xref: /petsc/src/dm/impls/plex/plexgmsh.c (revision 1690c2ae071c7584458d4e437df7b47bc4686b3c)

#define PETSCDM_DLL
#include <petsc/private/dmpleximpl.h> /*I   "petscdmplex.h"   I*/
#include <petsc/private/hashmapi.h>

#include <../src/dm/impls/plex/gmshlex.h>

#define GMSH_LEXORDER_ITEM(T, p) \
  static int *GmshLexOrder_##T##_##p(void) \
  { \
    static int Gmsh_LexOrder_##T##_##p[GmshNumNodes_##T(p)] = {-1}; \
    int       *lex                                          = Gmsh_LexOrder_##T##_##p; \
    if (lex[0] == -1) (void)GmshLexOrder_##T(p, lex, 0); \
    return lex; \
  }

static int *GmshLexOrder_QUA_2_Serendipity(void)
{
  static int Gmsh_LexOrder_QUA_2_Serendipity[9] = {-1};
  int       *lex                                = Gmsh_LexOrder_QUA_2_Serendipity;
  if (lex[0] == -1) {
    /* Vertices */
    lex[0] = 0;
    lex[2] = 1;
    lex[8] = 2;
    lex[6] = 3;
    /* Edges */
    lex[1] = 4;
    lex[5] = 5;
    lex[7] = 6;
    lex[3] = 7;
    /* Cell */
    lex[4] = -8;
  }
  return lex;
}

static int *GmshLexOrder_HEX_2_Serendipity(void)
{
  static int Gmsh_LexOrder_HEX_2_Serendipity[27] = {-1};
  int       *lex                                 = Gmsh_LexOrder_HEX_2_Serendipity;
  if (lex[0] == -1) {
    /* Vertices */
    lex[0]  = 0;
    lex[2]  = 1;
    lex[8]  = 2;
    lex[6]  = 3;
    lex[18] = 4;
    lex[20] = 5;
    lex[26] = 6;
    lex[24] = 7;
    /* Edges */
    lex[1]  = 8;
    lex[3]  = 9;
    lex[9]  = 10;
    lex[5]  = 11;
    lex[11] = 12;
    lex[7]  = 13;
    lex[17] = 14;
    lex[15] = 15;
    lex[19] = 16;
    lex[21] = 17;
    lex[23] = 18;
    lex[25] = 19;
    /* Faces */
    lex[4]  = -20;
    lex[10] = -21;
    lex[12] = -22;
    lex[14] = -23;
    lex[16] = -24;
    lex[22] = -25;
    /* Cell */
    lex[13] = -26;
  }
  return lex;
}

#define GMSH_LEXORDER_LIST(T) \
  GMSH_LEXORDER_ITEM(T, 1) \
  GMSH_LEXORDER_ITEM(T, 2) \
  GMSH_LEXORDER_ITEM(T, 3) \
  GMSH_LEXORDER_ITEM(T, 4) \
  GMSH_LEXORDER_ITEM(T, 5) \
  GMSH_LEXORDER_ITEM(T, 6) \
  GMSH_LEXORDER_ITEM(T, 7) \
  GMSH_LEXORDER_ITEM(T, 8) \
  GMSH_LEXORDER_ITEM(T, 9) \
  GMSH_LEXORDER_ITEM(T, 10)

GMSH_LEXORDER_ITEM(VTX, 0)
GMSH_LEXORDER_LIST(SEG)
GMSH_LEXORDER_LIST(TRI)
GMSH_LEXORDER_LIST(QUA)
GMSH_LEXORDER_LIST(TET)
GMSH_LEXORDER_LIST(HEX)
GMSH_LEXORDER_LIST(PRI)
GMSH_LEXORDER_LIST(PYR)

typedef enum {
  GMSH_VTX           = 0,
  GMSH_SEG           = 1,
  GMSH_TRI           = 2,
  GMSH_QUA           = 3,
  GMSH_TET           = 4,
  GMSH_HEX           = 5,
  GMSH_PRI           = 6,
  GMSH_PYR           = 7,
  GMSH_NUM_POLYTOPES = 8
} GmshPolytopeType;

typedef struct {
  int cellType;
  int polytope;
  int dim;
  int order;
  int numVerts;
  int numNodes;
  int *(*lexorder)(void);
} GmshCellInfo;

// clang-format off
#define GmshCellEntry(cellType, polytope, dim, order) {cellType, GMSH_##polytope, dim, order, GmshNumNodes_##polytope(1), GmshNumNodes_##polytope(order), GmshLexOrder_##polytope##_##order}
// clang-format on

static const GmshCellInfo GmshCellTable[] = {
  GmshCellEntry(15, VTX, 0, 0),

  GmshCellEntry(1, SEG, 1, 1),   GmshCellEntry(8, SEG, 1, 2),   GmshCellEntry(26, SEG, 1, 3),
  GmshCellEntry(27, SEG, 1, 4),  GmshCellEntry(28, SEG, 1, 5),  GmshCellEntry(62, SEG, 1, 6),
  GmshCellEntry(63, SEG, 1, 7),  GmshCellEntry(64, SEG, 1, 8),  GmshCellEntry(65, SEG, 1, 9),
  GmshCellEntry(66, SEG, 1, 10),

  GmshCellEntry(2, TRI, 2, 1),   GmshCellEntry(9, TRI, 2, 2),   GmshCellEntry(21, TRI, 2, 3),
  GmshCellEntry(23, TRI, 2, 4),  GmshCellEntry(25, TRI, 2, 5),  GmshCellEntry(42, TRI, 2, 6),
  GmshCellEntry(43, TRI, 2, 7),  GmshCellEntry(44, TRI, 2, 8),  GmshCellEntry(45, TRI, 2, 9),
  GmshCellEntry(46, TRI, 2, 10),

  GmshCellEntry(3, QUA, 2, 1),   GmshCellEntry(10, QUA, 2, 2),  {16, GMSH_QUA, 2, 2, 4, 8,  GmshLexOrder_QUA_2_Serendipity},
  GmshCellEntry(36, QUA, 2, 3),  GmshCellEntry(37, QUA, 2, 4),  GmshCellEntry(38, QUA, 2, 5),
  GmshCellEntry(47, QUA, 2, 6),  GmshCellEntry(48, QUA, 2, 7),  GmshCellEntry(49, QUA, 2, 8),
  GmshCellEntry(50, QUA, 2, 9),  GmshCellEntry(51, QUA, 2, 10),

  GmshCellEntry(4, TET, 3, 1),   GmshCellEntry(11, TET, 3, 2),  GmshCellEntry(29, TET, 3, 3),
  GmshCellEntry(30, TET, 3, 4),  GmshCellEntry(31, TET, 3, 5),  GmshCellEntry(71, TET, 3, 6),
  GmshCellEntry(72, TET, 3, 7),  GmshCellEntry(73, TET, 3, 8),  GmshCellEntry(74, TET, 3, 9),
  GmshCellEntry(75, TET, 3, 10),

  GmshCellEntry(5, HEX, 3, 1),   GmshCellEntry(12, HEX, 3, 2),  {17, GMSH_HEX, 3, 2, 8, 20, GmshLexOrder_HEX_2_Serendipity},
  GmshCellEntry(92, HEX, 3, 3),  GmshCellEntry(93, HEX, 3, 4),  GmshCellEntry(94, HEX, 3, 5),
  GmshCellEntry(95, HEX, 3, 6),  GmshCellEntry(96, HEX, 3, 7),  GmshCellEntry(97, HEX, 3, 8),
  GmshCellEntry(98, HEX, 3, 9),  GmshCellEntry(-1, HEX, 3, 10),

  GmshCellEntry(6, PRI, 3, 1),   GmshCellEntry(13, PRI, 3, 2),  GmshCellEntry(90, PRI, 3, 3),
  GmshCellEntry(91, PRI, 3, 4),  GmshCellEntry(106, PRI, 3, 5), GmshCellEntry(107, PRI, 3, 6),
  GmshCellEntry(108, PRI, 3, 7), GmshCellEntry(109, PRI, 3, 8), GmshCellEntry(110, PRI, 3, 9),
  GmshCellEntry(-1, PRI, 3, 10),

  GmshCellEntry(7, PYR, 3, 1),   GmshCellEntry(14, PYR, 3, 2),  GmshCellEntry(118, PYR, 3, 3),
  GmshCellEntry(119, PYR, 3, 4), GmshCellEntry(120, PYR, 3, 5), GmshCellEntry(121, PYR, 3, 6),
  GmshCellEntry(122, PYR, 3, 7), GmshCellEntry(123, PYR, 3, 8), GmshCellEntry(124, PYR, 3, 9),
  GmshCellEntry(-1, PYR, 3, 10)

#if 0
  {20, GMSH_TRI, 2, 3, 3,  9, NULL},
  {18, GMSH_PRI, 3, 2, 6, 15, NULL},
  {19, GMSH_PYR, 3, 2, 5, 13, NULL},
#endif
};

static GmshCellInfo GmshCellMap[150];

static PetscErrorCode GmshCellInfoSetUp(void)
{
  size_t           i, n;
  static PetscBool called = PETSC_FALSE;

  PetscFunctionBegin;
  if (called) PetscFunctionReturn(PETSC_SUCCESS);
  called = PETSC_TRUE;
  n      = PETSC_STATIC_ARRAY_LENGTH(GmshCellMap);
  for (i = 0; i < n; ++i) {
    GmshCellMap[i].cellType = -1;
    GmshCellMap[i].polytope = -1;
  }
  n = PETSC_STATIC_ARRAY_LENGTH(GmshCellTable);
  for (i = 0; i < n; ++i) {
    if (GmshCellTable[i].cellType <= 0) continue;
    GmshCellMap[GmshCellTable[i].cellType] = GmshCellTable[i];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

#define GmshCellTypeCheck(ct) \
  PetscMacroReturnStandard(const int _ct_ = (int)ct; PetscCheck(_ct_ >= 0 && _ct_ < (int)PETSC_STATIC_ARRAY_LENGTH(GmshCellMap), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid Gmsh element type %d", _ct_); PetscCheck(GmshCellMap[_ct_].cellType == _ct_, PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported Gmsh element type %d", _ct_); \
                           PetscCheck(GmshCellMap[_ct_].polytope != -1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported Gmsh element type %d", _ct_);)

typedef struct {
  PetscViewer viewer;
  int         fileFormat;
  int         dataSize;
  PetscBool   binary;
  PetscBool   byteSwap;
  size_t      wlen;
  void       *wbuf;
  size_t      slen;
  void       *sbuf;
  PetscInt   *nbuf;
  PetscInt    nodeStart;
  PetscInt    nodeEnd;
  PetscInt   *nodeMap;
} GmshFile;

/*
   Returns an array of count items each with a sizeof(eltsize)
*/
static PetscErrorCode GmshBufferGet(GmshFile *gmsh, PetscCount count, size_t eltsize, void *buf)
{
  size_t size = count * eltsize;

  PetscFunctionBegin;
  if (gmsh->wlen < size) {
    PetscCall(PetscFree(gmsh->wbuf));
    PetscCall(PetscMalloc(size, &gmsh->wbuf));
    gmsh->wlen = size;
  }
  *(void **)buf = size ? gmsh->wbuf : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    Returns an array of count items each with the size determined by the GmshFile
*/
static PetscErrorCode GmshBufferSizeGet(GmshFile *gmsh, PetscCount count, void *buf)
{
  size_t dataSize = (size_t)gmsh->dataSize;
  size_t size     = count * dataSize;

  PetscFunctionBegin;
  if (gmsh->slen < size) {
    PetscCall(PetscFree(gmsh->sbuf));
    PetscCall(PetscMalloc(size, &gmsh->sbuf));
    gmsh->slen = size;
  }
  *(void **)buf = size ? gmsh->sbuf : NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
    Reads an array of count items each with the size determined by the PetscDataType
*/
static PetscErrorCode GmshRead(GmshFile *gmsh, void *buf, PetscCount count, PetscDataType dtype)
{
  PetscInt icount;

  PetscFunctionBegin;
  PetscCall(PetscIntCast(count, &icount));
  PetscCall(PetscViewerRead(gmsh->viewer, buf, icount, NULL, dtype));
  if (gmsh->byteSwap) PetscCall(PetscByteSwap(buf, dtype, icount));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadString(GmshFile *gmsh, char *buf, PetscCount count)
{
  PetscInt icount;

  PetscFunctionBegin;
  PetscCall(PetscIntCast(count, &icount));
  PetscCall(PetscViewerRead(gmsh->viewer, buf, icount, NULL, PETSC_STRING));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshMatch(PETSC_UNUSED GmshFile *gmsh, const char Section[], char line[PETSC_MAX_PATH_LEN], PetscBool *match)
{
  PetscFunctionBegin;
  PetscCall(PetscStrcmp(line, Section, match));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshExpect(GmshFile *gmsh, const char Section[], char line[PETSC_MAX_PATH_LEN])
{
  PetscBool match;

  PetscFunctionBegin;
  PetscCall(GmshMatch(gmsh, Section, line, &match));
  PetscCheck(match, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file, expecting %s, not %s", Section, line);
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadSection(GmshFile *gmsh, char line[PETSC_MAX_PATH_LEN])
{
  PetscBool match;

