PolygonConcentricCircleMeshGeneratorBase.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#include "PolygonConcentricCircleMeshGeneratorBase.h"
#include "libmesh/mesh_smoother_laplace.h"
#include "MooseUtils.h"
#include "PolygonalMeshGenerationUtils.h"
#include "MooseMeshUtils.h"
 
#include "libmesh/parsed_function.h"
#include "libmesh/poly2tri_triangulator.h"
 
#include <cmath>
 
InputParameters
PolygonConcentricCircleMeshGeneratorBase::validParams()
{
  InputParameters params = ConcentricCircleGeneratorBase::validParams();
  params.addRequiredRangeCheckedParam<std::vector<unsigned int>>(
      "num_sectors_per_side",
      "num_sectors_per_side>0",
      "Number of azimuthal sectors per polygon side (rotating counterclockwise from top right "
      "face).");
  params.addRangeCheckedParam<unsigned int>(
      "background_intervals",
      1,
      "background_intervals>0",
      "Number of radial meshing intervals in background region (area "
      "between rings and ducts) excluding the background's boundary layers.");
  params.addRangeCheckedParam<Real>(
      "background_radial_bias",
      1.0,
      "background_radial_bias>0",
      "Value used to create biasing in radial meshing for background region.");
  params.addRangeCheckedParam<Real>(
      "background_inner_boundary_layer_width",
      0.0,
      "background_inner_boundary_layer_width>=0",
      "Width of background region that is assigned to be the inner boundary layer.");
  params.addRangeCheckedParam<unsigned int>(
      "background_inner_boundary_layer_intervals",
      1,
      "background_inner_boundary_layer_intervals>0",
      "Number of radial intervals of the background inner boundary layer");
  params.addRangeCheckedParam<Real>(
      "background_inner_boundary_layer_bias",
      1.0,
      "background_inner_boundary_layer_bias>0",
      "Growth factor used for mesh biasing of the background inner boundary layer.");
  params.addRangeCheckedParam<Real>(
      "background_outer_boundary_layer_width",
      0.0,
      "background_outer_boundary_layer_width>=0",
      "Width of background region that is assigned to be the outer boundary layer.");
  params.addRangeCheckedParam<unsigned int>(
      "background_outer_boundary_layer_intervals",
      1,
      "background_outer_boundary_layer_intervals>0",
      "Number of radial intervals of the background outer boundary layer");
  params.addRangeCheckedParam<Real>(
      "background_outer_boundary_layer_bias",
      1.0,
      "background_outer_boundary_layer_bias>0",
      "Growth factor used for mesh biasing of the background outer boundary layer.");
  params.addParam<std::vector<subdomain_id_type>>(
      "background_block_ids", "Optional customized block id for the background block.");
  params.addParam<std::vector<SubdomainName>>(
      "background_block_names", "Optional customized block names for the background block.");
  params.addParam<std::vector<Real>>(
      "duct_sizes", "Distance(s) from polygon center to duct(s) inner boundaries.");
  MooseEnum duct_sizes_style("apothem radius", "radius");
  params.addParam<MooseEnum>(
      "duct_sizes_style",
      duct_sizes_style,
      "Style in which polygon center to duct inner boundary distance is "
      "given (apothem = center to face, radius = center to vertex). Options: " +
          duct_sizes_style.getRawNames());
  params.addRangeCheckedParam<std::vector<unsigned int>>(
      "duct_intervals",
      "duct_intervals>0",
      "Number of meshing intervals in each enclosing duct excluding duct boundary layers.");
  params.addRangeCheckedParam<std::vector<Real>>(
      "duct_radial_biases",
      "duct_radial_biases>0",
      "Values used to create biasing in radial meshing for duct regions.");
  params.addRangeCheckedParam<std::vector<Real>>(
      "duct_inner_boundary_layer_widths",
      "duct_inner_boundary_layer_widths>=0",
      "Widths of duct regions that are assigned to be the inner boundary layers.");
  params.addParam<std::vector<unsigned int>>(
      "duct_inner_boundary_layer_intervals",
      "Number of radial intervals of the duct inner boundary layers");
  params.addRangeCheckedParam<std::vector<Real>>(
      "duct_inner_boundary_layer_biases",
      "duct_inner_boundary_layer_biases>0",
      "Growth factors used for mesh biasing of the duct inner boundary layers.");
  params.addRangeCheckedParam<std::vector<Real>>(
      "duct_outer_boundary_layer_widths",
      "duct_outer_boundary_layer_widths>=0",
      "Widths of duct regions that are assigned to be the outer boundary layers.");
  params.addParam<std::vector<unsigned int>>(
      "duct_outer_boundary_layer_intervals",
      "Number of radial intervals of the duct outer boundary layers");
  params.addRangeCheckedParam<std::vector<Real>>(
      "duct_outer_boundary_layer_biases",
      "duct_outer_boundary_layer_biases>0",
      "Growth factors used for mesh biasing of the duct outer boundary layers.");
  params.addParam<std::vector<subdomain_id_type>>(
      "duct_block_ids", "Optional customized block ids for each duct geometry block.");
  params.addParam<std::vector<SubdomainName>>(
      "duct_block_names", "Optional customized block names for each duct geometry block.");
  params.addParam<bool>("uniform_mesh_on_sides",
                        false,
                        "Whether the side elements are reorganized to have a uniform size.");
  params.addParam<unsigned int>("smoothing_max_it",
                                0,
                                "Number of Laplacian smoothing iterations. This number is "
                                "disregarded when duct_sizes is present.");
  params.addParam<bool>(
      "flat_side_up",
      false,
      "Whether to rotate the generated polygon mesh to ensure that one flat side faces up.");
 
