             : 
    1306          22 :               break;
    1307             :             }
    1308             : 
    1309         142 :           case C0POLYHEDRON:
    1310             :             {
    1311             :               // Split a C0Polyhedron into the tetrahedra defined by its
    1312             :               // current tetrahedralization.  If the polyhedron required
    1313             :               // a mid-element node, the user is expected to have added
    1314             :               // that node to the mesh during construction; we just
    1315             :               // reference it via the polyhedron's node pointers.
    1316             :               const C0Polyhedron * polyhedron =
    1317         142 :                 cast_ptr<const C0Polyhedron *>(elem);
    1318           4 :               const unsigned int n_sub = polyhedron->n_subelements();
    1319        1917 :               for (unsigned int t = 0; t != n_sub; ++t)
    1320             :                 {
    1321        1775 :                   const std::array<int, 4> tet = polyhedron->subelement(t);
    1322        1775 :                   if (tet[0] < 0 || tet[1] < 0 || tet[2] < 0 || tet[3] < 0)
    1323           0 :                     libmesh_not_implemented_msg
    1324             :                       ("Cannot convert a C0Polyhedron whose triangulation\n"
    1325             :                        "introduces special (non-vertex) points");
    1326        1775 :                   subelem[t] = Elem::build(TET4);
    1327        1875 :                   subelem[t]->set_node(0, elem->node_ptr(tet[0]));
    1328        1875 :                   subelem[t]->set_node(1, elem->node_ptr(tet[1]));
    1329        1875 :                   subelem[t]->set_node(2, elem->node_ptr(tet[2]));
    1330        1875 :                   subelem[t]->set_node(3, elem->node_ptr(tet[3]));
    1331             :                 }
    1332             :               // There is a concern that two neighbor polyhedra might have
    1333             :               // a triangulation of a side that does not match. But the
    1334             :               // default triangulation is based on the side's triangulation
    1335             :               // and the side element is supposed to be shared (that's why
    1336             :               // shared pointers to polygons are used to build the polyhedra).
    1337             :               // So the default one should work.
    1338             : 
    1339           4 :               break;
    1340             :             }
    1341             : 
    1342             :             // No need to split elements that are already simplicial:
    1343       24163 :           case EDGE2:
    1344             :           case EDGE3:
    1345             :           case EDGE4:
    1346             :           case TRI3:
    1347             :           case TRI6:
    1348             :           case TRI7:
    1349             :           case TET4:
    1350             :           case TET10:
    1351             :           case TET14:
    1352             :           case INFEDGE2:
    1353             :             // No way to split infinite quad/prism elements, so
    1354             :             // hopefully no need to
    1355             :           case INFQUAD4:
    1356             :           case INFQUAD6:
    1357             :           case INFPRISM6:
    1358             :           case INFPRISM12:
    1359        1868 :             continue;
    1360             :             // If we're left with an unimplemented hex we're probably
    1361             :             // out of luck.  TODO: implement hexes
    1362           0 :           default:
    1363             :             {
    1364           0 :               libMesh::err << "Error, encountered unimplemented element "
    1365           0 :                            << Utility::enum_to_string<ElemType>(etype)
    1366           0 :                            << " in MeshTools::Modification::all_tri()..."
    1367           0 :                            << std::endl;
    1368           0 :               libmesh_not_implemented();
    1369         934 :             }
    1370       22295 :           } // end switch (etype)
    1371             : 
    1372             :         // Be sure the correct data is set for all subelems.
    1373       62424 :         const unsigned int nei = elem->n_extra_integers();
    1374      370882 :         for (unsigned int i=0; i != max_subelems; ++i)
    1375      321102 :           if (subelem[i]) {
    1376      302864 :             subelem[i]->processor_id() = elem->processor_id();
    1377      302864 :             subelem[i]->subdomain_id() = elem->subdomain_id();
    1378             : 
    1379             :             // Copy any extra element data.  Since the subelements
    1380             :             // haven't been added to the mesh yet any allocation has
    1381             :             // to be done manually.
    1382      302864 :             subelem[i]->add_extra_integers(nei);
    1383      309948 :             for (unsigned int ei=0; ei != nei; ++ei)
    1384        7588 :               subelem[ei]->set_extra_integer(ei, elem->get_extra_integer(ei));
    1385             : 
    1386             : 
    1387             :             // Copy any mapping data.
    1388      315420 :             subelem[i]->set_mapping_type(elem->mapping_type());
    1389       25112 :             subelem[i]->set_mapping_data(elem->mapping_data());
    1390             :           }
    1391             : 
    1392             :         // On a mesh with boundary data, we need to move that data to
    1393             :         // the new elements.
    1394             : 
    1395             :         // On a mesh which is distributed, we need to move
    1396             :         // remote_elem links to the new elements.
    1397       62424 :         bool mesh_is_serial = mesh.is_serial();
    1398             : 
    1399       62424 :         if (mesh_has_boundary_data || !mesh_is_serial)
    1400             :           {
    1401             :             // Container to key boundary IDs handed back by the BoundaryInfo object.
    1402         444 :             std::vector<boundary_id_type> bc_ids;
    1403             : 
    1404      117374 :             for (auto sn : elem->side_index_range())
    1405             :               {
    1406       97821 :                 mesh.get_boundary_info().boundary_ids(elem, sn, bc_ids);
    1407             : 
    1408       97821 :                 if (bc_ids.empty() && elem->neighbor_ptr(sn) != remote_elem)
    1409       78067 :                   continue;
    1410             : 
    1411             :                 // Make a sorted list of node ids for elem->side(sn)
    1412       19754 :                 elem->build_side_ptr(elem_side, sn);
    1413       20104 :                 std::vector<dof_id_type> elem_side_nodes(elem_side->n_nodes());
    1414       21652 :                 for (unsigned int esn=0,
    1415         700 :                      n_esn = cast_int<unsigned int>(elem_side_nodes.size());
    1416       89756 :                      esn != n_esn; ++esn)
    1417       71126 :                   elem_side_nodes[esn] = elem_side->node_id(esn);
    1418       19754 :                 std::sort(elem_side_nodes.begin(), elem_side_nodes.end());
    1419             : 
    1420      112508 :                 for (unsigned int i=0; i != max_subelems; ++i)
    1421       94154 :                   if (subelem[i])
    1422             :                     {
    1423      394661 :                       for (auto subside : subelem[i]->side_index_range())
    1424             :                         {
    1425      315596 :                           subelem[i]->build_side_ptr(subside_elem, subside);
    1426             : 
    1427             :                           // Make a list of *vertex* node ids for this subside, see if they are all present
    1428             :                           // in elem->side(sn).  Note 1: we can't just compare elem->key(sn) to
    1429             :                           // subelem[i]->key(subside) in the Prism cases, since the new side is
    1430             :                           // a different type.  Note 2: we only use vertex nodes since, in the future,
    1431             :                           // a Hex20 or Prism15's QUAD8 face may be split into two Tri6 faces, and the
    1432             :                           // original face will not contain the mid-edge node.