  PetscFunctionBegin;
  while (PETSC_TRUE) {
    PetscCall(GmshReadString(gmsh, line, 1));
    PetscCall(GmshMatch(gmsh, "$Comments", line, &match));
    if (!match) break;
    while (PETSC_TRUE) {
      PetscCall(GmshReadString(gmsh, line, 1));
      PetscCall(GmshMatch(gmsh, "$EndComments", line, &match));
      if (match) break;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadEndSection(GmshFile *gmsh, const char EndSection[], char line[PETSC_MAX_PATH_LEN])
{
  PetscFunctionBegin;
  PetscCall(GmshReadString(gmsh, line, 1));
  PetscCall(GmshExpect(gmsh, EndSection, line));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Read into buf[] count number of PetscInt integers (the file storage size may be different than PetscInt)
*/
static PetscErrorCode GmshReadPetscInt(GmshFile *gmsh, PetscInt *buf, PetscCount count)
{
  PetscCount i;
  size_t     dataSize = (size_t)gmsh->dataSize;

  PetscFunctionBegin;
  if (dataSize == sizeof(PetscInt)) {
    PetscCall(GmshRead(gmsh, buf, count, PETSC_INT));
  } else if (dataSize == sizeof(int)) {
    int *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_ENUM));
    for (i = 0; i < count; ++i) buf[i] = (PetscInt)ibuf[i];
  } else if (dataSize == sizeof(long)) {
    long *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_LONG));
    for (i = 0; i < count; ++i) buf[i] = (PetscInt)ibuf[i];
  } else if (dataSize == sizeof(PetscInt64)) {
    PetscInt64 *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_INT64));
    for (i = 0; i < count; ++i) buf[i] = (PetscInt)ibuf[i];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Read into buf[] count number of PetscCount integers  (the file storage size may be different than PetscCount)
*/
static PetscErrorCode GmshReadPetscCount(GmshFile *gmsh, PetscCount *buf, PetscCount count)
{
  PetscCount i;
  size_t     dataSize = (size_t)gmsh->dataSize;

  PetscFunctionBegin;
  if (dataSize == sizeof(PetscCount)) {
    PetscCall(GmshRead(gmsh, buf, count, PETSC_COUNT));
  } else if (dataSize == sizeof(int)) {
    int *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_ENUM));
    for (i = 0; i < count; ++i) buf[i] = (PetscCount)ibuf[i];
  } else if (dataSize == sizeof(long)) {
    long *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_LONG));
    for (i = 0; i < count; ++i) buf[i] = (PetscCount)ibuf[i];
  } else if (dataSize == sizeof(PetscInt64)) {
    PetscInt64 *ibuf = NULL;
    PetscCall(GmshBufferSizeGet(gmsh, count, &ibuf));
    PetscCall(GmshRead(gmsh, ibuf, count, PETSC_INT64));
    for (i = 0; i < count; ++i) buf[i] = (PetscCount)ibuf[i];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Read into buf[] count number of PetscEnum integers
*/
static PetscErrorCode GmshReadInt(GmshFile *gmsh, int *buf, PetscCount count)
{
  PetscFunctionBegin;
  PetscCall(GmshRead(gmsh, buf, count, PETSC_ENUM));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
     Read into buf[] count number of double
*/
static PetscErrorCode GmshReadDouble(GmshFile *gmsh, double *buf, PetscCount count)
{
  PetscFunctionBegin;
  PetscCall(GmshRead(gmsh, buf, count, PETSC_DOUBLE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

#define GMSH_MAX_TAGS 16

typedef struct {
  PetscInt id;                  /* Entity ID */
  PetscInt dim;                 /* Dimension */
  double   bbox[6];             /* Bounding box */
  PetscInt numTags;             /* Size of tag array */
  int      tags[GMSH_MAX_TAGS]; /* Tag array */
} GmshEntity;

typedef struct {
  GmshEntity *entity[4];
  PetscHMapI  entityMap[4];
} GmshEntities;

static PetscErrorCode GmshEntitiesCreate(PetscCount count[4], GmshEntities **entities)
{
  PetscFunctionBegin;
  PetscCall(PetscNew(entities));
  for (PetscInt dim = 0; dim < 4; ++dim) {
    PetscCall(PetscCalloc1(count[dim], &(*entities)->entity[dim]));
    PetscCall(PetscHMapICreate(&(*entities)->entityMap[dim]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshEntitiesDestroy(GmshEntities **entities)
{
  PetscInt dim;

  PetscFunctionBegin;
  if (!*entities) PetscFunctionReturn(PETSC_SUCCESS);
  for (dim = 0; dim < 4; ++dim) {
    PetscCall(PetscFree((*entities)->entity[dim]));
    PetscCall(PetscHMapIDestroy(&(*entities)->entityMap[dim]));
  }
  PetscCall(PetscFree(*entities));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshEntitiesAdd(GmshEntities *entities, PetscInt index, PetscInt dim, PetscInt eid, GmshEntity **entity)
{
  PetscFunctionBegin;
  PetscCall(PetscHMapISet(entities->entityMap[dim], eid, index));
  entities->entity[dim][index].dim = dim;
  entities->entity[dim][index].id  = eid;
  if (entity) *entity = &entities->entity[dim][index];
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshEntitiesGet(GmshEntities *entities, PetscInt dim, PetscInt eid, GmshEntity **entity)
{
  PetscInt index;

  PetscFunctionBegin;
  PetscCall(PetscHMapIGet(entities->entityMap[dim], eid, &index));
  *entity = &entities->entity[dim][index];
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef struct {
  PetscInt *id;  /* Node IDs */
  double   *xyz; /* Coordinates */
  PetscInt *tag; /* Physical tag */
} GmshNodes;

static PetscErrorCode GmshNodesCreate(PetscCount count, GmshNodes **nodes)
{
  PetscFunctionBegin;
  PetscCall(PetscNew(nodes));
  PetscCall(PetscMalloc1(count * 1, &(*nodes)->id));
  PetscCall(PetscMalloc1(count * 3, &(*nodes)->xyz));
  PetscCall(PetscMalloc1(count * GMSH_MAX_TAGS, &(*nodes)->tag));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshNodesDestroy(GmshNodes **nodes)
{
  PetscFunctionBegin;
  if (!*nodes) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscFree((*nodes)->id));
  PetscCall(PetscFree((*nodes)->xyz));
  PetscCall(PetscFree((*nodes)->tag));
  PetscCall(PetscFree(*nodes));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef struct {
  PetscInt  id;                  /* Element ID */
  PetscInt  dim;                 /* Dimension */
  PetscInt  cellType;            /* Cell type */
  PetscInt  numVerts;            /* Size of vertex array */
  PetscInt  numNodes;            /* Size of node array */
  PetscInt *nodes;               /* Vertex/Node array */
  PetscInt  numTags;             /* Size of physical tag array */
  int       tags[GMSH_MAX_TAGS]; /* Physical tag array */
} GmshElement;

static PetscErrorCode GmshElementsCreate(PetscCount count, GmshElement **elements)
{
  PetscFunctionBegin;
  PetscCall(PetscCalloc1(count, elements));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshElementsDestroy(GmshElement **elements)
{
  PetscFunctionBegin;
  if (!*elements) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscFree(*elements));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef struct {
  PetscInt       dim;
  PetscInt       order;
  GmshEntities  *entities;
  PetscInt       numNodes;
  GmshNodes     *nodelist;
  PetscInt       numElems;
  GmshElement   *elements;
  PetscInt       numVerts;
  PetscInt       numCells;
  PetscInt      *periodMap;
  PetscInt      *vertexMap;
  PetscSegBuffer segbuf;
  PetscInt       numRegions;
  PetscInt      *regionDims;
  PetscInt      *regionTags;
  char         **regionNames;
} GmshMesh;

static PetscErrorCode GmshMeshCreate(GmshMesh **mesh)
{
  PetscFunctionBegin;
  PetscCall(PetscNew(mesh));
  PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 0, &(*mesh)->segbuf));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshMeshDestroy(GmshMesh **mesh)
{
  PetscInt r;

  PetscFunctionBegin;
  if (!*mesh) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(GmshEntitiesDestroy(&(*mesh)->entities));
  PetscCall(GmshNodesDestroy(&(*mesh)->nodelist));
  PetscCall(GmshElementsDestroy(&(*mesh)->elements));
  PetscCall(PetscFree((*mesh)->periodMap));
  PetscCall(PetscFree((*mesh)->vertexMap));
  PetscCall(PetscSegBufferDestroy(&(*mesh)->segbuf));
  for (r = 0; r < (*mesh)->numRegions; ++r) PetscCall(PetscFree((*mesh)->regionNames[r]));
  PetscCall(PetscFree3((*mesh)->regionDims, (*mesh)->regionTags, (*mesh)->regionNames));
  PetscCall(PetscFree(*mesh));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadNodes_v22(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscViewer viewer   = gmsh->viewer;
  PetscBool   byteSwap = gmsh->byteSwap;
  char        line[PETSC_MAX_PATH_LEN];
  int         n, t, num, nid, snum;
  GmshNodes  *nodes;

  PetscFunctionBegin;
  PetscCall(PetscViewerRead(viewer, line, 1, NULL, PETSC_STRING));
  snum = sscanf(line, "%d", &num);
  PetscCheck(snum == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
  PetscCall(GmshNodesCreate(num, &nodes));
  mesh->numNodes = num;
  mesh->nodelist = nodes;
  for (n = 0; n < num; ++n) {
    double *xyz = nodes->xyz + n * 3;
    PetscCall(PetscViewerRead(viewer, &nid, 1, NULL, PETSC_ENUM));
    PetscCall(PetscViewerRead(viewer, xyz, 3, NULL, PETSC_DOUBLE));
    if (byteSwap) PetscCall(PetscByteSwap(&nid, PETSC_ENUM, 1));
    if (byteSwap) PetscCall(PetscByteSwap(xyz, PETSC_DOUBLE, 3));
    nodes->id[n] = nid;
    for (t = 0; t < GMSH_MAX_TAGS; ++t) nodes->tag[n * GMSH_MAX_TAGS + t] = -1;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Gmsh elements can be of any dimension/co-dimension, so we need to traverse the
   file contents multiple times to figure out the true number of cells and facets
   in the given mesh. To make this more efficient we read the file contents only
   once and store them in memory, while determining the true number of cells. */
static PetscErrorCode GmshReadElements_v22(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscViewer  viewer   = gmsh->viewer;
  PetscBool    binary   = gmsh->binary;
  PetscBool    byteSwap = gmsh->byteSwap;
  char         line[PETSC_MAX_PATH_LEN];
  int          i, c, p, num, ibuf[1 + 4 + 1000], snum;
  int          cellType, numElem, numVerts, numNodes, numTags;
  GmshElement *elements;
  PetscInt    *nodeMap = gmsh->nodeMap;

  PetscFunctionBegin;
  PetscCall(PetscViewerRead(viewer, line, 1, NULL, PETSC_STRING));
  snum = sscanf(line, "%d", &num);
  PetscCheck(snum == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
  PetscCall(GmshElementsCreate(num, &elements));
  mesh->numElems = num;
  mesh->elements = elements;
  for (c = 0; c < num;) {
    PetscCall(PetscViewerRead(viewer, ibuf, 3, NULL, PETSC_ENUM));
    if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, 3));

    cellType = binary ? ibuf[0] : ibuf[1];
    numElem  = binary ? ibuf[1] : 1;
    numTags  = ibuf[2];

    PetscCall(GmshCellTypeCheck(cellType));
    numVerts = GmshCellMap[cellType].numVerts;
    numNodes = GmshCellMap[cellType].numNodes;

    for (i = 0; i < numElem; ++i, ++c) {
      GmshElement *element = elements + c;
      const int    off = binary ? 0 : 1, nint = 1 + numTags + numNodes - off;
      const int   *id = ibuf, *nodes = ibuf + 1 + numTags, *tags = ibuf + 1;
      PetscCall(PetscViewerRead(viewer, ibuf + off, nint, NULL, PETSC_ENUM));
      if (byteSwap) PetscCall(PetscByteSwap(ibuf + off, PETSC_ENUM, nint));
      element->id       = id[0];
      element->dim      = GmshCellMap[cellType].dim;
      element->cellType = cellType;
      element->numVerts = numVerts;
      element->numNodes = numNodes;
      element->numTags  = PetscMin(numTags, GMSH_MAX_TAGS);
      PetscCall(PetscSegBufferGet(mesh->segbuf, (size_t)element->numNodes, &element->nodes));
      for (p = 0; p < element->numNodes; p++) element->nodes[p] = nodeMap[nodes[p]];
      for (p = 0; p < element->numTags; p++) element->tags[p] = tags[p];
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
$Entities
  numPoints(unsigned long) numCurves(unsigned long)
    numSurfaces(unsigned long) numVolumes(unsigned long)
  // points
  tag(int) boxMinX(double) boxMinY(double) boxMinZ(double)
    boxMaxX(double) boxMaxY(double) boxMaxZ(double)
    numPhysicals(unsigned long) phyisicalTag[...](int)
  ...
  // curves
  tag(int) boxMinX(double) boxMinY(double) boxMinZ(double)
     boxMaxX(double) boxMaxY(double) boxMaxZ(double)
     numPhysicals(unsigned long) physicalTag[...](int)
     numBREPVert(unsigned long) tagBREPVert[...](int)
  ...
  // surfaces
  tag(int) boxMinX(double) boxMinY(double) boxMinZ(double)
    boxMaxX(double) boxMaxY(double) boxMaxZ(double)
    numPhysicals(unsigned long) physicalTag[...](int)
    numBREPCurve(unsigned long) tagBREPCurve[...](int)
  ...
  // volumes
  tag(int) boxMinX(double) boxMinY(double) boxMinZ(double)
    boxMaxX(double) boxMaxY(double) boxMaxZ(double)
    numPhysicals(unsigned long) physicalTag[...](int)
    numBREPSurfaces(unsigned long) tagBREPSurfaces[...](int)
  ...
$EndEntities
*/
static PetscErrorCode GmshReadEntities_v40(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscViewer viewer   = gmsh->viewer;
  PetscBool   byteSwap = gmsh->byteSwap;
  long        lnum, lbuf[4];
  int         dim, eid, numTags, *ibuf, t;
  PetscCount  index, count[4];
  PetscInt    i, num;
  GmshEntity *entity = NULL;