  params.addParam<bool>(
      "quad_center_elements", false, "Whether the center elements are quad or triangular.");
  params.addRangeCheckedParam<Real>(
      "center_quad_factor",
      "center_quad_factor>0&center_quad_factor<1",
      "A fractional radius factor used to determine the radial positions of transition nodes in "
      "the center region meshed by quad elements.");
  params.addParam<bool>("replace_inner_ring_with_delaunay_mesh",
                        false,
                        "True to replace the inner ring mesh with a Delaunay unstructured mesh");
  params.addParam<std::string>(
      "inner_ring_desired_area",
      std::string(),
      "Desired area as a function of x,y; omit to use the default constant area (square of the "
      "smallest side length on the ring circle)");
 
  params.addParamNamesToGroup(
      "background_block_ids background_block_names duct_block_ids duct_block_names",
      "Customized Subdomain/Boundary");
  params.addParamNamesToGroup("num_sectors_per_side background_intervals duct_intervals "
                              "uniform_mesh_on_sides",
                              "General Mesh Density");
  params.addParamNamesToGroup(
      "ring_radial_biases ring_inner_boundary_layer_biases ring_inner_boundary_layer_widths "
      "ring_inner_boundary_layer_intervals ring_outer_boundary_layer_biases "
      "ring_outer_boundary_layer_widths ring_outer_boundary_layer_intervals",
      "Mesh Boundary Layers and Biasing Options");
  params.addParamNamesToGroup("quad_center_elements center_quad_factor "
                              "replace_inner_ring_with_delaunay_mesh inner_ring_desired_area ",
                              "Inner ring");
 
  addRingAndSectorIDParams(params);
  params.addClassDescription("This PolygonConcentricCircleMeshGeneratorBase object is a base class "
                             "to be inherited for polygon mesh generators.");
 