    1433      315596 :                           std::vector<dof_id_type> subside_nodes(subside_elem->n_vertices());
    1434      328156 :                           for (unsigned int ssn=0,
    1435        7984 :                                n_ssn = cast_int<unsigned int>(subside_nodes.size());
    1436     1184544 :                                ssn != n_ssn; ++ssn)
    1437      883212 :                             subside_nodes[ssn] = subside_elem->node_id(ssn);
    1438      311604 :                           std::sort(subside_nodes.begin(), subside_nodes.end());
    1439             : 
    1440             :                           // std::includes returns true if every element of the second sorted range is
    1441             :                           // contained in the first sorted range.
    1442      311604 :                           if (std::includes(elem_side_nodes.begin(), elem_side_nodes.end(),
    1443             :                                             subside_nodes.begin(), subside_nodes.end()))
    1444             :                             {
    1445       39990 :                               for (const auto & b_id : bc_ids)
    1446       10723 :                                 if (b_id != BoundaryInfo::invalid_id)
    1447             :                                   {
    1448       10723 :                                     new_bndry_ids.push_back(b_id);
    1449       11117 :                                     new_bndry_elements.push_back(subelem[i].get());
    1450       10723 :                                     new_bndry_sides.push_back(subside);
    1451             :                                   }
    1452             : 
    1453             :                               // If the original element had a RemoteElem neighbor on side 'sn',
    1454             :                               // then the subelem has one on side 'subside'.
    1455       29685 :                               if (elem->neighbor_ptr(sn) == remote_elem)
    1456          72 :                                 subelem[i]->set_neighbor(subside, const_cast<RemoteElem*>(remote_elem));
    1457             :                             }
    1458             :                         }
    1459             :                     } // end for loop over subelem
    1460             :               } // end for loop over sides
    1461             : 
    1462             :             // Remove the original element from the BoundaryInfo structure.
    1463       19331 :             mesh.get_boundary_info().remove(elem);
    1464             : 
    1465             :           } // end if (mesh_has_boundary_data)
    1466             : 
    1467             :         // Determine new IDs for the split elements which will be
    1468             :         // the same on all processors, therefore keeping the Mesh
    1469             :         // in sync.  Note: we offset the new IDs by max_orig_id to
    1470             :         // avoid overwriting any of the original IDs.
    1471      370882 :         for (unsigned int i=0; i != max_subelems; ++i)
    1472      321102 :           if (subelem[i])
    1473             :             {
    1474             :               // Determine new IDs for the split elements which will be
    1475             :               // the same on all processors, therefore keeping the Mesh
    1476             :               // in sync.  Note: we offset the new IDs by the max of the
    1477             :               // pre-existing ids to avoid conflicting with originals.
    1478      302864 :               subelem[i]->set_id( max_orig_id + max_subelems*elem->id() + i );
    1479             : 
    1480             : #ifdef LIBMESH_ENABLE_UNIQUE_ID
    1481      302864 :               subelem[i]->set_unique_id(max_unique_id + max_subelems*elem->unique_id() + i);
    1482             : #endif
    1483             : 
    1484             :               // Prepare to add the newly-created simplices
    1485       12556 :               new_elements.push_back(std::move(subelem[i]));
    1486             :             }
    1487             : 
    1488             :         // Delete the original element
    1489       62424 :         mesh.delete_elem(elem);
    1490       82548 :       } // End for loop over elements
    1491        3149 :   } // end scope
    1492             : 
    1493             : 
    1494             :   // Now, iterate over the new elements vector, and add them each to
    1495             :   // the Mesh.
    1496      306201 :   for (auto & elem : new_elements)
    1497      327976 :     mesh.add_elem(std::move(elem));
    1498             : 
    1499        3337 :   if (mesh_has_boundary_data)
    1500             :     {
    1501             :       // If the old mesh had boundary data, the new mesh better have
    1502             :       // some.  However, we can't assert that the size of
    1503             :       // new_bndry_elements vector is > 0, since we may not have split
    1504             :       // any elements actually on the boundary.  We also can't assert
    1505             :       // that the original number of boundary sides is equal to the
    1506             :       // sum of the boundary sides currently in the mesh and the
    1507             :       // newly-added boundary sides, since in 3D, we may have split a
    1508             :       // boundary QUAD into two boundary TRIs.  Therefore, we won't be
    1509             :       // too picky about the actual number of BCs, and just assert that
    1510             :       // there are some, somewhere.
    1511             : #ifndef NDEBUG
    1512          44 :       bool nbe_nonempty = new_bndry_elements.size();
    1513          44 :       mesh.comm().max(nbe_nonempty);
    1514          44 :       libmesh_assert(nbe_nonempty ||
    1515             :                      mesh.get_boundary_info().n_boundary_conds()>0);
    1516             : #endif
    1517             : 
    1518             :       // We should also be sure that the lengths of the new boundary data vectors
    1519             :       // are all the same.