  PetscFunctionBegin;
  PetscCall(PetscViewerRead(viewer, lbuf, 4, NULL, PETSC_LONG));
  if (byteSwap) PetscCall(PetscByteSwap(lbuf, PETSC_LONG, 4));
  for (i = 0; i < 4; ++i) count[i] = (PetscCount)lbuf[i];
  PetscCall(GmshEntitiesCreate(count, &mesh->entities));
  for (dim = 0; dim < 4; ++dim) {
    for (index = 0; index < count[dim]; ++index) {
      PetscCall(PetscViewerRead(viewer, &eid, 1, NULL, PETSC_ENUM));
      if (byteSwap) PetscCall(PetscByteSwap(&eid, PETSC_ENUM, 1));
      PetscCall(GmshEntitiesAdd(mesh->entities, (PetscInt)index, dim, eid, &entity));
      PetscCall(PetscViewerRead(viewer, entity->bbox, 6, NULL, PETSC_DOUBLE));
      if (byteSwap) PetscCall(PetscByteSwap(entity->bbox, PETSC_DOUBLE, 6));
      PetscCall(PetscViewerRead(viewer, &lnum, 1, NULL, PETSC_LONG));
      if (byteSwap) PetscCall(PetscByteSwap(&lnum, PETSC_LONG, 1));
      PetscCall(PetscIntCast(lnum, &num));
      PetscCall(GmshBufferGet(gmsh, num, sizeof(int), &ibuf));
      PetscCall(PetscViewerRead(viewer, ibuf, num, NULL, PETSC_ENUM));
      if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, num));
      entity->numTags = numTags = (int)PetscMin(num, GMSH_MAX_TAGS);
      for (t = 0; t < numTags; ++t) entity->tags[t] = ibuf[t];
      if (dim == 0) continue;
      PetscCall(PetscViewerRead(viewer, &lnum, 1, NULL, PETSC_LONG));
      if (byteSwap) PetscCall(PetscByteSwap(&lnum, PETSC_LONG, 1));
      PetscCall(GmshBufferGet(gmsh, lnum, sizeof(int), &ibuf));
      PetscCall(PetscIntCast(lnum, &num));
      PetscCall(PetscViewerRead(viewer, ibuf, num, NULL, PETSC_ENUM));
      if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, num));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
$Nodes
  numEntityBlocks(unsigned long) numNodes(unsigned long)
  tagEntity(int) dimEntity(int) typeNode(int) numNodes(unsigned long)
    tag(int) x(double) y(double) z(double)
    ...
  ...
$EndNodes
*/
static PetscErrorCode GmshReadNodes_v40(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscViewer viewer   = gmsh->viewer;
  PetscBool   byteSwap = gmsh->byteSwap;
  long        block, node, n, t, numEntityBlocks, numTotalNodes, numNodes;
  int         info[3], nid;
  GmshNodes  *nodes;

  PetscFunctionBegin;
  PetscCall(PetscViewerRead(viewer, &numEntityBlocks, 1, NULL, PETSC_LONG));
  if (byteSwap) PetscCall(PetscByteSwap(&numEntityBlocks, PETSC_LONG, 1));
  PetscCall(PetscViewerRead(viewer, &numTotalNodes, 1, NULL, PETSC_LONG));
  if (byteSwap) PetscCall(PetscByteSwap(&numTotalNodes, PETSC_LONG, 1));
  PetscCall(GmshNodesCreate(numTotalNodes, &nodes));
  PetscCall(PetscIntCast(numTotalNodes, &mesh->numNodes));
  mesh->nodelist = nodes;
  for (n = 0, block = 0; block < numEntityBlocks; ++block) {
    PetscCall(PetscViewerRead(viewer, info, 3, NULL, PETSC_ENUM));
    PetscCall(PetscViewerRead(viewer, &numNodes, 1, NULL, PETSC_LONG));
    if (byteSwap) PetscCall(PetscByteSwap(&numNodes, PETSC_LONG, 1));
    if (gmsh->binary) {
      size_t   nbytes = sizeof(int) + 3 * sizeof(double);
      char    *cbuf   = NULL; /* dummy value to prevent warning from compiler about possible uninitialized value */
      PetscInt icnt;

      PetscCall(GmshBufferGet(gmsh, numNodes, nbytes, &cbuf));
      PetscCall(PetscIntCast(numNodes * nbytes, &icnt));
      PetscCall(PetscViewerRead(viewer, cbuf, icnt, NULL, PETSC_CHAR));
      for (node = 0; node < numNodes; ++node, ++n) {
        char   *cnid = cbuf + node * nbytes, *cxyz = cnid + sizeof(int);
        double *xyz = nodes->xyz + n * 3;

        if (!PetscBinaryBigEndian()) PetscCall(PetscByteSwap(cnid, PETSC_ENUM, 1));
        if (!PetscBinaryBigEndian()) PetscCall(PetscByteSwap(cxyz, PETSC_DOUBLE, 3));
        PetscCall(PetscMemcpy(&nid, cnid, sizeof(int)));
        PetscCall(PetscMemcpy(xyz, cxyz, 3 * sizeof(double)));
        if (byteSwap) PetscCall(PetscByteSwap(&nid, PETSC_ENUM, 1));
        if (byteSwap) PetscCall(PetscByteSwap(xyz, PETSC_DOUBLE, 3));
        nodes->id[n] = nid;
        for (t = 0; t < GMSH_MAX_TAGS; ++t) nodes->tag[n * GMSH_MAX_TAGS + t] = -1;
      }
    } else {
      for (node = 0; node < numNodes; ++node, ++n) {
        double *xyz = nodes->xyz + n * 3;

        PetscCall(PetscViewerRead(viewer, &nid, 1, NULL, PETSC_ENUM));
        PetscCall(PetscViewerRead(viewer, xyz, 3, NULL, PETSC_DOUBLE));
        if (byteSwap) PetscCall(PetscByteSwap(&nid, PETSC_ENUM, 1));
        if (byteSwap) PetscCall(PetscByteSwap(xyz, PETSC_DOUBLE, 3));
        nodes->id[n] = nid;
        for (t = 0; t < GMSH_MAX_TAGS; ++t) nodes->tag[n * GMSH_MAX_TAGS + t] = -1;
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
$Elements
  numEntityBlocks(unsigned long) numElements(unsigned long)
  tagEntity(int) dimEntity(int) typeEle(int) numElements(unsigned long)
    tag(int) numVert[...](int)
    ...
  ...
$EndElements
*/
static PetscErrorCode GmshReadElements_v40(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscViewer  viewer   = gmsh->viewer;
  PetscBool    byteSwap = gmsh->byteSwap;
  long         c, block, numEntityBlocks, numTotalElements, elem, numElements;
  int          p, info[3], *ibuf = NULL;
  int          eid, dim, cellType, numVerts, numNodes, numTags;
  GmshEntity  *entity = NULL;
  GmshElement *elements;
  PetscInt    *nodeMap = gmsh->nodeMap, icnt;

  PetscFunctionBegin;
  PetscCall(PetscViewerRead(viewer, &numEntityBlocks, 1, NULL, PETSC_LONG));
  if (byteSwap) PetscCall(PetscByteSwap(&numEntityBlocks, PETSC_LONG, 1));
  PetscCall(PetscViewerRead(viewer, &numTotalElements, 1, NULL, PETSC_LONG));
  if (byteSwap) PetscCall(PetscByteSwap(&numTotalElements, PETSC_LONG, 1));
  PetscCall(GmshElementsCreate(numTotalElements, &elements));
  PetscCall(PetscIntCast(numTotalElements, &mesh->numElems));
  mesh->elements = elements;
  for (c = 0, block = 0; block < numEntityBlocks; ++block) {
    PetscCall(PetscViewerRead(viewer, info, 3, NULL, PETSC_ENUM));
    if (byteSwap) PetscCall(PetscByteSwap(info, PETSC_ENUM, 3));
    eid      = info[0];
    dim      = info[1];
    cellType = info[2];
    PetscCall(GmshEntitiesGet(mesh->entities, dim, eid, &entity));
    PetscCall(GmshCellTypeCheck(cellType));
    numVerts = GmshCellMap[cellType].numVerts;
    numNodes = GmshCellMap[cellType].numNodes;
    numTags  = (int)entity->numTags;
    PetscCall(PetscViewerRead(viewer, &numElements, 1, NULL, PETSC_LONG));
    if (byteSwap) PetscCall(PetscByteSwap(&numElements, PETSC_LONG, 1));
    PetscCall(GmshBufferGet(gmsh, (1 + numNodes) * numElements, sizeof(int), &ibuf));
    PetscCall(PetscIntCast((1 + numNodes) * numElements, &icnt));
    PetscCall(PetscViewerRead(viewer, ibuf, icnt, NULL, PETSC_ENUM));
    if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, (1 + numNodes) * numElements));
    for (elem = 0; elem < numElements; ++elem, ++c) {
      GmshElement *element = elements + c;
      const int   *id = ibuf + elem * (1 + numNodes), *nodes = id + 1;
      element->id       = id[0];
      element->dim      = dim;
      element->cellType = cellType;
      element->numVerts = numVerts;
      element->numNodes = numNodes;
      element->numTags  = numTags;
      PetscCall(PetscSegBufferGet(mesh->segbuf, (size_t)element->numNodes, &element->nodes));
      for (p = 0; p < element->numNodes; p++) element->nodes[p] = nodeMap[nodes[p]];
      for (p = 0; p < element->numTags; p++) element->tags[p] = entity->tags[p];
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadPeriodic_v40(GmshFile *gmsh, PetscInt periodicMap[])
{
  PetscViewer viewer     = gmsh->viewer;
  int         fileFormat = gmsh->fileFormat;
  PetscBool   binary     = gmsh->binary;
  PetscBool   byteSwap   = gmsh->byteSwap;
  int         numPeriodic, snum, i;
  char        line[PETSC_MAX_PATH_LEN];
  PetscInt   *nodeMap = gmsh->nodeMap;

  PetscFunctionBegin;
  if (fileFormat == 22 || !binary) {
    PetscCall(PetscViewerRead(viewer, line, 1, NULL, PETSC_STRING));
    snum = sscanf(line, "%d", &numPeriodic);
    PetscCheck(snum == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
  } else {
    PetscCall(PetscViewerRead(viewer, &numPeriodic, 1, NULL, PETSC_ENUM));
    if (byteSwap) PetscCall(PetscByteSwap(&numPeriodic, PETSC_ENUM, 1));
  }
  for (i = 0; i < numPeriodic; i++) {
    int    ibuf[3], correspondingDim = -1, correspondingTag = -1, primaryTag = -1, correspondingNode, primaryNode;
    long   j, nNodes;
    double affine[16];

    if (fileFormat == 22 || !binary) {
      PetscCall(PetscViewerRead(viewer, line, 3, NULL, PETSC_STRING));
      snum = sscanf(line, "%d %d %d", &correspondingDim, &correspondingTag, &primaryTag);
      PetscCheck(snum == 3, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
    } else {
      PetscCall(PetscViewerRead(viewer, ibuf, 3, NULL, PETSC_ENUM));
      if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, 3));
      correspondingDim = ibuf[0];
      correspondingTag = ibuf[1];
      primaryTag       = ibuf[2];
    }
    (void)correspondingDim;
    (void)correspondingTag;
    (void)primaryTag; /* unused */

    if (fileFormat == 22 || !binary) {
      PetscCall(PetscViewerRead(viewer, line, 1, NULL, PETSC_STRING));
      snum = sscanf(line, "%ld", &nNodes);
      if (snum != 1) { /* discard transformation and try again */
        PetscCall(PetscViewerRead(viewer, line, -PETSC_MAX_PATH_LEN, NULL, PETSC_STRING));
        PetscCall(PetscViewerRead(viewer, line, 1, NULL, PETSC_STRING));
        snum = sscanf(line, "%ld", &nNodes);
        PetscCheck(snum == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
      }
    } else {
      PetscCall(PetscViewerRead(viewer, &nNodes, 1, NULL, PETSC_LONG));
      if (byteSwap) PetscCall(PetscByteSwap(&nNodes, PETSC_LONG, 1));
      if (nNodes == -1) { /* discard transformation and try again */
        PetscCall(PetscViewerRead(viewer, affine, 16, NULL, PETSC_DOUBLE));
        PetscCall(PetscViewerRead(viewer, &nNodes, 1, NULL, PETSC_LONG));
        if (byteSwap) PetscCall(PetscByteSwap(&nNodes, PETSC_LONG, 1));
      }
    }

    for (j = 0; j < nNodes; j++) {
      if (fileFormat == 22 || !binary) {
        PetscCall(PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING));
        snum = sscanf(line, "%d %d", &correspondingNode, &primaryNode);
        PetscCheck(snum == 2, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
      } else {
        PetscCall(PetscViewerRead(viewer, ibuf, 2, NULL, PETSC_ENUM));
        if (byteSwap) PetscCall(PetscByteSwap(ibuf, PETSC_ENUM, 2));
        correspondingNode = ibuf[0];
        primaryNode       = ibuf[1];
      }
      correspondingNode              = (int)nodeMap[correspondingNode];
      primaryNode                    = (int)nodeMap[primaryNode];
      periodicMap[correspondingNode] = primaryNode;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
$Entities
  numPoints(size_t) numCurves(size_t)
    numSurfaces(size_t) numVolumes(size_t)
  pointTag(int) X(double) Y(double) Z(double)
    numPhysicalTags(size_t) physicalTag(int) ...
  ...
  curveTag(int) minX(double) minY(double) minZ(double)
    maxX(double) maxY(double) maxZ(double)
    numPhysicalTags(size_t) physicalTag(int) ...
    numBoundingPoints(size_t) pointTag(int) ...
  ...
  surfaceTag(int) minX(double) minY(double) minZ(double)
    maxX(double) maxY(double) maxZ(double)
    numPhysicalTags(size_t) physicalTag(int) ...
    numBoundingCurves(size_t) curveTag(int) ...
  ...
  volumeTag(int) minX(double) minY(double) minZ(double)
    maxX(double) maxY(double) maxZ(double)
    numPhysicalTags(size_t) physicalTag(int) ...
    numBoundngSurfaces(size_t) surfaceTag(int) ...
  ...
$EndEntities
*/
static PetscErrorCode GmshReadEntities_v41(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscCount  count[4], index, numTags;
  int         dim, eid, *tags = NULL;
  GmshEntity *entity = NULL;