  return params;
}
 
PolygonConcentricCircleMeshGeneratorBase::PolygonConcentricCircleMeshGeneratorBase(
    const InputParameters & parameters)
  : ConcentricCircleGeneratorBase(parameters),
    _num_sides(isParamValid("num_sides")
                   ? getParam<unsigned int>("num_sides")
                   : (isParamValid("hexagon_size") ? (unsigned int)HEXAGON_NUM_SIDES
                                                   : (unsigned int)SQUARE_NUM_SIDES)),
    _duct_sizes_style(getParam<MooseEnum>("duct_sizes_style").template getEnum<PolygonSizeStyle>()),
    _duct_sizes(isParamValid("duct_sizes") ? getParam<std::vector<Real>>("duct_sizes")
                                           : std::vector<Real>()),
    _duct_intervals(isParamValid("duct_intervals")
                        ? getParam<std::vector<unsigned int>>("duct_intervals")
                        : std::vector<unsigned int>()),
    _duct_radial_biases(isParamValid("duct_radial_biases")
                            ? getParam<std::vector<Real>>("duct_radial_biases")
                            : std::vector<Real>(_duct_intervals.size(), 1.0)),
    _duct_inner_boundary_layer_params(
        {isParamValid("duct_inner_boundary_layer_widths")
             ? getParam<std::vector<Real>>("duct_inner_boundary_layer_widths")
             : std::vector<Real>(_duct_intervals.size(), 0.0),
         std::vector<Real>(),
         isParamValid("duct_inner_boundary_layer_intervals")
             ? getParam<std::vector<unsigned int>>("duct_inner_boundary_layer_intervals")
             : std::vector<unsigned int>(_duct_intervals.size(), 0),
         isParamValid("duct_inner_boundary_layer_biases")
             ? getParam<std::vector<Real>>("duct_inner_boundary_layer_biases")
             : std::vector<Real>(_duct_intervals.size(), 0.0)}),
    _duct_outer_boundary_layer_params(
        {isParamValid("duct_outer_boundary_layer_widths")
             ? getParam<std::vector<Real>>("duct_outer_boundary_layer_widths")
             : std::vector<Real>(_duct_intervals.size(), 0.0),
         std::vector<Real>(),
         isParamValid("duct_outer_boundary_layer_intervals")
             ? getParam<std::vector<unsigned int>>("duct_outer_boundary_layer_intervals")
             : std::vector<unsigned int>(_duct_intervals.size(), 0),
         isParamValid("duct_outer_boundary_layer_biases")
             ? getParam<std::vector<Real>>("duct_outer_boundary_layer_biases")
             : std::vector<Real>(_duct_intervals.size(), 0.0)}),
    _duct_block_ids(isParamValid("duct_block_ids")
                        ? getParam<std::vector<subdomain_id_type>>("duct_block_ids")
                        : std::vector<subdomain_id_type>()),
    _duct_block_names(isParamValid("duct_block_names")
                          ? getParam<std::vector<SubdomainName>>("duct_block_names")
                          : std::vector<SubdomainName>()),
    _has_rings(isParamValid("ring_radii")),
    _has_ducts(isParamValid("duct_sizes")),
    _polygon_size_style(
        isParamValid("polygon_size_style")
            ? getParam<MooseEnum>("polygon_size_style").template getEnum<PolygonSizeStyle>()
            : (isParamValid("hexagon_size_style")
                   ? getParam<MooseEnum>("hexagon_size_style").template getEnum<PolygonSizeStyle>()
                   : getParam<MooseEnum>("square_size_style")
                         .template getEnum<PolygonSizeStyle>())),
    _polygon_size(isParamValid("polygon_size")
                      ? getParam<Real>("polygon_size")
                      : (isParamValid("hexagon_size") ? getParam<Real>("hexagon_size")
                                                      : (getParam<Real>("square_size") /
                                                         2.0))), // square size is twice as apothem
    _num_sectors_per_side(getParam<std::vector<unsigned int>>("num_sectors_per_side")),
    _background_intervals(getParam<unsigned int>("background_intervals")),
    // background is usually a single block; however, when there are no rings, background has two
    // blocks.
    _background_radial_bias(getParam<Real>("background_radial_bias")),
    _background_inner_boundary_layer_params(
        {getParam<Real>("background_inner_boundary_layer_width"),
         0.0,
         getParam<Real>("background_inner_boundary_layer_width") > 0.0
             ? getParam<unsigned int>("background_inner_boundary_layer_intervals")
             : 0,
         getParam<Real>("background_inner_boundary_layer_bias")}),
    _background_outer_boundary_layer_params(
        {getParam<Real>("background_outer_boundary_layer_width"),
         0.0,
         getParam<Real>("background_outer_boundary_layer_width") > 0.0
             ? getParam<unsigned int>("background_outer_boundary_layer_intervals")
             : 0,
         getParam<Real>("background_outer_boundary_layer_bias")}),
    _background_block_ids(isParamValid("background_block_ids")
                              ? getParam<std::vector<subdomain_id_type>>("background_block_ids")
                              : std::vector<subdomain_id_type>()),
    _background_block_names(isParamValid("background_block_names")
                                ? getParam<std::vector<SubdomainName>>("background_block_names")
                                : std::vector<SubdomainName>()),
    _uniform_mesh_on_sides(getParam<bool>("uniform_mesh_on_sides")),
    _quad_center_elements(getParam<bool>("quad_center_elements")),
    _center_quad_factor(isParamValid("center_quad_factor") ? getParam<Real>("center_quad_factor")
                                                           : 0.0),
    _smoothing_max_it(getParam<unsigned int>("smoothing_max_it")),
    _sides_to_adapt(isParamValid("sides_to_adapt")
                        ? getParam<std::vector<unsigned int>>("sides_to_adapt")
                        : std::vector<unsigned int>()),
    _node_id_background_meta(declareMeshProperty<dof_id_type>("node_id_background_meta", 0)),
    _is_control_drum_meta(declareMeshProperty<bool>("is_control_drum_meta", false))
{
  declareMeshProperty<bool>("flat_side_up", getParam<bool>("flat_side_up"));
  declareMeshProperty<unsigned int>("background_intervals_meta", 0);
  declareMeshProperty<Real>("pattern_pitch_meta", 0.0);
  declareMeshProperty<std::vector<Real>>("azimuthal_angle_meta", std::vector<Real>());
  declareMeshProperty<Real>("max_radius_meta", 0.0);
 