    1520          44 :       libmesh_assert_equal_to (new_bndry_elements.size(), new_bndry_sides.size());
    1521          44 :       libmesh_assert_equal_to (new_bndry_sides.size(), new_bndry_ids.size());
    1522             : 
    1523             :       // Add the new boundary info to the mesh
    1524       12285 :       for (auto s : index_range(new_bndry_elements))
    1525       11511 :         mesh.get_boundary_info().add_side(new_bndry_elements[s],
    1526         788 :                                           new_bndry_sides[s],
    1527         788 :                                           new_bndry_ids[s]);
    1528             :     }
    1529             : 
    1530             :   // In a DistributedMesh any newly added ghost node ids may be
    1531             :   // inconsistent, and unique_ids of newly added ghost nodes remain
    1532             :   // unset.
    1533             :   // make_nodes_parallel_consistent() will fix all this.
    1534        3337 :   if (!mesh.is_serial())
    1535             :     {
    1536        1287 :       mesh.comm().max(added_new_ghost_point);
    1537             : 
    1538        1287 :       if (added_new_ghost_point)
    1539           0 :         MeshCommunication().make_nodes_parallel_consistent (mesh);
    1540             :     }
    1541             : 
    1542             :   // Prepare the newly created mesh for use.
    1543        3337 :   mesh.prepare_for_use();
    1544             : 
    1545             :   // Let the new_elements and new_bndry_elements vectors go out of scope.
    1546        3605 : }
    1547             : 
    1548             : 
    1549             : 
    1550        2130 : void MeshTools::Modification::all_rbb (MeshBase & mesh)
    1551             : {
    1552         120 :   LOG_SCOPE("all_rbb()", "MeshTools::Modification");
    1553             : 
    1554             :   // By default, use 1.0 as the weight on every RATIONAL_BERNSTEIN
    1555             :   // mapped node
    1556        2130 :   const Real default_weight = 1.0;
    1557             : 
    1558             :   const auto weight_index =
    1559        4200 :     (mesh.add_node_datum<Real>("rational_weight", true,
    1560             :                                &default_weight));
    1561             : 
    1562          60 :   mesh.set_default_mapping_type(RATIONAL_BERNSTEIN_MAP);
    1563        2130 :   mesh.set_default_mapping_data(weight_index);
    1564             : 
    1565             :   // Out of loop to reduce heap allocations
    1566        2130 :   std::unique_ptr<Elem> edge_ptr, face_ptr;
    1567             : 
    1568       57426 :   for (auto & elem : mesh.element_ptr_range())
    1569             :     {
    1570       28397 :       if (elem->level())
    1571           0 :         libmesh_not_implemented_msg
    1572             :           ("all_rbb() currently only supports flat meshes with no refinement levels");
    1573             : 
    1574             : #ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
    1575        4460 :       if (elem->infinite())
    1576           0 :         libmesh_not_implemented_msg
    1577             :           ("all_rbb() currently only supports finite geometric elements");
    1578             : #endif
    1579             : 
    1580       28397 :       elem->set_mapping_type(RATIONAL_BERNSTEIN_MAP);
    1581        1784 :       elem->set_mapping_data(weight_index);
    1582             : 
    1583             :       // Nothing to do unless we have curves to correct
    1584       28397 :       if (elem->default_order() == FIRST)
    1585        2920 :         continue;
    1586             : 
    1587             :       // Modify the center node of an "edge" - possibly an actual edge
    1588             :       // element's node, possibly a center node between points on a
    1589             :       // face's or cell's edge - for RBB interpolation.  This should fit
    1590             :       // a circular curve exactly in cases where the original nodes are
    1591             :       // equispaced and the outer nodes' weights are equal, and should
    1592             :       // be a good fit otherwise.
    1593             :       //
    1594             :       // We want to use this to interpolate "internal" conceptual
    1595             :       // edges of a Hex27 too, so we'll handle the cases where w0 and
    1596             :       // w1 aren't 1, as well as the cases where the Nodes n0 and n1
    1597             :       // are already control points which don't match their
    1598             :       // corresponding physical points.
    1599      129773 :       auto make_edge_rbb = [default_weight, weight_index]
    1600             :         (const Node & n0, const Node & n1, Node & n_center,
    1601      167144 :          const Point & p0, const Point & p1)
    1602             :       {
    1603             :         // Skip edges we've already modified; the center node for
    1604             :         // these is no longer at the curve point we wish to
    1605             :         // interpolate, it should already be at the control point that
    1606             :         // accomplishes the interpolation.
    1607      118136 :         const Real old_weight = n_center.get_extra_datum<Real>(weight_index);
    1608      118136 :         if (old_weight != default_weight)
    1609        1588 :           return;
    1610             : 
    1611        5332 :         Point & p2 = n_center;
    1612             : 
    1613       97742 :         const Real w0 = n0.get_extra_datum<Real>(weight_index);
    1614       97742 :         const Real w1 = n1.get_extra_datum<Real>(weight_index);
    1615             : 
    1616        5332 :         const Point e02 = p2-p0,
    1617        5332 :                     e21 = p1-p2;
    1618        5332 :         const Real chord_02_len_sq = e02.norm_sq(),
    1619        5332 :                    chord_21_len_sq = e21.norm_sq();
    1620             : 
    1621             :         // First find the cosine of phi, the angle between our two
    1622             :         // subchords (turning from the direction of one to the
    1623             :         // direction of the other; this is the supplementary angle to
    1624             :         // the angle at the midpoint).  This is the same as half of
    1625             :         // the angle of our circular arc, which nicely enough is also
    1626             :         // the angle we take cos and sec of in NURBS formulae
    1627       97742 :         const Real cos_phi = (e02*e21)/std::sqrt(chord_02_len_sq*chord_21_len_sq);
    1628             : 
    1629             :         // There's a way to do really large arcs using negative
    1630             :         // weights, but we're going to get lousy approximation quality
    1631             :         // from isoparametric elements if we go too low, as well as
    1632             :         // bad numerics here, so let's just disallow it.