  PetscFunctionBegin;
  PetscCall(GmshReadPetscCount(gmsh, count, 4));
  PetscCall(GmshEntitiesCreate(count, &mesh->entities));
  for (dim = 0; dim < 4; ++dim) {
    for (index = 0; index < count[dim]; ++index) {
      PetscCall(GmshReadInt(gmsh, &eid, 1));
      PetscCall(GmshEntitiesAdd(mesh->entities, (PetscInt)index, dim, eid, &entity));
      PetscCall(GmshReadDouble(gmsh, entity->bbox, (dim == 0) ? 3 : 6));
      PetscCall(GmshReadPetscCount(gmsh, &numTags, 1));
      PetscCall(GmshBufferGet(gmsh, numTags, sizeof(int), &tags));
      PetscCall(GmshReadInt(gmsh, tags, numTags));
      PetscCheck(numTags <= GMSH_MAX_TAGS, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "PETSc currently supports up to %" PetscInt_FMT " tags per entity, not %" PetscCount_FMT, (PetscInt)GMSH_MAX_TAGS, numTags);
      PetscCall(PetscIntCast(numTags, &entity->numTags));
      for (PetscInt i = 0; i < entity->numTags; ++i) entity->tags[i] = tags[i];
      if (dim == 0) continue;
      PetscCall(GmshReadPetscCount(gmsh, &numTags, 1));
      PetscCall(GmshBufferGet(gmsh, numTags, sizeof(int), &tags));
      PetscCall(GmshReadInt(gmsh, tags, numTags));
      /* Currently, we do not save the ids for the bounding entities */
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
$Nodes
  numEntityBlocks(size_t) numNodes(size_t)
    minNodeTag(size_t) maxNodeTag(size_t)
  entityDim(int) entityTag(int) parametric(int; 0 or 1) numNodesBlock(size_t)
    nodeTag(size_t)
    ...
    x(double) y(double) z(double)
       < u(double; if parametric and entityDim = 1 or entityDim = 2) >
       < v(double; if parametric and entityDim = 2) >
    ...
  ...
$EndNodes
*/
static PetscErrorCode GmshReadNodes_v41(GmshFile *gmsh, GmshMesh *mesh)
{
  int         info[3], dim, eid, parametric;
  PetscCount  sizes[4], numEntityBlocks, numNodes, numNodesBlock = 0;
  PetscInt    numTags;
  GmshEntity *entity = NULL;
  GmshNodes  *nodes;

  PetscFunctionBegin;
  PetscCall(GmshReadPetscCount(gmsh, sizes, 4));
  numEntityBlocks = sizes[0];
  numNodes        = sizes[1];
  PetscCall(GmshNodesCreate(numNodes, &nodes));
  PetscCall(PetscIntCast(numNodes, &mesh->numNodes));
  mesh->nodelist = nodes;
  if (numEntityBlocks && !mesh->entities) PetscCall(PetscInfo(NULL, "File specifies %" PetscCount_FMT " entity blocks, but was missing the $Entities section\n", numEntityBlocks));
  for (PetscCount block = 0, node = 0; block < numEntityBlocks; ++block, node += numNodesBlock) {
    PetscCall(GmshReadInt(gmsh, info, 3));
    dim        = info[0];
    eid        = info[1];
    parametric = info[2];
    if (mesh->entities) PetscCall(GmshEntitiesGet(mesh->entities, dim, eid, &entity));
    numTags = entity ? entity->numTags : 0;
    PetscCheck(!parametric, PETSC_COMM_SELF, PETSC_ERR_SUP, "Parametric coordinates not supported");
    PetscCall(GmshReadPetscCount(gmsh, &numNodesBlock, 1));
    PetscCall(GmshReadPetscInt(gmsh, nodes->id + node, numNodesBlock));
    PetscCall(GmshReadDouble(gmsh, nodes->xyz + node * 3, numNodesBlock * 3));
    for (PetscCount n = 0; n < numNodesBlock; ++n) {
      PetscInt *tags = &nodes->tag[node * GMSH_MAX_TAGS];

      for (PetscInt t = 0; t < numTags; ++t) tags[n * GMSH_MAX_TAGS + t] = entity->tags[t];
      for (PetscInt t = numTags; t < GMSH_MAX_TAGS; ++t) tags[n * GMSH_MAX_TAGS + t] = -1;
    }
  }
  PetscCall(PetscIntCast(sizes[2], &gmsh->nodeStart));
  PetscCall(PetscIntCast(sizes[3] + 1, &gmsh->nodeEnd));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
$Elements
  numEntityBlocks(size_t) numElements(size_t)
    minElementTag(size_t) maxElementTag(size_t)
  entityDim(int) entityTag(int) elementType(int; see below) numElementsBlock(size_t)
    elementTag(size_t) nodeTag(size_t) ...
    ...
  ...
$EndElements
*/
static PetscErrorCode GmshReadElements_v41(GmshFile *gmsh, GmshMesh *mesh)
{
  int          info[3], eid, dim, cellType;
  PetscCount   sizes[4], numEntityBlocks, numElements, numBlockElements, numVerts, numNodes, numTags, block, elem, c, p;
  GmshEntity  *entity = NULL;
  GmshElement *elements;
  PetscInt    *nodeMap = gmsh->nodeMap, *ibuf = NULL;

  PetscFunctionBegin;
  PetscCall(GmshReadPetscCount(gmsh, sizes, 4));
  numEntityBlocks = sizes[0];
  numElements     = sizes[1];
  PetscCall(GmshElementsCreate(numElements, &elements));
  PetscCall(PetscIntCast(numElements, &mesh->numElems));
  mesh->elements = elements;
  if (numEntityBlocks && !mesh->entities) PetscCall(PetscInfo(NULL, "File specifies %" PetscCount_FMT " entity blocks, but was missing the $Entities section\n", numEntityBlocks));
  for (c = 0, block = 0; block < numEntityBlocks; ++block) {
    PetscCall(GmshReadInt(gmsh, info, 3));
    dim      = info[0];
    eid      = info[1];
    cellType = info[2];
    if (mesh->entities) PetscCall(GmshEntitiesGet(mesh->entities, dim, eid, &entity));
    PetscCall(GmshCellTypeCheck(cellType));
    numVerts = GmshCellMap[cellType].numVerts;
    numNodes = GmshCellMap[cellType].numNodes;
    numTags  = entity ? entity->numTags : 0;
    PetscCall(GmshReadPetscCount(gmsh, &numBlockElements, 1));
    PetscCall(GmshBufferGet(gmsh, (1 + numNodes) * numBlockElements, sizeof(PetscInt), &ibuf));
    PetscCall(GmshReadPetscInt(gmsh, ibuf, (1 + numNodes) * numBlockElements));
    for (elem = 0; elem < numBlockElements; ++elem, ++c) {
      GmshElement    *element = elements + c;
      const PetscInt *id = ibuf + elem * (1 + numNodes), *nodes = id + 1;

      element->id       = id[0];
      element->dim      = dim;
      element->cellType = cellType;
      PetscCall(PetscIntCast(numVerts, &element->numVerts));
      PetscCall(PetscIntCast(numNodes, &element->numNodes));
      PetscCall(PetscIntCast(numTags, &element->numTags));
      PetscCall(PetscSegBufferGet(mesh->segbuf, element->numNodes, &element->nodes));
      for (p = 0; p < element->numNodes; p++) element->nodes[p] = nodeMap[nodes[p]];
      for (p = 0; p < element->numTags; p++) element->tags[p] = entity->tags[p];
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
$Periodic
  numPeriodicLinks(size_t)
  entityDim(int) entityTag(int) entityTagPrimary(int)
  numAffine(size_t) value(double) ...
  numCorrespondingNodes(size_t)
    nodeTag(size_t) nodeTagPrimary(size_t)
    ...
  ...
$EndPeriodic
*/
static PetscErrorCode GmshReadPeriodic_v41(GmshFile *gmsh, PetscInt periodicMap[])
{
  int        info[3];
  double     dbuf[16];
  PetscCount numPeriodicLinks, numAffine, numCorrespondingNodes;
  PetscInt  *nodeMap = gmsh->nodeMap, *nodeTags = NULL;

  PetscFunctionBegin;
  PetscCall(GmshReadPetscCount(gmsh, &numPeriodicLinks, 1));
  for (PetscCount link = 0; link < numPeriodicLinks; ++link) {
    PetscCall(GmshReadInt(gmsh, info, 3));
    PetscCall(GmshReadPetscCount(gmsh, &numAffine, 1));
    PetscCall(GmshReadDouble(gmsh, dbuf, numAffine));
    PetscCall(GmshReadPetscCount(gmsh, &numCorrespondingNodes, 1));
    PetscCall(GmshBufferGet(gmsh, numCorrespondingNodes, sizeof(PetscInt), &nodeTags));
    PetscCall(GmshReadPetscInt(gmsh, nodeTags, numCorrespondingNodes * 2));
    for (PetscCount node = 0; node < numCorrespondingNodes; ++node) {
      PetscInt correspondingNode = nodeMap[nodeTags[node * 2 + 0]];
      PetscInt primaryNode       = nodeMap[nodeTags[node * 2 + 1]];

      periodicMap[correspondingNode] = primaryNode;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
$MeshFormat // same as MSH version 2
  version(ASCII double; currently 4.1)
  file-type(ASCII int; 0 for ASCII mode, 1 for binary mode)
  data-size(ASCII int; sizeof(size_t))
  < int with value one; only in binary mode, to detect endianness >
$EndMeshFormat
*/
static PetscErrorCode GmshReadMeshFormat(GmshFile *gmsh)
{
  char  line[PETSC_MAX_PATH_LEN];
  int   snum, fileType, fileFormat, dataSize, checkEndian;
  float version;

  PetscFunctionBegin;
  PetscCall(GmshReadString(gmsh, line, 3));
  snum       = sscanf(line, "%f %d %d", &version, &fileType, &dataSize);
  fileFormat = (int)roundf(version * 10);
  PetscCheck(snum == 3, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Unable to parse Gmsh file header: %s", line);
  PetscCheck(fileFormat >= 22, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f must be at least 2.2", (double)version);
  PetscCheck((int)version != 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f not supported", (double)version);
  PetscCheck(fileFormat <= 41, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f must be at most 4.1", (double)version);
  PetscCheck(!gmsh->binary || fileType, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Viewer is binary but Gmsh file is ASCII");
  PetscCheck(gmsh->binary || !fileType, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Viewer is ASCII but Gmsh file is binary");
  PetscCheck(fileFormat > 40 || dataSize == sizeof(double), PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Data size %d is not valid for a Gmsh file", dataSize);
  PetscCheck(fileFormat < 41 || dataSize == sizeof(int) || dataSize == sizeof(PetscInt64), PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Data size %d is not valid for a Gmsh file", dataSize);
  gmsh->fileFormat = fileFormat;
  gmsh->dataSize   = dataSize;
  gmsh->byteSwap   = PETSC_FALSE;
  if (gmsh->binary) {
    PetscCall(GmshReadInt(gmsh, &checkEndian, 1));
    if (checkEndian != 1) {
      PetscCall(PetscByteSwap(&checkEndian, PETSC_ENUM, 1));
      PetscCheck(checkEndian == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Unable to detect endianness in Gmsh file header: %s", line);
      gmsh->byteSwap = PETSC_TRUE;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
Neper: https://neper.info/ adds this section