  const unsigned short tri_order = _tri_elem_type == TRI_ELEM_TYPE::TRI3 ? 1 : 2;
  const unsigned short quad_order = _quad_elem_type == QUAD_ELEM_TYPE::QUAD4 ? 1 : 2;
  // 1. If the central elements are quad, then no triangular elements are generated;
  // 2. If the generated mesh has only one radial layer of triangular elements, then no
  // quad elements are generated; (For PCCMG, that layer must be background)
  // 3. Otherwise, both types of elements are generated.
  _order = quad_order;
  if (_quad_center_elements)
  {
    if (tri_order != quad_order)
      _tri_elem_type = quad_order == 1 ? TRI_ELEM_TYPE::TRI3 : TRI_ELEM_TYPE::TRI6;
  }
  else if (_ring_radii.empty() && _background_intervals == 1 &&
           _background_inner_boundary_layer_params.intervals == 0 &&
           _background_outer_boundary_layer_params.intervals == 0 && _duct_sizes.empty())
  {
    _order = tri_order;
    if (tri_order != quad_order)
      _quad_elem_type = tri_order == 1 ? QUAD_ELEM_TYPE::QUAD4 : QUAD_ELEM_TYPE::QUAD9;
  }
  else if (tri_order != quad_order)
    paramError("tri_element_type",
               "the element types of triangular and quadrilateral elements must be compatible if "
               "both types of elements are generated.");
 
  // This error message is only reserved for future derived classes. Neither of the current derived
  // classes will trigger this error.
  if (!_sides_to_adapt.empty() && _num_sides != HEXAGON_NUM_SIDES && _num_sides != SQUARE_NUM_SIDES)
    paramError("sides_to_adapt", "If provided, the generated mesh must be a hexagon or a square.");
  _pitch = 2.0 * (_polygon_size_style == PolygonSizeStyle::apothem
                      ? _polygon_size
                      : _polygon_size * std::cos(M_PI / Real(_num_sides)));
  declareMeshProperty<Real>("pitch_meta", _pitch);
  if (_inward_interface_boundary_names.size() > 0 &&
      _inward_interface_boundary_names.size() != _duct_sizes.size() + _ring_radii.size())
    paramError("inward_interface_boundary_names",
               "If provided, the length of this parameter must be identical to the total number of "
               "interfaces.");
  if (_outward_interface_boundary_names.size() > 0 &&
      _outward_interface_boundary_names.size() != _duct_sizes.size() + _ring_radii.size())
    paramError("outward_interface_boundary_names",
               "If provided, the length of this parameter must be identical to the total number of "
               "interfaces.");
  const unsigned int num_total_background_layers =
      _background_intervals + _background_inner_boundary_layer_params.intervals +
      _background_outer_boundary_layer_params.intervals;
  if ((_has_rings || num_total_background_layers == 1) && _background_block_ids.size() > 1)
    paramError(
        "background_block_ids",
        "This parameter must be either unset or have a unity length when ring_radii is "
        "provided or the number of background intervals (including boundary layers) is unity.");
  if ((_has_rings || num_total_background_layers == 1) && _background_block_names.size() > 1)
    paramError(
        "background_block_names",
        "This parameter must be either unset or have a unity length when ring_radii is "
        "provided or the number of background intervals (including boundary layers) is unity.");
  if (!_has_rings && num_total_background_layers > 1 && _quad_center_elements &&
      _background_block_ids.size() == 1)
    _background_block_ids.insert(_background_block_ids.begin(), _background_block_ids.front());
  if ((!_has_rings && _background_intervals > 1) &&
      (!_background_block_ids.empty() && _background_block_ids.size() != 2))
    paramError("background_block_ids",
               "This parameter must be either unset or have a length of two when ring_radii is not "
               "provided and background intervals (including boundary layers) is not unity. It can "
               "optionally to have a unity length if `quad_center_elements` is enabled.");
  if (!_has_rings && num_total_background_layers > 1 && _quad_center_elements &&
      _background_block_names.size() == 1)
    _background_block_names.insert(_background_block_names.begin(),
                                   _background_block_names.front());
  if ((!_has_rings && _background_intervals > 1) &&
      (!_background_block_names.empty() && _background_block_names.size() != 2))
    paramError("background_block_names",
               "This parameter must be either unset or have a length of two when ring_radii is not "
               "provided and background intervals (including boundary layers) is not unity. It can "
               "optionally have a unity length if `quad_center_elements` is enabled.");
  if (_num_sectors_per_side.size() != _num_sides)
    paramError("num_sectors_per_side",
               "This parameter must have a length that is consistent with num_sides.");
  for (auto it = _num_sectors_per_side.begin(); it != _num_sectors_per_side.end(); ++it)
    if (*it % 2 == 1)
      paramError("num_sectors_per_side", "This parameter must be even.");
  declareMeshProperty("num_sectors_per_side_meta", _num_sectors_per_side);
 