    1633       97742 :         if (cos_phi < 0.5)
    1634           0 :           libmesh_not_implemented_msg
    1635             :             ("all_rbb() is not recommended for extremely sharp curves on one edge");
    1636             : 
    1637       97742 :         const Real w_center = cos_phi*std::sqrt(w0*w1);
    1638             : 
    1639       92410 :         n_center.set_extra_datum<Real>(weight_index, w_center);
    1640             : 
    1641             :         // Now let's get the control point location.  This comes from
    1642             :         // a lot of back-and-forth with Gemini, but fortunately I'm
    1643             :         // rewriting it after I've already added unit tests that
    1644             :         // should scream if it's badly wrong.
    1645       97742 :         const Real w_mid = w0/4 + w1/4 + w_center/2;
    1646       97742 :         n_center *= 2*w_mid;
    1647       97742 :         n_center -= (w0 * p0 + w1 * p1)/2;
    1648        5332 :         n_center /= w_center;
    1649       25477 :       };
    1650             : 
    1651      128314 :       auto make_face_rbb = [weight_index] (Elem & face)
    1652             :       {
    1653             :         // Prisms and pyramids may need to skip some faces while
    1654             :         // adjusting others
    1655       20659 :         if (face.type() == TRI6)
    1656           0 :           return;
    1657             : 
    1658       20659 :         if (face.type() != QUAD9)
    1659           0 :           libmesh_not_implemented_msg
    1660             :             ("all_rbb() currently only supports mid-face nodes on Quad9 faces");
    1661             : 
    1662             :         // We only use [4,8) but matching indices is nice and stack is
    1663             :         // cheap.
    1664             :         Real w[9];
    1665             : 
    1666      103295 :         for (unsigned int i : make_range(4u, 8u))
    1667       86996 :           w[i] = face.node_ref(i).get_extra_datum<Real>(weight_index);
    1668             : 
    1669             :         // We can't currently handle arbitrary vertex weights
    1670             : #ifndef NDEBUG
    1671        5450 :         for (unsigned int i : make_range(4u))
    1672        4360 :           libmesh_assert_equal_to
    1673             :             (face.node_ref(i).get_extra_datum<Real>(weight_index), 1);
    1674             : #endif
    1675             : 
    1676             :         // For the mid-face point, if we want to exactly match
    1677             :         // any cylinders and cones and spheres, we're actually already
    1678             :         // entirely constrained by the other points.
    1679             :         //
    1680             :         // This formula gives the minimum-energy Steiner surface based
    1681             :         // on the outer 8 points.
    1682             :         //
    1683             :         // That's an isogeometric representation of a cylinder aligned
    1684             :         // to either axis, or of a sphere where the quad edges are on
    1685             :         // latitude/longitude lines, or of a cone where two edges are
    1686             :         // segments of cone generating lines and the other two are
    1687             :         // arcs perpendicular to the axis.
    1688             :         //
    1689             :         // It's not perfectly isogeometric for the spheres we generate
    1690             :         // (where the quad edges are all great circles), but it should
    1691             :         // still converge asymptotically faster than non-rational
    1692             :         // quadratic Lagrange.
    1693        2180 :         const Point xi_avg = (face.point(7) + face.point(5))/2;
    1694        1090 :         const Point eta_avg = (face.point(4) + face.point(6))/2;
    1695        1090 :         const Point vertex_avg = (face.point(0) + face.point(1) +
    1696        2180 :                                   face.point(2) + face.point(3))/4;
    1697             : 
    1698       20659 :         const Real w_xi  = (w[7] + w[5])/2;
    1699       20659 :         const Real w_eta = (w[4] + w[6])/2;
    1700       20659 :         const Real w_mid = w_xi * w_eta;
    1701             : 
    1702        1090 :         Node & midnode = face.node_ref(8);
    1703       20659 :         midnode.set_extra_datum<Real>(weight_index, w_mid);
    1704       20659 :         midnode = ((1+w_mid)/(w_xi+w_eta) * (w_xi*xi_avg + w_eta*eta_avg) - vertex_avg)/w_mid;
    1705       25477 :       };
    1706             : 
    1707             :       // If we're on a Hex27, our formula for the mid-volume node
    1708             :       // relies on the locations of the mid-face points.  We could
    1709             :       // re-calculate those later but let's just save them now.
    1710      178339 :       Point midfacepts[6];
    1711       25477 :       if (elem->type() == HEX27)
    1712       16366 :         for (auto i : make_range(6))
    1713       14652 :           midfacepts[i] = elem->point(20+i);
    1714             : 
    1715             :       // Check each edge for a curve, and adjust it if needed.
    1716      137599 :       for (auto e : elem->edge_index_range())
    1717             :         {
    1718      110454 :           elem->build_edge_ptr(edge_ptr, e);
    1719             : 
    1720             :           // We should add EDGE4 once we have QUAD16/TRI10/HEX64 to
    1721             :           // use it
    1722      110454 :           if (edge_ptr->type() != EDGE3)
    1723           0 :             libmesh_not_implemented_msg
    1724             :               ("all_rbb() currently only supports meshes with 2- and/or 3-node edges");
    1725             : 
    1726      123550 :           make_edge_rbb(edge_ptr->node_ref(0), edge_ptr->node_ref(1),
    1727             :                         edge_ptr->node_ref(2),
    1728        6548 :                         edge_ptr->node_ref(0), edge_ptr->node_ref(1));
    1729             : 
    1730             :         }
    1731             : 
    1732             :       // If we're in 3D, we may have face nodes that also need to be
    1733             :       // adjusted to replace an interpolated curve with a spline
    1734             :       // curve.  We know what to do with a quad face, but we'll have
    1735             :       // to scream and die if we see a Tri7 face node.