$MeshVersion
  <major>.<minor>,<patch>
$EndMeshVersion
*/
static PetscErrorCode GmshReadMeshVersion(GmshFile *gmsh)
{
  char line[PETSC_MAX_PATH_LEN];
  int  snum, major, minor, patch;

  PetscFunctionBegin;
  PetscCall(GmshReadString(gmsh, line, 1));
  snum = sscanf(line, "%d.%d.%d", &major, &minor, &patch);
  PetscCheck(snum == 3, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Unable to parse Gmsh file header: %s", line);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* http://gmsh.info/dev/doc/texinfo/gmsh.html#MSH-file-format
Neper: https://neper.info/ adds this section

$Domain
  <shape>
$EndDomain
*/
static PetscErrorCode GmshReadMeshDomain(GmshFile *gmsh)
{
  char line[PETSC_MAX_PATH_LEN];

  PetscFunctionBegin;
  PetscCall(GmshReadString(gmsh, line, 1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
PhysicalNames
  numPhysicalNames(ASCII int)
  dimension(ASCII int) physicalTag(ASCII int) "name"(127 characters max)
  ...
$EndPhysicalNames
*/
static PetscErrorCode GmshReadPhysicalNames(GmshFile *gmsh, GmshMesh *mesh)
{
  char line[PETSC_MAX_PATH_LEN], name[128 + 2], *p = NULL, *q = NULL, *r = NULL;
  int  snum, region, dim, tag;

  PetscFunctionBegin;
  PetscCall(GmshReadString(gmsh, line, 1));
  snum             = sscanf(line, "%d", &region);
  mesh->numRegions = region;
  PetscCheck(snum == 1, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
  PetscCall(PetscMalloc3(mesh->numRegions, &mesh->regionDims, mesh->numRegions, &mesh->regionTags, mesh->numRegions, &mesh->regionNames));
  for (region = 0; region < mesh->numRegions; ++region) {
    PetscCall(GmshReadString(gmsh, line, 2));
    snum = sscanf(line, "%d %d", &dim, &tag);
    PetscCheck(snum == 2, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
    PetscCall(GmshReadString(gmsh, line, -(PetscInt)sizeof(line)));
    PetscCall(PetscStrchr(line, '"', &p));
    PetscCheck(p, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
    PetscCall(PetscStrrchr(line, '"', &q));
    PetscCheck(q != p, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "File is not a valid Gmsh file");
    PetscCall(PetscStrrchr(line, ':', &r));
    if (p != r) q = r;
    PetscCall(PetscStrncpy(name, p + 1, (size_t)(q - p - 1)));
    mesh->regionDims[region] = dim;
    mesh->regionTags[region] = tag;
    PetscCall(PetscStrallocpy(name, &mesh->regionNames[region]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadEntities(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscFunctionBegin;
  switch (gmsh->fileFormat) {
  case 41:
    PetscCall(GmshReadEntities_v41(gmsh, mesh));
    break;
  default:
    PetscCall(GmshReadEntities_v40(gmsh, mesh));
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadNodes(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscFunctionBegin;
  switch (gmsh->fileFormat) {
  case 41:
    PetscCall(GmshReadNodes_v41(gmsh, mesh));
    break;
  case 40:
    PetscCall(GmshReadNodes_v40(gmsh, mesh));
    break;
  default:
    PetscCall(GmshReadNodes_v22(gmsh, mesh));
    break;
  }

  { /* Gmsh v2.2/v4.0 does not provide min/max node tags */
    if (mesh->numNodes > 0 && gmsh->nodeEnd >= gmsh->nodeStart) {
      PetscInt   tagMin = PETSC_INT_MAX, tagMax = PETSC_INT_MIN, n;
      GmshNodes *nodes = mesh->nodelist;
      for (n = 0; n < mesh->numNodes; ++n) {
        const PetscInt tag = nodes->id[n];
        tagMin             = PetscMin(tag, tagMin);
        tagMax             = PetscMax(tag, tagMax);
      }
      gmsh->nodeStart = tagMin;
      gmsh->nodeEnd   = tagMax + 1;
    }
  }

  { /* Support for sparse node tags */
    PetscInt   n, t;
    GmshNodes *nodes = mesh->nodelist;
    PetscCall(PetscMalloc1(gmsh->nodeEnd - gmsh->nodeStart, &gmsh->nbuf));
    for (t = 0; t < gmsh->nodeEnd - gmsh->nodeStart; ++t) gmsh->nbuf[t] = PETSC_INT_MIN;
    gmsh->nodeMap = gmsh->nbuf - gmsh->nodeStart;
    for (n = 0; n < mesh->numNodes; ++n) {
      const PetscInt tag = nodes->id[n];
      PetscCheck(gmsh->nodeMap[tag] < 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Repeated node tag %" PetscInt_FMT, tag);
      gmsh->nodeMap[tag] = n;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadElements(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscFunctionBegin;
  switch (gmsh->fileFormat) {
  case 41:
    PetscCall(GmshReadElements_v41(gmsh, mesh));
    break;
  case 40:
    PetscCall(GmshReadElements_v40(gmsh, mesh));
    break;
  default:
    PetscCall(GmshReadElements_v22(gmsh, mesh));
    break;
  }

  { /* Reorder elements by codimension and polytope type */
    PetscInt     ne       = mesh->numElems;
    GmshElement *elements = mesh->elements;
    PetscInt     keymap[GMSH_NUM_POLYTOPES], nk = 0;
    PetscInt     offset[GMSH_NUM_POLYTOPES + 1], e, k;

    for (k = 0; k < GMSH_NUM_POLYTOPES; ++k) keymap[k] = PETSC_INT_MIN;
    PetscCall(PetscMemzero(offset, sizeof(offset)));

    keymap[GMSH_TET] = nk++;
    keymap[GMSH_HEX] = nk++;
    keymap[GMSH_PRI] = nk++;
    keymap[GMSH_PYR] = nk++;
    keymap[GMSH_TRI] = nk++;
    keymap[GMSH_QUA] = nk++;
    keymap[GMSH_SEG] = nk++;
    keymap[GMSH_VTX] = nk++;

    PetscCall(GmshElementsCreate(mesh->numElems, &mesh->elements));
#define key(eid) keymap[GmshCellMap[elements[eid].cellType].polytope]
    for (e = 0; e < ne; ++e) offset[1 + key(e)]++;
    for (k = 1; k < nk; ++k) offset[k] += offset[k - 1];
    for (e = 0; e < ne; ++e) mesh->elements[offset[key(e)]++] = elements[e];
#undef key
    PetscCall(GmshElementsDestroy(&elements));
  }

  { /* Mesh dimension and order */
    GmshElement *elem = mesh->numElems ? mesh->elements : NULL;
    mesh->dim         = elem ? GmshCellMap[elem->cellType].dim : 0;
    mesh->order       = elem ? GmshCellMap[elem->cellType].order : 0;
  }

  {
    PetscBT  vtx;
    PetscInt dim = mesh->dim, e, n, v;

    PetscCall(PetscBTCreate(mesh->numNodes, &vtx));

    /* Compute number of cells and set of vertices */
    mesh->numCells = 0;
    for (e = 0; e < mesh->numElems; ++e) {
      GmshElement *elem = mesh->elements + e;
      if (elem->dim == dim && dim > 0) mesh->numCells++;
      for (v = 0; v < elem->numVerts; v++) PetscCall(PetscBTSet(vtx, elem->nodes[v]));
    }

    /* Compute numbering for vertices */
    mesh->numVerts = 0;
    PetscCall(PetscMalloc1(mesh->numNodes, &mesh->vertexMap));
    for (n = 0; n < mesh->numNodes; ++n) mesh->vertexMap[n] = PetscBTLookup(vtx, n) ? mesh->numVerts++ : PETSC_INT_MIN;

    PetscCall(PetscBTDestroy(&vtx));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GmshReadPeriodic(GmshFile *gmsh, GmshMesh *mesh)
{
  PetscInt n;

  PetscFunctionBegin;
  PetscCall(PetscMalloc1(mesh->numNodes, &mesh->periodMap));
  for (n = 0; n < mesh->numNodes; ++n) mesh->periodMap[n] = n;
  switch (gmsh->fileFormat) {
  case 41:
    PetscCall(GmshReadPeriodic_v41(gmsh, mesh->periodMap));
    break;
  default:
    PetscCall(GmshReadPeriodic_v40(gmsh, mesh->periodMap));
    break;
  }

  /* Find canonical primary nodes */
  for (n = 0; n < mesh->numNodes; ++n)
    while (mesh->periodMap[n] != mesh->periodMap[mesh->periodMap[n]]) mesh->periodMap[n] = mesh->periodMap[mesh->periodMap[n]];

  /* Renumber vertices (filter out correspondings) */
  mesh->numVerts = 0;
  for (n = 0; n < mesh->numNodes; ++n)
    if (mesh->vertexMap[n] >= 0)   /* is vertex */
      if (mesh->periodMap[n] == n) /* is primary */
        mesh->vertexMap[n] = mesh->numVerts++;
  for (n = 0; n < mesh->numNodes; ++n)
    if (mesh->vertexMap[n] >= 0)   /* is vertex */
      if (mesh->periodMap[n] != n) /* is corresponding  */
        mesh->vertexMap[n] = mesh->vertexMap[mesh->periodMap[n]];
  PetscFunctionReturn(PETSC_SUCCESS);
}

#define DM_POLYTOPE_VERTEX DM_POLYTOPE_POINT
static const DMPolytopeType DMPolytopeMap[] = {
  /* GMSH_VTX */ DM_POLYTOPE_VERTEX,
  /* GMSH_SEG */ DM_POLYTOPE_SEGMENT,
  /* GMSH_TRI */ DM_POLYTOPE_TRIANGLE,
  /* GMSH_QUA */ DM_POLYTOPE_QUADRILATERAL,
  /* GMSH_TET */ DM_POLYTOPE_TETRAHEDRON,
  /* GMSH_HEX */ DM_POLYTOPE_HEXAHEDRON,
  /* GMSH_PRI */ DM_POLYTOPE_TRI_PRISM,
  /* GMSH_PYR */ DM_POLYTOPE_PYRAMID,       DM_POLYTOPE_UNKNOWN};

static inline DMPolytopeType DMPolytopeTypeFromGmsh(PetscInt cellType)
{
  return DMPolytopeMap[GmshCellMap[cellType].polytope];
}

static PetscErrorCode GmshCreateFE(MPI_Comm comm, const char prefix[], PetscBool isSimplex, PetscBool continuity, PetscDTNodeType nodeType, PetscInt dim, PetscInt Nc, PetscInt k, PetscFE *fem)
{
  DM              K;
  PetscSpace      P;
  PetscDualSpace  Q;
  PetscQuadrature q, fq;
  PetscBool       isTensor = isSimplex ? PETSC_FALSE : PETSC_TRUE;
  PetscBool       endpoint = PETSC_TRUE;
  char            name[32];

  PetscFunctionBegin;
  /* Create space */
  PetscCall(PetscSpaceCreate(comm, &P));
  PetscCall(PetscSpaceSetType(P, PETSCSPACEPOLYNOMIAL));
  PetscCall(PetscSpacePolynomialSetTensor(P, isTensor));
  PetscCall(PetscSpaceSetNumComponents(P, Nc));
  PetscCall(PetscSpaceSetNumVariables(P, dim));
  PetscCall(PetscSpaceSetDegree(P, k, PETSC_DETERMINE));
  if (prefix) {
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, prefix));
    PetscCall(PetscSpaceSetFromOptions(P));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)P, NULL));
    PetscCall(PetscSpaceGetDegree(P, &k, NULL));
  }
  PetscCall(PetscSpaceSetUp(P));
  /* Create dual space */
  PetscCall(PetscDualSpaceCreate(comm, &Q));
  PetscCall(PetscDualSpaceSetType(Q, PETSCDUALSPACELAGRANGE));
  PetscCall(PetscDualSpaceLagrangeSetTensor(Q, isTensor));
  PetscCall(PetscDualSpaceLagrangeSetContinuity(Q, continuity));
  PetscCall(PetscDualSpaceLagrangeSetNodeType(Q, nodeType, endpoint, 0));
  PetscCall(PetscDualSpaceSetNumComponents(Q, Nc));
  PetscCall(PetscDualSpaceSetOrder(Q, k));
  PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(dim, isSimplex), &K));
  PetscCall(PetscDualSpaceSetDM(Q, K));
  PetscCall(DMDestroy(&K));
  if (prefix) {
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, prefix));
    PetscCall(PetscDualSpaceSetFromOptions(Q));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)Q, NULL));
  }
  PetscCall(PetscDualSpaceSetUp(Q));
  /* Create quadrature */
  if (isSimplex) {
    PetscCall(PetscDTStroudConicalQuadrature(dim, 1, k + 1, -1, +1, &q));
    PetscCall(PetscDTStroudConicalQuadrature(dim - 1, 1, k + 1, -1, +1, &fq));
  } else {
    PetscCall(PetscDTGaussTensorQuadrature(dim, 1, k + 1, -1, +1, &q));
    PetscCall(PetscDTGaussTensorQuadrature(dim - 1, 1, k + 1, -1, +1, &fq));
  }
  /* Create finite element */
  PetscCall(PetscFECreate(comm, fem));
  PetscCall(PetscFESetType(*fem, PETSCFEBASIC));
  PetscCall(PetscFESetNumComponents(*fem, Nc));
  PetscCall(PetscFESetBasisSpace(*fem, P));
  PetscCall(PetscFESetDualSpace(*fem, Q));
  PetscCall(PetscFESetQuadrature(*fem, q));
  PetscCall(PetscFESetFaceQuadrature(*fem, fq));
  if (prefix) {
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, prefix));
    PetscCall(PetscFESetFromOptions(*fem));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*fem, NULL));
  }
  PetscCall(PetscFESetUp(*fem));
  /* Cleanup */
  PetscCall(PetscSpaceDestroy(&P));
  PetscCall(PetscDualSpaceDestroy(&Q));
  PetscCall(PetscQuadratureDestroy(&q));
  PetscCall(PetscQuadratureDestroy(&fq));
  /* Set finite element name */
  PetscCall(PetscSNPrintf(name, sizeof(name), "%s%" PetscInt_FMT, isSimplex ? "P" : "Q", k));
  PetscCall(PetscFESetName(*fem, name));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateGmshFromFile - Create a `DMPLEX` mesh from a Gmsh file