  if (!getParam<bool>("replace_inner_ring_with_delaunay_mesh") &&
      isParamSetByUser("inner_ring_desired_area"))
    paramError(
        "inner_ring_desired_area",
        "This parameter should be set only when 'replace_inner_ring_with_delaunay_mesh=true'");
 
  if (_has_rings)
  {
    const unsigned int num_innermost_ring_layers =
        _ring_inner_boundary_layer_params.intervals.front() + _ring_intervals.front() +
        _ring_outer_boundary_layer_params.intervals.front();
    // If conditions are met, duplicate the first element of _ring_block_ids at the start.
    if (!_ring_block_ids.empty() && _quad_center_elements && num_innermost_ring_layers > 1 &&
        _ring_block_ids.size() == _ring_intervals.size())
      _ring_block_ids.insert(_ring_block_ids.begin(), _ring_block_ids.front());
    // check if the number of ring block ids is appropiate
    if (!_ring_block_ids.empty() &&
        _ring_block_ids.size() !=
            (_ring_intervals.size() + (unsigned int)(num_innermost_ring_layers != 1)))
    {
      // Create an ostringstream for the debug information
      std::ostringstream debug_info;
      debug_info << "quad_center_elements is : " << (_quad_center_elements ? "true" : "false")
                 << std::endl;
      debug_info << "ring_block_ids size is : " << _ring_block_ids.size() << std::endl;
      debug_info << "ring_intervals size is : " << _ring_intervals.size() << std::endl;
      debug_info << "number of innermost ring layers is : " << num_innermost_ring_layers
                 << std::endl;
 
      // error message
      if (!_quad_center_elements)
      {
        paramError(
            "ring_block_ids",
            "This parameter must have the appropriate size if it is provided: "
            "Since the number of the innermost ring layers (" +
                std::to_string(num_innermost_ring_layers) +
                " :first ring interval and inner/outer boundaries of the first ring) is more than "
                "one, and we have non-quad central elements, the size of 'ring_block_ids' must be "
                "equal to the size of 'ring_intervals' + 1.\n",
            debug_info.str());
      }
      else
      {
        paramError(
            "ring_block_ids",
            "This parameter must have the appropriate size if it is provided: "
            "Since the number of the innermost ring layers (" +
                std::to_string(num_innermost_ring_layers) +
                " :first ring interval and inner/outer boundaries of the first ring) is more than "
                "one, and we have quad central elements, the size of 'ring_block_ids' can be either"
                "equal to the size of 'ring_intervals' or 'ring_intervals' + 1.\n",
            debug_info.str());
      }
    }
    // If conditions are met, duplicate the first element of _ring_block_names at the start.
    if (!_ring_block_names.empty() && _quad_center_elements && num_innermost_ring_layers > 1 &&
        _ring_block_names.size() == _ring_intervals.size())
      _ring_block_names.insert(_ring_block_names.begin(), _ring_block_names.front());
    // check if the number of ring block names is appropiate
    if (!_ring_block_names.empty() &&
        _ring_block_names.size() !=
            (_ring_intervals.size() + (unsigned int)(num_innermost_ring_layers != 1)))
    {
      // Create an ostringstream for the debug information
      std::ostringstream debug_info;
      debug_info << "quad_center_elements is : " << (_quad_center_elements ? "true" : "false")
                 << std::endl;
      debug_info << "ring_block_names size is : " << _ring_block_names.size() << std::endl;
      debug_info << "ring_intervals size is : " << _ring_intervals.size() << std::endl;
      debug_info << "number of innermost ring layers is : " << num_innermost_ring_layers
                 << std::endl;
 