    1736       25681 :       bool check_face_points = (elem->dim() > 2) &&
    1737        5035 :         (elem->n_nodes() > elem->n_edges() + elem->n_vertices());
    1738             : 
    1739        1668 :       if (check_face_points)
    1740       16470 :         for (auto f : elem->side_index_range())
    1741             :           {
    1742             :             // Prisms and pyramids may need to skip some faces while
    1743             :             // adjusting others
    1744       14028 :             if (elem->side_type(f) == TRI6)
    1745           0 :               continue;
    1746             : 
    1747       14028 :             elem->build_side_ptr(face_ptr, f);
    1748             : 
    1749       14028 :             make_face_rbb(*face_ptr);
    1750             :           }
    1751             : 
    1752             :       bool check_interior_points =
    1753       25477 :         elem->n_nodes() > elem->n_edges() + elem->n_vertices() + elem->n_faces();
    1754             : 
    1755       25477 :       if (check_interior_points)
    1756             :         {
    1757        9637 :           if (elem->type() == EDGE3)
    1758             :             {
    1759         788 :               make_edge_rbb(elem->node_ref(0), elem->node_ref(1),
    1760             :                             elem->node_ref(2),
    1761         668 :                             elem->node_ref(0), elem->node_ref(1));
    1762             :             }
    1763        8969 :           else if (elem->dim() == 2)
    1764             :             {
    1765        6631 :               make_face_rbb(*elem);
    1766             :             }
    1767        2338 :           else if (elem->type() == HEX27)
    1768             :             {
    1769             :               // We still have the midnode left to go.  We want
    1770             :               // something here that will preserve the tensor product
    1771             :               // structure for 2.5D extrusions of IGA faces, but also
    1772             :               // be at least near to the minimum-energy control point
    1773             :               // and weight for general cases.  We'll treat opposing
    1774             :               // mid-face nodes as the endpoints of a (more general
    1775             :               // than our edges, since they might have non-1 weights)
    1776             :               // Edge3, and see what we'd need on the midnode to
    1777             :               // interpolate the center point with them.  If we've got
    1778             :               // something isogeometric like an extrusion then our
    1779             :               // results should agree; for a quick-but-good output in
    1780             :               // general we'll take an average.
    1781        2338 :               const int opposite_sides[3][2] = {{0,5}, {1,3}, {2,4}};
    1782             : 
    1783        2338 :               Node & midnode = elem->node_ref(26);
    1784        2338 :               const Point original_midpoint = midnode;
    1785             : 
    1786             :               // Averaging in projective space
    1787         104 :               Point sum_weighted_point = 0;
    1788         104 :               Real sum_weight = 0;
    1789             : 
    1790        9352 :               for (int i : make_range(3))
    1791             :                 {
    1792        7014 :                   Node & n0 = elem->node_ref(20+opposite_sides[i][0]);
    1793        7014 :                   Node & n1 = elem->node_ref(20+opposite_sides[i][1]);
    1794             : 
    1795        7014 :                   make_edge_rbb(n0, n1, midnode,
    1796        7014 :                                 midfacepts[opposite_sides[i][0]],
    1797        7014 :                                 midfacepts[opposite_sides[i][1]]);
    1798             : 
    1799             :                   const Real midweight =
    1800        7014 :                     midnode.get_extra_datum<Real>(weight_index);
    1801        7014 :                   sum_weight += midweight;
    1802         312 :                   sum_weighted_point += midweight * midnode;
    1803             : 
    1804             :                   // Reset for next run
    1805         312 :                   midnode = original_midpoint;
    1806        6702 :                   midnode.set_extra_datum<Real>(weight_index,
    1807             :                                                 default_weight);
    1808             : 
    1809             :                 }
    1810             : 
    1811        2338 :               const Real midweight = sum_weight/3;
    1812        2338 :               midnode.set_extra_datum<Real>(weight_index,
    1813             :                                             midweight);
    1814             : 
    1815         104 :               midnode = sum_weighted_point / 3 / midweight;
    1816             :             }
    1817             :           else
    1818           0 :             libmesh_not_implemented_msg
    1819             :               ("all_rbb() doesn't yet support " << elem->type());
    1820             :         }
    1821        2010 :     }
    1822        2130 : }
    1823             : 
    1824             : 
    1825             : 
    1826           0 : void MeshTools::Modification::smooth (MeshBase & mesh,
    1827             :                                       const unsigned int n_iterations,
    1828             :                                       const Real power)
    1829             : {
    1830             :   /**
    1831             :    * This implementation assumes every element "side" has only 2 nodes.
    1832             :    */
    1833           0 :   libmesh_assert_equal_to (mesh.mesh_dimension(), 2);
    1834             : 
    1835             :   /*
    1836             :    * Create a quickly-searchable list of boundary nodes.
    1837             :    */
    1838             :   std::unordered_set<dof_id_type> boundary_node_ids =
    1839           0 :     MeshTools::find_boundary_nodes (mesh);
    1840             : 
    1841             :   // For avoiding extraneous element side allocation
    1842           0 :   ElemSideBuilder side_builder;
    1843             : 
    1844           0 :   for (unsigned int iter=0; iter<n_iterations; iter++)
    1845             :     {
    1846             :       /*
    1847             :        * loop over the mesh refinement level
    1848             :        */
    1849           0 :       unsigned int n_levels = MeshTools::n_levels(mesh);
    1850           0 :       for (unsigned int refinement_level=0; refinement_level != n_levels;
    1851             :            refinement_level++)
    1852             :         {
    1853             :           // initialize the storage (have to do it on every level to get empty vectors
    1854           0 :           std::vector<Point> new_positions;
    1855           0 :           std::vector<Real>   weight;
    1856           0 :           new_positions.resize(mesh.n_nodes());
    1857           0 :           weight.resize(mesh.n_nodes());
    1858             : 
    1859             :           {
    1860             :             // Loop over the elements to calculate new node positions
    1861           0 :             for (const auto & elem : as_range(mesh.level_elements_begin(refinement_level),
    1862           0 :                                               mesh.level_elements_end(refinement_level)))
    1863             :               {
    1864             :                 /*
    1865             :                  * We relax all nodes on level 0 first
    1866             :                  * If the element is refined (level > 0), we interpolate the
    1867             :                  * parents nodes with help of the embedding matrix
    1868             :                  */
    1869           0 :                 if (refinement_level == 0)
    1870             :                   {
    1871           0 :                     for (auto s : elem->side_index_range())
    1872             :                       {
    1873             :                         /*
    1874             :                          * Only operate on sides which are on the
    1875             :                          * boundary or for which the current element's
    1876             :                          * id is greater than its neighbor's.