  Input Parameters:
+ comm        - The MPI communicator
. filename    - Name of the Gmsh file
- interpolate - Create faces and edges in the mesh

  Output Parameter:
. dm - The `DM` object representing the mesh

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromFile()`, `DMPlexCreateGmsh()`, `DMPlexCreate()`
@*/
PetscErrorCode DMPlexCreateGmshFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
{
  PetscViewer     viewer;
  PetscMPIInt     rank;
  int             fileType;
  PetscViewerType vtype;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(comm, &rank));

  /* Determine Gmsh file type (ASCII or binary) from file header */
  if (rank == 0) {
    GmshFile gmsh[1];
    char     line[PETSC_MAX_PATH_LEN];
    int      snum;
    float    version;
    int      fileFormat;

    PetscCall(PetscArrayzero(gmsh, 1));
    PetscCall(PetscViewerCreate(PETSC_COMM_SELF, &gmsh->viewer));
    PetscCall(PetscViewerSetType(gmsh->viewer, PETSCVIEWERASCII));
    PetscCall(PetscViewerFileSetMode(gmsh->viewer, FILE_MODE_READ));
    PetscCall(PetscViewerFileSetName(gmsh->viewer, filename));
    /* Read only the first two lines of the Gmsh file */
    PetscCall(GmshReadSection(gmsh, line));
    PetscCall(GmshExpect(gmsh, "$MeshFormat", line));
    PetscCall(GmshReadString(gmsh, line, 2));
    snum       = sscanf(line, "%f %d", &version, &fileType);
    fileFormat = (int)roundf(version * 10);
    PetscCheck(snum == 2, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Unable to parse Gmsh file header: %s", line);
    PetscCheck(fileFormat >= 22, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f must be at least 2.2", (double)version);
    PetscCheck((int)version != 3, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f not supported", (double)version);
    PetscCheck(fileFormat <= 41, PETSC_COMM_SELF, PETSC_ERR_SUP, "Gmsh file version %3.1f must be at most 4.1", (double)version);
    PetscCall(PetscViewerDestroy(&gmsh->viewer));
  }
  PetscCallMPI(MPI_Bcast(&fileType, 1, MPI_INT, 0, comm));
  vtype = (fileType == 0) ? PETSCVIEWERASCII : PETSCVIEWERBINARY;

  /* Create appropriate viewer and build plex */
  PetscCall(PetscViewerCreate(comm, &viewer));
  PetscCall(PetscViewerSetType(viewer, vtype));
  PetscCall(PetscViewerFileSetMode(viewer, FILE_MODE_READ));
  PetscCall(PetscViewerFileSetName(viewer, filename));
  PetscCall(DMPlexCreateGmsh(comm, viewer, interpolate, dm));
  PetscCall(PetscViewerDestroy(&viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateGmsh - Create a `DMPLEX` mesh from a Gmsh file viewer

  Collective

  Input Parameters:
+ comm        - The MPI communicator
. viewer      - The `PetscViewer` associated with a Gmsh file
- interpolate - Create faces and edges in the mesh

  Output Parameter:
. dm - The `DM` object representing the mesh

  Options Database Keys:
+ -dm_plex_gmsh_hybrid        - Force triangular prisms to use tensor order
. -dm_plex_gmsh_periodic      - Read Gmsh periodic section and construct a periodic Plex
. -dm_plex_gmsh_highorder     - Generate high-order coordinates
. -dm_plex_gmsh_project       - Project high-order coordinates to a different space, use the prefix dm_plex_gmsh_project_ to define the space
. -dm_plex_gmsh_use_generic   - Generate generic labels, i.e. Cell Sets, Face Sets, etc.
. -dm_plex_gmsh_use_regions   - Generate labels with region names
. -dm_plex_gmsh_mark_vertices - Add vertices to generated labels
. -dm_plex_gmsh_multiple_tags - Allow multiple tags for default labels
- -dm_plex_gmsh_spacedim <d>  - Embedding space dimension, if different from topological dimension

  Level: beginner

  Notes:
  The Gmsh file format is described in <http://gmsh.info/doc/texinfo/gmsh.html#MSH-file-format>

  By default, the "Cell Sets", "Face Sets", and "Vertex Sets" labels are created, and only insert the first tag on a point. By using `-dm_plex_gmsh_multiple_tags`, all tags can be inserted. Alternatively, `-dm_plex_gmsh_use_regions` creates labels based on the region names from the `PhysicalNames` section, and all tags are used, but you can retain the generic labels using `-dm_plex_gmsh_use_generic`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`
@*/
PetscErrorCode DMPlexCreateGmsh(MPI_Comm comm, PetscViewer viewer, PetscBool interpolate, DM *dm)
{
  GmshMesh    *mesh          = NULL;
  PetscViewer  parentviewer  = NULL;
  PetscBT      periodicVerts = NULL;
  PetscBT     *periodicCells = NULL;
  DM           cdm, cdmCell = NULL;
  PetscSection cs, csCell   = NULL;
  Vec          coordinates, coordinatesCell;
  DMLabel      cellSets = NULL, faceSets = NULL, edgeSets = NULL, vertSets = NULL, marker = NULL, *regionSets;
  PetscInt     dim = 0, coordDim = -1, order = 0, maxHeight = 0;
  PetscInt     numNodes = 0, numElems = 0, numVerts = 0, numCells = 0, vStart, vEnd;
  PetscInt     cell, cone[8], e, n, v, d;
  PetscBool    usegeneric = PETSC_TRUE, useregions = PETSC_FALSE, markvertices = PETSC_FALSE, multipleTags = PETSC_FALSE;
  PetscBool    flg, binary, hybrid = interpolate, periodic = PETSC_TRUE;
  PetscBool    highOrder = PETSC_TRUE, highOrderSet, project = PETSC_FALSE;
  PetscBool    isSimplex = PETSC_FALSE, isHybrid = PETSC_FALSE, hasTetra = PETSC_FALSE;
  PetscMPIInt  rank;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  PetscObjectOptionsBegin((PetscObject)viewer);
  PetscOptionsHeadBegin(PetscOptionsObject, "DMPlex Gmsh options");
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_hybrid", "Force triangular prisms to use tensor order", "DMPlexCreateGmsh", hybrid, &hybrid, NULL));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_periodic", "Read Gmsh periodic section", "DMPlexCreateGmsh", periodic, &periodic, NULL));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_highorder", "Generate high-order coordinates", "DMPlexCreateGmsh", highOrder, &highOrder, &highOrderSet));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_project", "Project high-order coordinates to a different space", "DMPlexCreateGmsh", project, &project, NULL));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_use_regions", "Generate labels with region names", "DMPlexCreateGmsh", useregions, &useregions, NULL));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_use_generic", "Generate generic labels, i.e. Cell Sets, Face Sets, etc", "DMPlexCreateGmsh", usegeneric, &usegeneric, &flg));
  if (!flg && useregions) usegeneric = PETSC_FALSE;
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_mark_vertices", "Add vertices to generated labels", "DMPlexCreateGmsh", markvertices, &markvertices, NULL));
  PetscCall(PetscOptionsBool("-dm_plex_gmsh_multiple_tags", "Allow multiple tags for default labels", "DMPlexCreateGmsh", multipleTags, &multipleTags, NULL));
  PetscCall(PetscOptionsBoundedInt("-dm_plex_gmsh_spacedim", "Embedding space dimension", "DMPlexCreateGmsh", coordDim, &coordDim, NULL, PETSC_DECIDE));
  PetscCall(PetscOptionsBoundedInt("-dm_localize_height", "Localize edges and faces in addition to cells", "", maxHeight, &maxHeight, NULL, 0));
  PetscOptionsHeadEnd();
  PetscOptionsEnd();

  PetscCall(GmshCellInfoSetUp());

  PetscCall(DMCreate(comm, dm));
  PetscCall(DMSetType(*dm, DMPLEX));
  PetscCall(PetscLogEventBegin(DMPLEX_CreateGmsh, *dm, NULL, NULL, NULL));

  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &binary));

  /* Binary viewers read on all ranks, get subviewer to read only in rank 0 */
  if (binary) {
    parentviewer = viewer;
    PetscCall(PetscViewerGetSubViewer(parentviewer, PETSC_COMM_SELF, &viewer));
  }

  if (rank == 0) {
    GmshFile  gmsh[1];
    char      line[PETSC_MAX_PATH_LEN];
    PetscBool match;

    PetscCall(PetscArrayzero(gmsh, 1));
    gmsh->viewer = viewer;
    gmsh->binary = binary;

    PetscCall(GmshMeshCreate(&mesh));

    /* Read mesh format */
    PetscCall(GmshReadSection(gmsh, line));
    PetscCall(GmshExpect(gmsh, "$MeshFormat", line));
    PetscCall(GmshReadMeshFormat(gmsh));
    PetscCall(GmshReadEndSection(gmsh, "$EndMeshFormat", line));

    /* OPTIONAL Read mesh version (Neper only) */
    PetscCall(GmshReadSection(gmsh, line));
    PetscCall(GmshMatch(gmsh, "$MeshVersion", line, &match));
    if (match) {
      PetscCall(GmshExpect(gmsh, "$MeshVersion", line));
      PetscCall(GmshReadMeshVersion(gmsh));
      PetscCall(GmshReadEndSection(gmsh, "$EndMeshVersion", line));
      /* Initial read for entity section */
      PetscCall(GmshReadSection(gmsh, line));
    }

    /* OPTIONAL Read mesh domain (Neper only) */
    PetscCall(GmshMatch(gmsh, "$Domain", line, &match));
    if (match) {
      PetscCall(GmshExpect(gmsh, "$Domain", line));
      PetscCall(GmshReadMeshDomain(gmsh));
      PetscCall(GmshReadEndSection(gmsh, "$EndDomain", line));
      /* Initial read for entity section */
      PetscCall(GmshReadSection(gmsh, line));
    }

    /* OPTIONAL Read physical names */
    PetscCall(GmshMatch(gmsh, "$PhysicalNames", line, &match));
    if (match) {
      PetscCall(GmshExpect(gmsh, "$PhysicalNames", line));
      PetscCall(GmshReadPhysicalNames(gmsh, mesh));
      PetscCall(GmshReadEndSection(gmsh, "$EndPhysicalNames", line));
      /* Initial read for entity section */
      PetscCall(GmshReadSection(gmsh, line));
    }

    /* OPTIONAL Read entities */
    if (gmsh->fileFormat >= 40) {
      PetscCall(GmshMatch(gmsh, "$Entities", line, &match));
      if (match) {
        PetscCall(GmshExpect(gmsh, "$Entities", line));
        PetscCall(GmshReadEntities(gmsh, mesh));
        PetscCall(GmshReadEndSection(gmsh, "$EndEntities", line));
        /* Initial read for nodes section */
        PetscCall(GmshReadSection(gmsh, line));
      }
    }

    /* Read nodes */
    PetscCall(GmshExpect(gmsh, "$Nodes", line));
    PetscCall(GmshReadNodes(gmsh, mesh));
    PetscCall(GmshReadEndSection(gmsh, "$EndNodes", line));

    /* Read elements */
    PetscCall(GmshReadSection(gmsh, line));
    PetscCall(GmshExpect(gmsh, "$Elements", line));
    PetscCall(GmshReadElements(gmsh, mesh));
    PetscCall(GmshReadEndSection(gmsh, "$EndElements", line));

    /* Read periodic section (OPTIONAL) */
    if (periodic) {
      PetscCall(GmshReadSection(gmsh, line));
      PetscCall(GmshMatch(gmsh, "$Periodic", line, &periodic));
    }
    if (periodic) {
      PetscCall(GmshExpect(gmsh, "$Periodic", line));
      PetscCall(GmshReadPeriodic(gmsh, mesh));
      PetscCall(GmshReadEndSection(gmsh, "$EndPeriodic", line));
    }

    PetscCall(PetscFree(gmsh->wbuf));
    PetscCall(PetscFree(gmsh->sbuf));
    PetscCall(PetscFree(gmsh->nbuf));

    dim      = mesh->dim;
    order    = mesh->order;
    numNodes = mesh->numNodes;
    numElems = mesh->numElems;
    numVerts = mesh->numVerts;
    numCells = mesh->numCells;