      // error message
      if (!_quad_center_elements)
      {
        paramError(
            "ring_block_names",
            "This parameter must have the appropriate size if it is provided: "
            "Since the number of the innermost ring layers (" +
                std::to_string(num_innermost_ring_layers) +
                " :first ring interval and inner/outer boundaries of the first ring) is more than "
                "one, and we have non-quad central elements, the size of 'ring_block_names' must "
                "be equal to the size of 'ring_intervals' + 1.\n",
            debug_info.str());
      }
      else
      {
        paramError(
            "ring_block_names",
            "This parameter must have the appropriate size if it is provided: "
            "Since the number of the innermost ring layers (" +
                std::to_string(num_innermost_ring_layers) +
                " :first ring interval and inner/outer boundaries of the first ring) is more than "
                "one, and we have quad central elements, the size of 'ring_block_names' can be "
                "either equal to the size of 'ring_intervals' or 'ring_intervals' + 1.\n",
            debug_info.str());
      }
    }
    for (unsigned int i = 0; i < _ring_radii.size(); i++)
    {
      const Real layer_width = _ring_radii[i] - (i == 0 ? 0.0 : _ring_radii[i - 1]);
      _ring_inner_boundary_layer_params.fractions.push_back(
          _ring_inner_boundary_layer_params.widths[i] / layer_width);
      _ring_outer_boundary_layer_params.fractions.push_back(
          _ring_outer_boundary_layer_params.widths[i] / layer_width);
    }
    for (unsigned int i = 0; i < _ring_inner_boundary_layer_params.fractions.size(); i++)
      if (MooseUtils::absoluteFuzzyEqual(_ring_inner_boundary_layer_params.fractions[i], 0.0) &&
          _ring_inner_boundary_layer_params.intervals[i] > 0)
        paramError("ring_inner_boundary_layer_intervals",
                   "Ring inner boundary layer must have zero interval if its thickness is zero.");
      else if (MooseUtils::absoluteFuzzyGreaterThan(_ring_inner_boundary_layer_params.fractions[i],
                                                    0.0) &&
               _ring_inner_boundary_layer_params.intervals[i] == 0)
        paramError("ring_inner_boundary_layer_intervals",
                   "Ring inner boundary layer must have non-zero interval if its thickness is "
                   "not zero.");
    for (unsigned int i = 0; i < _ring_outer_boundary_layer_params.fractions.size(); i++)
    {
      if (MooseUtils::absoluteFuzzyEqual(_ring_outer_boundary_layer_params.fractions[i], 0.0) &&
          _ring_outer_boundary_layer_params.intervals[i] > 0)
        paramError("ring_outer_boundary_layer_intervals",
                   "Ring outer boundary layer must have zero interval if its thickness is zero.");
      else if (MooseUtils::absoluteFuzzyGreaterThan(_ring_outer_boundary_layer_params.fractions[i],
                                                    0.0) &&
               _ring_outer_boundary_layer_params.intervals[i] == 0)
        paramError("ring_outer_boundary_layer_intervals",
                   "Ring outer boundary layer must have non-zero interval if its thickness is "
                   "not zero.");
      if (_ring_inner_boundary_layer_params.fractions[i] +
              _ring_outer_boundary_layer_params.fractions[i] >=
          1.0)
        paramError("ring_inner_boundary_layer_widths",
                   "Summation of ring_inner_boundary_layer_widths and "
                   "ring_outer_boundary_layer_widths cannot exceeds the ring layer width.");
    }
  }
  // Ducts related error messages
  if (_duct_sizes.size() != _duct_intervals.size())
    paramError("duct_sizes", "This parameter and duct_intervals must have the same length.");
  if (_duct_sizes.size() != _duct_radial_biases.size())
    paramError("duct_sizes", "This parameter and duct_radial_biases must have the same length.");
  if (!_duct_block_ids.empty() && _duct_block_ids.size() != _duct_intervals.size())
    paramError("duct_block_ids",
               "This parameter must have the same length as duct_intervals if set.");
  if (!_duct_block_names.empty() && _duct_block_names.size() != _duct_intervals.size())
    paramError("duct_block_names",
               "This parameter must have the same length as duct_intervals if set.");
  if (_duct_sizes.size() != _duct_inner_boundary_layer_params.widths.size() ||
      _duct_sizes.size() != _duct_inner_boundary_layer_params.intervals.size() ||
      _duct_sizes.size() != _duct_inner_boundary_layer_params.biases.size() ||
      _duct_sizes.size() != _duct_outer_boundary_layer_params.widths.size() ||
      _duct_sizes.size() != _duct_outer_boundary_layer_params.intervals.size() ||
      _duct_sizes.size() != _duct_outer_boundary_layer_params.biases.size())
    paramError("duct_sizes",
               "The inner and outer duct boundary layer parameters must have the same sizes as "
               "duct_sizes.");
  if (_has_ducts)
  {
    if (_duct_sizes_style == PolygonSizeStyle::apothem)
      for (unsigned int i = 0; i < _duct_sizes.size(); i++)
        _duct_sizes[i] /= std::cos(M_PI / Real(_num_sides));
    for (unsigned int i = 1; i < _duct_sizes.size(); i++)
      if (_duct_sizes[i] <= _duct_sizes[i - 1])