    1877             :                          * Sides get only built once.
    1878             :                          */
    1879           0 :                         if ((elem->neighbor_ptr(s) != nullptr) &&
    1880           0 :                             (elem->id() > elem->neighbor_ptr(s)->id()))
    1881             :                           {
    1882           0 :                             const Elem & side = side_builder(*elem, s);
    1883           0 :                             const Node & node0 = side.node_ref(0);
    1884           0 :                             const Node & node1 = side.node_ref(1);
    1885             : 
    1886           0 :                             Real node_weight = 1.;
    1887             :                             // calculate the weight of the nodes
    1888           0 :                             if (power > 0)
    1889             :                               {
    1890           0 :                                 Point diff = node0-node1;
    1891           0 :                                 node_weight = std::pow(diff.norm(), power);
    1892             :                               }
    1893             : 
    1894           0 :                             const dof_id_type id0 = node0.id(), id1 = node1.id();
    1895           0 :                             new_positions[id0].add_scaled( node1, node_weight );
    1896           0 :                             new_positions[id1].add_scaled( node0, node_weight );
    1897           0 :                             weight[id0] += node_weight;
    1898           0 :                             weight[id1] += node_weight;
    1899             :                           }
    1900             :                       } // element neighbor loop
    1901             :                   }
    1902             : #ifdef LIBMESH_ENABLE_AMR
    1903             :                 else   // refinement_level > 0
    1904             :                   {
    1905             :                     /*
    1906             :                      * Find the positions of the hanging nodes of refined elements.
    1907             :                      * We do this by calculating their position based on the parent
    1908             :                      * (one level less refined) element, and the embedding matrix
    1909             :                      */
    1910             : 
    1911           0 :                     const Elem * parent = elem->parent();
    1912             : 
    1913             :                     /*
    1914             :                      * find out which child I am
    1915             :                      */
    1916           0 :                     unsigned int c = parent->which_child_am_i(elem);
    1917             :                     /*
    1918             :                      *loop over the childs (that is, the current elements) nodes
    1919             :                      */
    1920           0 :                     for (auto nc : elem->node_index_range())
    1921             :                       {
    1922             :                         /*
    1923             :                          * the new position of the node
    1924             :                          */
    1925           0 :                         Point point;
    1926           0 :                         for (auto n : parent->node_index_range())
    1927             :                           {
    1928             :                             /*
    1929             :                              * The value from the embedding matrix
    1930             :                              */
    1931           0 :                             const Real em_val = parent->embedding_matrix(c,nc,n);
    1932             : 
    1933           0 :                             if (em_val != 0.)
    1934           0 :                               point.add_scaled (parent->point(n), em_val);
    1935             :                           }
    1936             : 
    1937           0 :                         const dof_id_type id = elem->node_ptr(nc)->id();
    1938           0 :                         new_positions[id] = point;
    1939           0 :                         weight[id] = 1.;
    1940             :                       }
    1941             :                   } // if element refinement_level
    1942             : #endif // #ifdef LIBMESH_ENABLE_AMR
    1943             : 
    1944           0 :               } // element loop
    1945             : 
    1946             :             /*
    1947             :              * finally reposition the vertex nodes
    1948             :              */
    1949           0 :             for (auto nid : make_range(mesh.n_nodes()))
    1950           0 :               if (!boundary_node_ids.count(nid) && weight[nid] > 0.)
    1951           0 :                 mesh.node_ref(nid) = new_positions[nid]/weight[nid];
    1952             :           }
    1953             : 
    1954             :           // Now handle the additional second_order nodes by calculating
    1955             :           // their position based on the vertex positions
    1956             :           // we do a second loop over the level elements
    1957           0 :           for (auto & elem : as_range(mesh.level_elements_begin(refinement_level),
    1958           0 :                                       mesh.level_elements_end(refinement_level)))
    1959             :             {
    1960           0 :               const unsigned int son_begin = elem->n_vertices();
    1961           0 :               const unsigned int son_end   = elem->n_nodes();
    1962           0 :               for (unsigned int n=son_begin; n<son_end; n++)
    1963             :                 {
    1964             :                   const unsigned int n_adjacent_vertices =
    1965           0 :                     elem->n_second_order_adjacent_vertices(n);
    1966             : 
    1967           0 :                   Point point;
    1968           0 :                   for (unsigned int v=0; v<n_adjacent_vertices; v++)
    1969           0 :                     point.add(elem->point( elem->second_order_adjacent_vertex(n,v) ));
    1970             : 
    1971           0 :                   const dof_id_type id = elem->node_ptr(n)->id();
    1972           0 :                   mesh.node_ref(id) = point/n_adjacent_vertices;
    1973             :                 }
    1974           0 :             }
    1975             :         } // refinement_level loop
    1976             :     } // end iteration
    1977             : 
    1978             :   // We haven't changed any topology, but just changing geometry could
    1979             :   // have invalidated a point locator.
    1980           0 :   mesh.clear_point_locator();
    1981           0 : }
    1982             : 
    1983             : 
    1984             : 
    1985        3209 : void MeshTools::Modification::interpolate_surface (MeshBase & mesh,
    1986             :                                                    const Surface & surface,
    1987             :                                                    std::set<std::size_t> ids,
    1988             :                                                    bool use_boundary_nodes)
    1989             : {
    1990        3209 :   const bool is_serial = mesh.is_serial();
    1991         192 :   const processor_id_type mesh_pid = mesh.processor_id();
    1992             : 
    1993             :   // We might have to move ghost nodes on a distributed mesh if their
    1994             :   // owners don't see a requisite element or boundary they're on.