    {
      GmshElement *elemA = mesh->numCells > 0 ? mesh->elements : NULL;
      GmshElement *elemB = PetscSafePointerPlusOffset(elemA, mesh->numCells - 1);
      int          ptA   = elemA ? GmshCellMap[elemA->cellType].polytope : -1;
      int          ptB   = elemB ? GmshCellMap[elemB->cellType].polytope : -1;
      isSimplex          = (ptA == GMSH_QUA || ptA == GMSH_HEX) ? PETSC_FALSE : PETSC_TRUE;
      isHybrid           = (ptA == ptB) ? PETSC_FALSE : PETSC_TRUE;
      hasTetra           = (ptA == GMSH_TET) ? PETSC_TRUE : PETSC_FALSE;
    }
  }

  if (parentviewer) PetscCall(PetscViewerRestoreSubViewer(parentviewer, PETSC_COMM_SELF, &viewer));

  {
    int buf[6];

    buf[0] = (int)dim;
    buf[1] = (int)order;
    buf[2] = periodic;
    buf[3] = isSimplex;
    buf[4] = isHybrid;
    buf[5] = hasTetra;

    PetscCallMPI(MPI_Bcast(buf, 6, MPI_INT, 0, comm));

    dim       = buf[0];
    order     = buf[1];
    periodic  = buf[2] ? PETSC_TRUE : PETSC_FALSE;
    isSimplex = buf[3] ? PETSC_TRUE : PETSC_FALSE;
    isHybrid  = buf[4] ? PETSC_TRUE : PETSC_FALSE;
    hasTetra  = buf[5] ? PETSC_TRUE : PETSC_FALSE;
  }

  if (!highOrderSet) highOrder = (order > 1) ? PETSC_TRUE : PETSC_FALSE;
  PetscCheck(!highOrder || !isHybrid, comm, PETSC_ERR_SUP, "No support for discretization on hybrid meshes yet");

  /* We do not want this label automatically computed, instead we fill it here */
  PetscCall(DMCreateLabel(*dm, "celltype"));

  /* Allocate the cell-vertex mesh */
  PetscCall(DMPlexSetChart(*dm, 0, numCells + numVerts));
  for (cell = 0; cell < numCells; ++cell) {
    GmshElement   *elem  = mesh->elements + cell;
    DMPolytopeType ctype = DMPolytopeTypeFromGmsh(elem->cellType);
    if (hybrid && hasTetra && ctype == DM_POLYTOPE_TRI_PRISM) ctype = DM_POLYTOPE_TRI_PRISM_TENSOR;
    PetscCall(DMPlexSetConeSize(*dm, cell, elem->numVerts));
    PetscCall(DMPlexSetCellType(*dm, cell, ctype));
  }
  for (v = numCells; v < numCells + numVerts; ++v) PetscCall(DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT));
  PetscCall(DMSetUp(*dm));

  /* Add cell-vertex connections */
  for (cell = 0; cell < numCells; ++cell) {
    GmshElement *elem = mesh->elements + cell;
    for (v = 0; v < elem->numVerts; ++v) {
      const PetscInt nn = elem->nodes[v];
      const PetscInt vv = mesh->vertexMap[nn];
      cone[v]           = numCells + vv;
    }
    PetscCall(DMPlexReorderCell(*dm, cell, cone));
    PetscCall(DMPlexSetCone(*dm, cell, cone));
  }

  PetscCall(DMSetDimension(*dm, dim));
  PetscCall(DMPlexSymmetrize(*dm));
  PetscCall(DMPlexStratify(*dm));
  if (interpolate) {
    DM idm;

    PetscCall(DMPlexInterpolate(*dm, &idm));
    PetscCall(DMDestroy(dm));
    *dm = idm;
  }
  PetscCall(DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd));

  if (rank == 0) {
    const PetscInt Nr = useregions ? mesh->numRegions : 0;

    PetscCall(PetscCalloc1(Nr, &regionSets));
    for (cell = 0, e = 0; e < numElems; ++e) {
      GmshElement *elem = mesh->elements + e;

      /* Create cell sets */
      if (elem->dim == dim && dim > 0) {
        if (elem->numTags > 0) {
          PetscInt Nt = elem->numTags, t, r;

          for (t = 0; t < Nt; ++t) {
            const PetscInt  tag     = elem->tags[t];
            const PetscBool generic = usegeneric && (!t || multipleTags) ? PETSC_TRUE : PETSC_FALSE;

            if (generic) PetscCall(DMSetLabelValue_Fast(*dm, &cellSets, "Cell Sets", cell, tag));
            for (r = 0; r < Nr; ++r) {
              if (mesh->regionDims[r] != dim) continue;
              if (mesh->regionTags[r] == tag) PetscCall(DMSetLabelValue_Fast(*dm, &regionSets[r], mesh->regionNames[r], cell, tag));
            }
          }
        }
        cell++;
      }

      /* Create face sets */
      if (elem->numTags && interpolate && elem->dim == dim - 1) {
        PetscInt        joinSize;
        const PetscInt *join = NULL;
        PetscInt        Nt   = elem->numTags, pdepth;

        /* Find the relevant facet with vertex joins */
        for (v = 0; v < elem->numVerts; ++v) {
          const PetscInt nn = elem->nodes[v];
          const PetscInt vv = mesh->vertexMap[nn];
          cone[v]           = vStart + vv;
        }
        PetscCall(DMPlexGetFullJoin(*dm, elem->numVerts, cone, &joinSize, &join));
        PetscCheck(joinSize == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Could not determine Plex facet for Gmsh element %" PetscInt_FMT " (Plex cell %" PetscInt_FMT ")", elem->id, e);
        PetscCall(DMPlexGetPointDepth(*dm, join[0], &pdepth));
        PetscCheck(pdepth == dim - 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Plex facet %" PetscInt_FMT " for Gmsh element %" PetscInt_FMT " had depth %" PetscInt_FMT " != %" PetscInt_FMT, join[0], elem->id, pdepth, dim - 1);
        for (PetscInt t = 0; t < Nt; ++t) {
          const PetscInt  tag     = elem->tags[t];
          const PetscBool generic = usegeneric && (!t || multipleTags) ? PETSC_TRUE : PETSC_FALSE;

          if (generic) PetscCall(DMSetLabelValue_Fast(*dm, &faceSets, "Face Sets", join[0], tag));
          for (PetscInt r = 0; r < Nr; ++r) {
            if (mesh->regionDims[r] != dim - 1) continue;
            if (mesh->regionTags[r] == tag) PetscCall(DMSetLabelValue_Fast(*dm, &regionSets[r], mesh->regionNames[r], join[0], tag));
          }
        }
        PetscCall(DMPlexRestoreJoin(*dm, elem->numVerts, cone, &joinSize, &join));
      }

      /* Create edge sets */
      if (elem->numTags && interpolate && dim > 2 && elem->dim == 1) {
        PetscInt        joinSize;
        const PetscInt *join = NULL;
        PetscInt        Nt   = elem->numTags, t, r;

        /* Find the relevant edge with vertex joins */
        for (v = 0; v < elem->numVerts; ++v) {
          const PetscInt nn = elem->nodes[v];
          const PetscInt vv = mesh->vertexMap[nn];
          cone[v]           = vStart + vv;
        }
        PetscCall(DMPlexGetJoin(*dm, elem->numVerts, cone, &joinSize, &join));
        PetscCheck(joinSize == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Could not determine Plex edge for Gmsh element %" PetscInt_FMT " (Plex cell %" PetscInt_FMT ")", elem->id, e);
        for (t = 0; t < Nt; ++t) {
          const PetscInt  tag     = elem->tags[t];
          const PetscBool generic = usegeneric && (!t || multipleTags) ? PETSC_TRUE : PETSC_FALSE;

          if (generic) PetscCall(DMSetLabelValue_Fast(*dm, &edgeSets, "Edge Sets", join[0], tag));
          for (r = 0; r < Nr; ++r) {
            if (mesh->regionDims[r] != 1) continue;
            if (mesh->regionTags[r] == tag) PetscCall(DMSetLabelValue_Fast(*dm, &regionSets[r], mesh->regionNames[r], join[0], tag));
          }
        }
        PetscCall(DMPlexRestoreJoin(*dm, elem->numVerts, cone, &joinSize, &join));
      }

      /* Create vertex sets */
      if (elem->numTags && elem->dim == 0 && markvertices) {
        const PetscInt nn  = elem->nodes[0];
        const PetscInt vv  = mesh->vertexMap[nn];
        const PetscInt tag = elem->tags[0];
        PetscInt       r;

        if (vv < 0) continue;
        if (usegeneric) PetscCall(DMSetLabelValue_Fast(*dm, &vertSets, "Vertex Sets", vStart + vv, tag));
        for (r = 0; r < Nr; ++r) {
          if (mesh->regionDims[r] != 0) continue;
          if (mesh->regionTags[r] == tag) PetscCall(DMSetLabelValue_Fast(*dm, &regionSets[r], mesh->regionNames[r], vStart + vv, tag));
        }
      }
    }
    if (markvertices) {
      for (v = 0; v < numNodes; ++v) {
        const PetscInt  vv   = mesh->vertexMap[v];
        const PetscInt *tags = &mesh->nodelist->tag[v * GMSH_MAX_TAGS];
        PetscInt        r, t;

        if (vv < 0) continue;
        for (t = 0; t < GMSH_MAX_TAGS; ++t) {
          const PetscInt  tag     = tags[t];
          const PetscBool generic = usegeneric && (!t || multipleTags) ? PETSC_TRUE : PETSC_FALSE;

          if (tag == -1) continue;
          if (generic) PetscCall(DMSetLabelValue_Fast(*dm, &vertSets, "Vertex Sets", vStart + vv, tag));
          for (r = 0; r < Nr; ++r) {
            if (mesh->regionTags[r] == tag) PetscCall(DMSetLabelValue_Fast(*dm, &regionSets[r], mesh->regionNames[r], vStart + vv, tag));
          }
        }
      }
    }
    PetscCall(PetscFree(regionSets));
  }

  { /* Create Cell/Face/Edge/Vertex Sets labels at all processes */
    enum {
      n = 5
    };
    PetscBool flag[n];

    flag[0] = cellSets ? PETSC_TRUE : PETSC_FALSE;
    flag[1] = faceSets ? PETSC_TRUE : PETSC_FALSE;
    flag[2] = edgeSets ? PETSC_TRUE : PETSC_FALSE;
    flag[3] = vertSets ? PETSC_TRUE : PETSC_FALSE;
    flag[4] = marker ? PETSC_TRUE : PETSC_FALSE;
    PetscCallMPI(MPI_Bcast(flag, n, MPIU_BOOL, 0, comm));
    if (flag[0]) PetscCall(DMCreateLabel(*dm, "Cell Sets"));
    if (flag[1]) PetscCall(DMCreateLabel(*dm, "Face Sets"));
    if (flag[2]) PetscCall(DMCreateLabel(*dm, "Edge Sets"));
    if (flag[3]) PetscCall(DMCreateLabel(*dm, "Vertex Sets"));
    if (flag[4]) PetscCall(DMCreateLabel(*dm, "marker"));
  }

  if (periodic) {
    PetscCall(PetscBTCreate(numVerts, &periodicVerts));
    for (n = 0; n < numNodes; ++n) {
      if (mesh->vertexMap[n] >= 0) {
        if (PetscUnlikely(mesh->periodMap[n] != n)) {
          PetscInt m = mesh->periodMap[n];
          PetscCall(PetscBTSet(periodicVerts, mesh->vertexMap[n]));
          PetscCall(PetscBTSet(periodicVerts, mesh->vertexMap[m]));
        }
      }
    }
    PetscCall(DMGetCoordinateDM(*dm, &cdm));
    PetscCall(PetscMalloc1(maxHeight + 1, &periodicCells));
    for (PetscInt h = 0; h <= maxHeight; ++h) {
      PetscInt pStart, pEnd;

      PetscCall(DMPlexGetHeightStratum(*dm, h, &pStart, &pEnd));
      PetscCall(PetscBTCreate(pEnd - pStart, &periodicCells[h]));
      for (PetscInt p = pStart; p < pEnd; ++p) {
        PetscInt *closure = NULL;
        PetscInt  Ncl;

        PetscCall(DMPlexGetTransitiveClosure(*dm, p, PETSC_TRUE, &Ncl, &closure));
        for (PetscInt cl = 0; cl < Ncl * 2; cl += 2) {
          if (closure[cl] >= vStart && closure[cl] < vEnd) {
            if (PetscUnlikely(PetscBTLookup(periodicVerts, closure[cl] - vStart))) {
              PetscCall(PetscBTSet(periodicCells[h], p - pStart));
              break;
            }
          }
        }
        PetscCall(DMPlexRestoreTransitiveClosure(*dm, p, PETSC_TRUE, &Ncl, &closure));
      }
    }
  }

  /* Setup coordinate DM */
  if (coordDim < 0) coordDim = dim;
  PetscCall(DMSetCoordinateDim(*dm, coordDim));
  PetscCall(DMGetCoordinateDM(*dm, &cdm));
  if (highOrder) {
    PetscFE         fe;
    PetscBool       continuity = periodic ? PETSC_FALSE : PETSC_TRUE;
    PetscDTNodeType nodeType   = PETSCDTNODES_EQUISPACED;

    if (isSimplex) continuity = PETSC_FALSE; /* XXX FIXME Requires DMPlexSetClosurePermutationLexicographic() */