        paramError("duct_sizes", "This parameter must be strictly ascending.");
    if (_duct_sizes.front() <=
        (_has_rings ? _ring_radii.back() / std::cos(M_PI / Real(_num_sides)) : 0.0))
      paramError("duct_sizes",
                 "This parameter must be positive and ensures no overlapping with rings.");
    if (_duct_sizes.back() >= _pitch / 2.0 / std::cos(M_PI / Real(_num_sides)))
      paramError("duct_sizes",
                 "This parameter must ensure that ducts are smaller than the polygon size.");
    if (*std::min_element(_duct_intervals.begin(), _duct_intervals.end()) <= 0)
      paramError("duct_intervals", "Elements of this parameter must be positive.");
    if (_duct_sizes_style == PolygonSizeStyle::apothem)
      for (unsigned int i = 0; i < _duct_sizes.size(); i++)
      {
        _duct_inner_boundary_layer_params.widths[i] /= std::cos(M_PI / Real(_num_sides));
        _duct_outer_boundary_layer_params.widths[i] /= std::cos(M_PI / Real(_num_sides));
      }
    for (unsigned int i = 0; i < _duct_sizes.size(); i++)
    {
      const Real layer_width =
          (i == _duct_sizes.size() - 1 ? _pitch / 2.0 / std::cos(M_PI / Real(_num_sides))
                                       : _duct_sizes[i + 1]) -
          _duct_sizes[i];
      _duct_inner_boundary_layer_params.fractions.push_back(
          _duct_inner_boundary_layer_params.widths[i] / layer_width);
      _duct_outer_boundary_layer_params.fractions.push_back(
          _duct_outer_boundary_layer_params.widths[i] / layer_width);
    }
    for (unsigned int i = 0; i < _duct_inner_boundary_layer_params.fractions.size(); i++)
      if (MooseUtils::absoluteFuzzyEqual(_duct_inner_boundary_layer_params.fractions[i], 0.0) &&
          _duct_inner_boundary_layer_params.intervals[i] > 0)
        paramError("duct_inner_boundary_layer_intervals",
                   "Duct inner boundary layer must have zero interval if its thickness is zero.");
      else if (MooseUtils::absoluteFuzzyGreaterThan(_duct_inner_boundary_layer_params.fractions[i],
                                                    0.0) &&
               _duct_inner_boundary_layer_params.intervals[i] == 0)
        paramError("duct_inner_boundary_layer_intervals",
                   "Duct inner boundary layer must have non-zero interval if its thickness is "
                   "not zero.");
    for (unsigned int i = 0; i < _duct_outer_boundary_layer_params.fractions.size(); i++)
    {
      if (MooseUtils::absoluteFuzzyEqual(_duct_outer_boundary_layer_params.fractions[i], 0.0) &&
          _duct_outer_boundary_layer_params.intervals[i] > 0)
        paramError("duct_outer_boundary_layer_intervals",
                   "Duct outer boundary layer must have zero interval if its thickness is zero.");
      else if (MooseUtils::absoluteFuzzyGreaterThan(_duct_outer_boundary_layer_params.fractions[i],
                                                    0.0) &&
               _duct_outer_boundary_layer_params.intervals[i] == 0)
        paramError("duct_outer_boundary_layer_intervals",
                   "Duct outer boundary layer must have non-zero interval if its thickness is "
                   "not zero.");
      if (_duct_inner_boundary_layer_params.fractions[i] +
              _duct_outer_boundary_layer_params.fractions[i] >=
          1.0)
        paramError("duct_inner_boundary_layer_widths",
                   "Summation of duct_inner_boundary_layer_widths and "
                   "duct_outer_boundary_layer_widths cannot exceeds the duct layer width.");
    }
  }
  if (MooseUtils::absoluteFuzzyGreaterThan(_background_inner_boundary_layer_params.width +
                                               _background_outer_boundary_layer_params.width,
                                           0.0))
  {
    const Real min_background_thickness =
        (_has_ducts ? (_duct_sizes.front() * std::cos(M_PI / Real(_num_sides))) : (_pitch / 2.0)) -
        (_has_rings ? _ring_radii.back() : 0.0);
    if (_background_inner_boundary_layer_params.width +
            _background_outer_boundary_layer_params.width *
                (_duct_sizes_style == PolygonSizeStyle::apothem
                     ? 1.0
                     : std::cos(M_PI / Real(_num_sides))) >=
        min_background_thickness)
      paramError("background_inner_boundary_layer_width",
                 "The summation of background_inner_boundary_layer_width and "
                 "background_outer_boundary_layer_width must be less than the minimum thickness of "
                 "the background region.");
    if (_duct_sizes_style == PolygonSizeStyle::apothem)
      _background_outer_boundary_layer_params.width /= std::cos(M_PI / Real(_num_sides));
  }
  if (!_quad_center_elements && _center_quad_factor)
    paramError("center_quad_factor",
               "this parameter is only applicable if quad_center_elements is set true.");
  if (_quad_center_elements)
    declareMeshProperty<subdomain_id_type>(
        "quad_center_block_id",
        _has_rings ? (_ring_block_ids.empty() ? _block_id_shift + 1 : _ring_block_ids.front())
                   : (_background_block_ids.empty() ? _block_id_shift + 1
                                                    : _background_block_ids.front()));
  else
    declareMeshProperty<subdomain_id_type>("quad_center_block_id",
                                           libMesh::Elem::invalid_subdomain_id);
 