    1995         192 :   std::unordered_set<dof_id_type> moved_ghost_nodes;
    1996             : 
    1997      180143 :   auto move_node = [& moved_ghost_nodes, & surface, is_serial, mesh_pid]
    1998       95311 :                    (Node & node) {
    1999      198687 :     node = surface.closest_point(node);
    2000             : 
    2001      198687 :     if (!is_serial && node.processor_id() != mesh_pid)
    2002       45991 :       moved_ghost_nodes.insert(node.id());
    2003       12385 :   };
    2004             : 
    2005          96 :   const bool no_ids = ids.empty();
    2006          96 :   const BoundaryInfo & boundary_info = mesh.get_boundary_info();
    2007             : 
    2008      436360 :   for (const auto & elem : mesh.active_element_ptr_range())
    2009             :     {
    2010      225335 :       if (elem->mapping_type() != LAGRANGE_MAP)
    2011           0 :         libmesh_not_implemented();
    2012             : 
    2013      225335 :       if (use_boundary_nodes)
    2014             :         {
    2015     1500603 :           for (auto s : elem->side_index_range())
    2016             :             {
    2017     1275268 :               if (no_ids)
    2018             :                 {
    2019             :                   // If we're not using boundary ids, we're
    2020             :                   // interpolating all external and no internal
    2021             :                   // boundaries
    2022     1333676 :                   if (elem->neighbor_ptr(s))
    2023     1165408 :                     continue;
    2024             :                 }
    2025             :               else
    2026             :                 {
    2027           0 :                   if (std::none_of(ids.begin(), ids.end(),
    2028           0 :                                    [&boundary_info,elem,s](std::size_t bcid)
    2029           0 :                                    {return boundary_info.has_boundary_id(elem, s, bcid);}))
    2030           0 :                     continue;
    2031             :                 }
    2032             : 
    2033      255211 :               for (auto n : elem->nodes_on_side(s))
    2034      207959 :                 move_node(elem->node_ref(n));
    2035             :             }
    2036             :         }
    2037             :       else
    2038             :         {
    2039           0 :           if (no_ids || ids.count(elem->subdomain_id()))
    2040           0 :             for (Node & node : elem->node_ref_range())
    2041           0 :               move_node(node);
    2042             :         }
    2043        3017 :     }
    2044             : 
    2045        3209 :   if (!is_serial)
    2046             :     {
    2047          24 :       std::map<processor_id_type, std::vector<dof_id_type>> moved_nodes_map;
    2048       21284 :       for (auto id : moved_ghost_nodes)
    2049             :         {
    2050       19216 :           const Node & node = mesh.node_ref(id);
    2051       19216 :           moved_nodes_map[node.processor_id()].push_back(node.id());
    2052             :         }
    2053             : 
    2054             :       auto action_functor =
    2055        5645 :         [& mesh, & surface]
    2056             :         (processor_id_type /* pid */,
    2057       38800 :          const std::vector<dof_id_type> & my_moved_nodes)
    2058             :         {
    2059       24893 :           for (auto id : my_moved_nodes)
    2060             :             {
    2061       19216 :               Node & node = mesh.node_ref(id);
    2062       19216 :               node = surface.closest_point(node);
    2063             :             }
    2064        2076 :         };
    2065             : 
    2066             :       // First get new node positions to their owners
    2067             :       Parallel::push_parallel_vector_data
    2068        2068 :         (mesh.comm(), moved_nodes_map, action_functor);
    2069             : 
    2070             :       // Then get node positions to anyone else with them ghosted
    2071        2068 :       SyncNodalPositions sync_object(mesh);
    2072             :       Parallel::sync_dofobject_data_by_id
    2073        4112 :         (mesh.comm(), mesh.nodes_begin(), mesh.nodes_end(),
    2074             :          sync_object);
    2075             :     }
    2076             : 
    2077             :   // We haven't changed any topology, but just changing geometry could
    2078             :   // have invalidated a point locator.
    2079        3209 :   mesh.clear_point_locator();
    2080        3209 : }
    2081             : 
    2082             : 
    2083             : 
    2084             : #ifdef LIBMESH_ENABLE_AMR
    2085        2352 : void MeshTools::Modification::flatten(MeshBase & mesh)
    2086             : {
    2087          70 :   libmesh_assert(mesh.is_prepared() || mesh.is_replicated());
    2088             : 
    2089             :   // Algorithm:
    2090             :   // .) For each active element in the mesh: construct a
    2091             :   //    copy which is the same in every way *except* it is
    2092             :   //    a level 0 element.  Store the pointers to these in
    2093             :   //    a separate vector. Save any boundary information as well.
    2094             :   //    Delete the active element from the mesh.
    2095             :   // .) Loop over all (remaining) elements in the mesh, delete them.
    2096             :   // .) Add the level-0 copies back to the mesh
    2097             : 
    2098             :   // Temporary storage for new element pointers
    2099         210 :   std::vector<std::unique_ptr<Elem>> new_elements;
    2100             : 
    2101             :   // BoundaryInfo Storage for element ids, sides, and BC ids
    2102         140 :   std::vector<Elem *>              saved_boundary_elements;
    2103         140 :   std::vector<boundary_id_type>   saved_bc_ids;
    2104         140 :   std::vector<unsigned short int> saved_bc_sides;
    2105             : 
    2106             :   // Container to catch boundary ids passed back by BoundaryInfo
    2107         140 :   std::vector<boundary_id_type> bc_ids;
    2108             : 
    2109             :   // Reserve a reasonable amt. of space for each
    2110        2352 :   new_elements.reserve(mesh.n_active_elem());
    2111        2352 :   saved_boundary_elements.reserve(mesh.get_boundary_info().n_boundary_conds());
    2112        2352 :   saved_bc_ids.reserve(mesh.get_boundary_info().n_boundary_conds());
    2113        2352 :   saved_bc_sides.reserve(mesh.get_boundary_info().n_boundary_conds());
    2114             : 
    2115      408622 :   for (auto & elem : mesh.active_element_ptr_range())
    2116             :     {
    2117             :       // Make a new element of the same type
    2118      221226 :       auto copy = Elem::build(elem->type());
    2119             : 
    2120             :       // Set node pointers (they still point to nodes in the original mesh)
    2121     1707972 :       for (auto n : elem->node_index_range())
    2122     1555544 :         copy->set_node(n, elem->node_ptr(n));
    2123             : 
    2124             :       // Copy over ids
    2125      211610 :       copy->processor_id() = elem->processor_id();
    2126      211610 :       copy->subdomain_id() = elem->subdomain_id();
    2127             : 
    2128             :       // Retain the original element's ID(s) as well, otherwise
    2129             :       // the Mesh may try to create them for you...