    PetscCall(GmshCreateFE(comm, NULL, isSimplex, continuity, nodeType, dim, coordDim, order, &fe));
    PetscCall(PetscFEViewFromOptions(fe, NULL, "-dm_plex_gmsh_fe_view"));
    PetscCall(DMSetField(cdm, 0, NULL, (PetscObject)fe));
    PetscCall(PetscFEDestroy(&fe));
    PetscCall(DMCreateDS(cdm));
  }
  if (periodic) {
    PetscCall(DMClone(cdm, &cdmCell));
    PetscCall(DMSetCellCoordinateDM(*dm, cdmCell));
  }

  /* Create coordinates */
  if (highOrder) {
    PetscInt     maxDof = GmshNumNodes_HEX(order) * coordDim;
    double      *coords = mesh ? mesh->nodelist->xyz : NULL;
    PetscSection section;
    PetscScalar *cellCoords;

    PetscCall(DMSetLocalSection(cdm, NULL));
    PetscCall(DMGetLocalSection(cdm, &cs));
    PetscCall(PetscSectionClone(cs, &section));
    PetscCall(DMPlexSetClosurePermutationTensor(cdm, 0, section)); /* XXX Implement DMPlexSetClosurePermutationLexicographic() */

    PetscCall(DMCreateLocalVector(cdm, &coordinates));
    PetscCall(PetscMalloc1(maxDof, &cellCoords));
    for (cell = 0; cell < numCells; ++cell) {
      GmshElement *elem     = mesh->elements + cell;
      const int   *lexorder = GmshCellMap[elem->cellType].lexorder();
      int          s        = 0;
      for (n = 0; n < elem->numNodes; ++n) {
        while (lexorder[n + s] < 0) ++s;
        const PetscInt node = elem->nodes[lexorder[n + s]];
        for (d = 0; d < coordDim; ++d) cellCoords[(n + s) * coordDim + d] = (PetscReal)coords[node * 3 + d];
      }
      if (s) {
        /* For the coordinate mapping we weight vertices by -1/4 and edges by 1/2, which we get from Q_2 interpolation */
        PetscReal quaCenterWeights[9] = {-0.25, 0.5, -0.25, 0.5, 0.0, 0.5, -0.25, 0.5, -0.25};
        /* For the coordinate mapping we weight vertices by -1/4 and edges by 1/2, which we get from Q_2 interpolation */
        PetscReal   hexBottomWeights[27] = {-0.25, 0.5, -0.25, 0.5, 0.0, 0.5, -0.25, 0.5, -0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
        PetscReal   hexFrontWeights[27]  = {-0.25, 0.5, -0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.25, 0.5, -0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
        PetscReal   hexLeftWeights[27]   = {-0.25, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25, 0.0, 0.0};
        PetscReal   hexRightWeights[27]  = {0.0, 0.0, -0.25, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25, 0.0, 0.0, 0.5, 0.0, 0.0, -0.25};
        PetscReal   hexBackWeights[27]   = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.25, 0.5, -0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.25, 0.5, -0.25};
        PetscReal   hexTopWeights[27]    = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.25, 0.5, -0.25, 0.5, 0.0, 0.5, -0.25, 0.5, -0.25};
        PetscReal   hexCenterWeights[27] = {-0.25, 0.25, -0.25, 0.25, 0.0, 0.25, -0.25, 0.25, -0.25, 0.25, 0.0, 0.25, 0.0, 0.0, 0.0, 0.25, 0.0, 0.25, -0.25, 0.25, -0.25, 0.25, 0.0, 0.25, -0.25, 0.25, -0.25};
        PetscReal  *sdWeights2[9]        = {NULL, NULL, NULL, NULL, quaCenterWeights, NULL, NULL, NULL, NULL};
        PetscReal  *sdWeights3[27]       = {NULL, NULL, NULL, NULL, hexBottomWeights, NULL, NULL, NULL, NULL, NULL, hexFrontWeights, NULL, hexLeftWeights, hexCenterWeights, hexRightWeights, NULL, hexBackWeights, NULL,
                                            NULL, NULL, NULL, NULL, hexTopWeights,    NULL, NULL, NULL, NULL};
        PetscReal **sdWeights[4]         = {NULL, NULL, sdWeights2, sdWeights3};

        /* Missing entries in serendipity cell, only works for 8-node quad and 20-node hex */
        for (n = 0; n < elem->numNodes + s; ++n) {
          if (lexorder[n] >= 0) continue;
          for (d = 0; d < coordDim; ++d) cellCoords[n * coordDim + d] = 0.0;
          for (int bn = 0; bn < elem->numNodes + s; ++bn) {
            if (lexorder[bn] < 0) continue;
            const PetscReal *weights = sdWeights[coordDim][n];
            const PetscInt   bnode   = elem->nodes[lexorder[bn]];
            for (d = 0; d < coordDim; ++d) cellCoords[n * coordDim + d] += weights[bn] * (PetscReal)coords[bnode * 3 + d];
          }
        }
      }
      PetscCall(DMPlexVecSetClosure(cdm, section, coordinates, cell, cellCoords, INSERT_VALUES));
    }
    PetscCall(PetscSectionDestroy(&section));
    PetscCall(PetscFree(cellCoords));
  } else {
    PetscInt    *nodeMap;
    double      *coords = mesh ? mesh->nodelist->xyz : NULL;
    PetscScalar *pointCoords;

    PetscCall(DMGetCoordinateSection(*dm, &cs));
    PetscCall(PetscSectionSetNumFields(cs, 1));
    PetscCall(PetscSectionSetFieldComponents(cs, 0, coordDim));
    PetscCall(PetscSectionSetChart(cs, numCells, numCells + numVerts));
    for (v = numCells; v < numCells + numVerts; ++v) {
      PetscCall(PetscSectionSetDof(cs, v, coordDim));
      PetscCall(PetscSectionSetFieldDof(cs, v, 0, coordDim));
    }
    PetscCall(PetscSectionSetUp(cs));

    /* We need to localize coordinates on cells */
    if (periodic) {
      PetscInt newStart = PETSC_INT_MAX, newEnd = -1, pStart, pEnd;

      PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)cdmCell), &csCell));
      PetscCall(PetscSectionSetNumFields(csCell, 1));
      PetscCall(PetscSectionSetFieldComponents(csCell, 0, coordDim));
      for (PetscInt h = 0; h <= maxHeight; h++) {
        PetscCall(DMPlexGetHeightStratum(cdmCell, h, &pStart, &pEnd));
        newStart = PetscMin(newStart, pStart);
        newEnd   = PetscMax(newEnd, pEnd);
      }
      PetscCall(PetscSectionSetChart(csCell, newStart, newEnd));
      for (PetscInt h = 0; h <= maxHeight; h++) {
        PetscCall(DMPlexGetHeightStratum(cdmCell, h, &pStart, &pEnd));
        for (PetscInt p = pStart; p < pEnd; ++p) {
          PetscInt *closure = NULL;
          PetscInt  Ncl, Nv = 0;

          if (PetscUnlikely(PetscBTLookup(periodicCells[h], p - pStart))) {
            PetscCall(DMPlexGetTransitiveClosure(*dm, p, PETSC_TRUE, &Ncl, &closure));
            for (PetscInt cl = 0; cl < Ncl * 2; cl += 2) {
              if (closure[cl] >= vStart && closure[cl] < vEnd) ++Nv;
            }
            PetscCall(DMPlexRestoreTransitiveClosure(*dm, p, PETSC_TRUE, &Ncl, &closure));
            PetscCall(PetscSectionSetDof(csCell, p, Nv * coordDim));
            PetscCall(PetscSectionSetFieldDof(csCell, p, 0, Nv * coordDim));
          }
        }
      }
      PetscCall(PetscSectionSetUp(csCell));
      PetscCall(DMSetCellCoordinateSection(*dm, PETSC_DETERMINE, csCell));
    }

    PetscCall(DMCreateLocalVector(cdm, &coordinates));
    PetscCall(VecGetArray(coordinates, &pointCoords));
    PetscCall(PetscMalloc1(numVerts, &nodeMap));
    for (n = 0; n < numNodes; n++)
      if (mesh->vertexMap[n] >= 0) nodeMap[mesh->vertexMap[n]] = n;
    for (v = 0; v < numVerts; ++v) {
      PetscInt off, node = nodeMap[v];

      PetscCall(PetscSectionGetOffset(cs, numCells + v, &off));
      for (d = 0; d < coordDim; ++d) pointCoords[off + d] = (PetscReal)coords[node * 3 + d];
    }
    PetscCall(VecRestoreArray(coordinates, &pointCoords));

    if (periodic) {
      PetscInt cStart, cEnd;

      PetscCall(DMPlexGetHeightStratum(cdmCell, 0, &cStart, &cEnd));
      PetscCall(DMCreateLocalVector(cdmCell, &coordinatesCell));
      PetscCall(VecGetArray(coordinatesCell, &pointCoords));
      for (PetscInt c = cStart; c < cEnd; ++c) {
        GmshElement *elem    = mesh->elements + c - cStart;
        PetscInt    *closure = NULL;
        PetscInt     verts[8];
        PetscInt     Ncl, Nv = 0;

        for (PetscInt v = 0; v < elem->numVerts; ++v) cone[v] = elem->nodes[v];
        PetscCall(DMPlexReorderCell(cdmCell, c, cone));
        PetscCall(DMPlexGetTransitiveClosure(cdmCell, c, PETSC_TRUE, &Ncl, &closure));
        for (PetscInt cl = 0; cl < Ncl * 2; cl += 2) {
          if (closure[cl] >= vStart && closure[cl] < vEnd) verts[Nv++] = closure[cl];
        }
        PetscCheck(Nv == elem->numVerts, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Number of vertices %" PetscInt_FMT " in closure does not match number of vertices %" PetscInt_FMT " in Gmsh cell", Nv, elem->numVerts);
        for (PetscInt cl = 0; cl < Ncl * 2; cl += 2) {
          const PetscInt point = closure[cl];
          PetscInt       hStart, h;

          PetscCall(DMPlexGetPointHeight(cdmCell, point, &h));
          if (h > maxHeight) continue;
          PetscCall(DMPlexGetHeightStratum(cdmCell, h, &hStart, NULL));
          if (PetscUnlikely(PetscBTLookup(periodicCells[h], point - hStart))) {
            PetscInt *pclosure = NULL;
            PetscInt  Npcl, off, v;

            PetscCall(PetscSectionGetOffset(csCell, point, &off));
            PetscCall(DMPlexGetTransitiveClosure(cdmCell, point, PETSC_TRUE, &Npcl, &pclosure));
            for (PetscInt pcl = 0; pcl < Npcl * 2; pcl += 2) {
              if (pclosure[pcl] >= vStart && pclosure[pcl] < vEnd) {
                for (v = 0; v < Nv; ++v)
                  if (verts[v] == pclosure[pcl]) break;
                PetscCheck(v < Nv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not find vertex %" PetscInt_FMT " in closure of cell %" PetscInt_FMT, pclosure[pcl], c);
                for (PetscInt d = 0; d < coordDim; ++d) pointCoords[off++] = (PetscReal)coords[cone[v] * 3 + d];
                ++v;
              }
            }
            PetscCall(DMPlexRestoreTransitiveClosure(cdmCell, point, PETSC_TRUE, &Npcl, &pclosure));
          }
        }
        PetscCall(DMPlexRestoreTransitiveClosure(cdmCell, c, PETSC_TRUE, &Ncl, &closure));
      }
      PetscCall(VecSetBlockSize(coordinatesCell, coordDim));
      PetscCall(VecRestoreArray(coordinatesCell, &pointCoords));
      PetscCall(DMSetCellCoordinatesLocal(*dm, coordinatesCell));
      PetscCall(VecDestroy(&coordinatesCell));
    }
    PetscCall(PetscFree(nodeMap));
    PetscCall(PetscSectionDestroy(&csCell));
    PetscCall(DMDestroy(&cdmCell));
  }

  PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
  PetscCall(VecSetBlockSize(coordinates, coordDim));
  PetscCall(DMSetCoordinatesLocal(*dm, coordinates));
  PetscCall(VecDestroy(&coordinates));

  PetscCall(GmshMeshDestroy(&mesh));
  PetscCall(PetscBTDestroy(&periodicVerts));
  if (periodic) {
    for (PetscInt h = 0; h <= maxHeight; ++h) PetscCall(PetscBTDestroy(periodicCells + h));
    PetscCall(PetscFree(periodicCells));
  }

  if (highOrder && project) {
    PetscFE         fe;
    const char      prefix[]   = "dm_plex_gmsh_project_";
    PetscBool       continuity = periodic ? PETSC_FALSE : PETSC_TRUE;
    PetscDTNodeType nodeType   = PETSCDTNODES_GAUSSJACOBI;

    if (isSimplex) continuity = PETSC_FALSE; /* XXX FIXME Requires DMPlexSetClosurePermutationLexicographic() */
    PetscCall(GmshCreateFE(comm, prefix, isSimplex, continuity, nodeType, dim, coordDim, order, &fe));
    PetscCall(PetscFEViewFromOptions(fe, NULL, "-dm_plex_gmsh_project_fe_view"));
    PetscCall(DMSetCoordinateDisc(*dm, fe, PETSC_TRUE));
    PetscCall(PetscFEDestroy(&fe));
  }

  PetscCall(PetscLogEventEnd(DMPLEX_CreateGmsh, *dm, NULL, NULL, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}