    2130       19232 :       copy->set_id( elem->id() );
    2131             : #ifdef LIBMESH_ENABLE_UNIQUE_ID
    2132       19232 :       copy->set_unique_id(elem->unique_id());
    2133             : #endif
    2134             : 
    2135             :       // This element could have boundary info or DistributedMesh
    2136             :       // remote_elem links as well.  We need to save the (elem,
    2137             :       // side, bc_id) triples and those links
    2138     1366452 :       for (auto s : elem->side_index_range())
    2139             :         {
    2140     1208122 :           if (elem->neighbor_ptr(s) == remote_elem)
    2141         744 :             copy->set_neighbor(s, const_cast<RemoteElem *>(remote_elem));
    2142             : 
    2143     1154842 :           mesh.get_boundary_info().boundary_ids(elem, s, bc_ids);
    2144     1155176 :           for (const auto & bc_id : bc_ids)
    2145         334 :             if (bc_id != BoundaryInfo::invalid_id)
    2146             :               {
    2147         334 :                 saved_boundary_elements.push_back(copy.get());
    2148         334 :                 saved_bc_ids.push_back(bc_id);
    2149         334 :                 saved_bc_sides.push_back(s);
    2150             :               }
    2151             :         }
    2152             : 
    2153             :       // Copy any extra element data.  Since the copy hasn't been
    2154             :       // added to the mesh yet any allocation has to be done manually.
    2155      211610 :       const unsigned int nei = elem->n_extra_integers();
    2156      211610 :       copy->add_extra_integers(nei);
    2157      211610 :       for (unsigned int i=0; i != nei; ++i)
    2158           0 :         copy->set_extra_integer(i, elem->get_extra_integer(i));
    2159             : 
    2160             :       // Copy any mapping data.
    2161      211610 :       copy->set_mapping_type(elem->mapping_type());
    2162       19232 :       copy->set_mapping_data(elem->mapping_data());
    2163             : 
    2164             :       // We're done with this element
    2165      211610 :       mesh.delete_elem(elem);
    2166             : 
    2167             :       // But save the copy
    2168        9616 :       new_elements.push_back(std::move(copy));
    2169      194590 :     }
    2170             : 
    2171             :   // Make sure we saved the same number of boundary conditions
    2172             :   // in each vector.
    2173          70 :   libmesh_assert_equal_to (saved_boundary_elements.size(), saved_bc_ids.size());
    2174          70 :   libmesh_assert_equal_to (saved_bc_ids.size(), saved_bc_sides.size());
    2175             : 
    2176             :   // Loop again, delete any remaining elements
    2177       92992 :   for (auto & elem : mesh.element_ptr_range())
    2178       48135 :     mesh.delete_elem(elem);
    2179             : 
    2180             :   // Add the copied (now level-0) elements back to the mesh
    2181      213962 :   for (auto & new_elem : new_elements)
    2182             :     {
    2183             :       // Save the original ID, because the act of adding the Elem can
    2184             :       // change new_elem's id!
    2185        9616 :       dof_id_type orig_id = new_elem->id();
    2186             : 
    2187      230842 :       Elem * added_elem = mesh.add_elem(std::move(new_elem));
    2188             : 
    2189             :       // If the Elem, as it was re-added to the mesh, now has a
    2190             :       // different ID (this is unlikely, so it's just an assert)
    2191             :       // the boundary information will no longer be correct.
    2192        9616 :       libmesh_assert_equal_to (orig_id, added_elem->id());
    2193             : 
    2194             :       // Avoid compiler warnings in opt mode.
    2195        9616 :       libmesh_ignore(added_elem, orig_id);
    2196             :     }
    2197             : 
    2198             :   // Finally, also add back the saved boundary information
    2199        2686 :   for (auto e : index_range(saved_boundary_elements))
    2200         358 :     mesh.get_boundary_info().add_side(saved_boundary_elements[e],
    2201          24 :                                       saved_bc_sides[e],
    2202          24 :                                       saved_bc_ids[e]);
    2203             : 
    2204             :   // Trim unused and renumber nodes and elements
    2205        2352 :   mesh.prepare_for_use();
    2206        2352 : }
    2207             : #endif // #ifdef LIBMESH_ENABLE_AMR
    2208             : 
    2209             : 
    2210             : 
    2211        3408 : void MeshTools::Modification::change_boundary_id (MeshBase & mesh,
    2212             :                                                   const boundary_id_type old_id,
    2213             :                                                   const boundary_id_type new_id)
    2214             : {
    2215             :   // This is just a shim around the member implementation, now
    2216        3408 :   mesh.get_boundary_info().renumber_id(old_id, new_id);
    2217        3408 : }
    2218             : 
    2219             : 
    2220             : 
    2221           0 : void MeshTools::Modification::change_subdomain_id (MeshBase & mesh,
    2222             :                                                    const subdomain_id_type old_id,
    2223             :                                                    const subdomain_id_type new_id)
    2224             : {
    2225           0 :   if (old_id == new_id)
    2226             :     {
    2227             :       // If the IDs are the same, this is a no-op.
    2228           0 :       return;
    2229             :     }
    2230             : 
    2231             :   Threads::parallel_for
    2232           0 :     (mesh.element_stored_range(),
    2233           0 :      [old_id, new_id](const ElemRange & range)
    2234             :      {
    2235           0 :        for (Elem * elem : range)
    2236           0 :          if (elem->subdomain_id() == old_id)
    2237           0 :            elem->subdomain_id() = new_id;
    2238           0 :      });
    2239             : 
    2240             :   // We just invalidated mesh.get_subdomain_ids(), but it might not be
    2241             :   // efficient to fix that here.
    2242           0 :   mesh.unset_has_cached_elem_data();
    2243             : }
    2244             : 
    2245             : 
    2246             : } // namespace libMesh

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