  // declare metadata for internal interface boundaries
  declareMeshProperty<bool>("interface_boundaries", false);
  declareMeshProperty<std::set<boundary_id_type>>("interface_boundary_ids", {});
}
 
std::unique_ptr<MeshBase>
PolygonConcentricCircleMeshGeneratorBase::generate()
{
  std::vector<std::unique_ptr<ReplicatedMesh>> input(_input_ptrs.size());
  for (const auto i : index_range(_input_ptrs))
  {
    input[i] = dynamic_pointer_cast<ReplicatedMesh>(std::move(*_input_ptrs[i]));
    if (!input[i])
      mooseError("A non-replicated mesh input was supplied but replicated meshes are required.");
    if ((_order == 1 && (*input[i]->elements_begin())->default_order() != FIRST) ||
        (_order == 2 && (*input[i]->elements_begin())->default_order() == FIRST))
      paramError("tri_element_type",
                 "The order of the input mesh to be adapted to does not match the order of the "
                 "mesh to be generated.");
  }
 
  unsigned int mesh_input_counter = 0;
  // azimuthal array used for radius radius_correction
  std::vector<Real> azimuthal_list;
  // loop over all sides of the polygon to collect azimuthal angles of all nodes
  for (unsigned int mesh_index = 0; mesh_index < _num_sides; mesh_index++)
  {
    // When adaptive boundaries exist (only possible for hexagon meshes thru
    // `HexagonConcentricCircleAdaptiveBoundaryMeshGenerator` or square meshes thru
    // `CartesianConcentricCircleAdaptiveBoundaryMeshGenerator`), nodes' azimuthal angle cannot be
    // arithmetically obtained. Instead, `azimuthalAnglesCollector() is used to get this
    // information from the mesh directly.`
    if (std::find(_sides_to_adapt.begin(), _sides_to_adapt.end(), mesh_index) !=
        _sides_to_adapt.end())
    {
      // The following lines only work for hexagon and square; and only a hexagon or a square needs
      // such functionality.
      Real lower_azi =
          _num_sides == 6 ? ((Real)mesh_index * 60.0 - 150.0) : ((Real)mesh_index * 90.0 - 135.0);
      Real upper_azi = _num_sides == 6 ? ((Real)((mesh_index + 1) % 6) * 60.0 - 150.0)
                                       : ((Real)((mesh_index + 1) % 4) * 90.0 - 135.0);
      _azimuthal_angles_array.push_back(azimuthalAnglesCollector(
          *input[mesh_input_counter], lower_azi, upper_azi, ANGLE_TANGENT, _num_sides));
      // loop over the _azimuthal_angles_array just collected to convert tangent to azimuthal
      // angles.
      for (unsigned int i = 1; i < _azimuthal_angles_array.back().size(); i++)
      {
        azimuthal_list.push_back(
            _num_sides == 6
                ? ((Real)mesh_index * 60.0 - 150.0 +
                   std::atan((_azimuthal_angles_array.back()[i - 1] - 1.0) / std::sqrt(3.0)) *
                       180.0 / M_PI)
                : ((Real)mesh_index * 90.0 - 135.0 +
                   std::atan((_azimuthal_angles_array.back()[i - 1] - 1.0)) * 180.0 / M_PI));
      }
      mesh_input_counter++;
    }
    else
    {
      _azimuthal_angles_array.push_back(std::vector<Real>());
      for (unsigned int i = 0; i < _num_sectors_per_side[mesh_index] * _order; i++)
      {
        azimuthal_list.push_back(
            std::atan(
                std::tan(M_PI / _num_sides) *
                (2.0 * (Real)i / (Real)_num_sectors_per_side[mesh_index] / (Real)_order - 1.0)) *
                180.0 / M_PI +
            (Real)mesh_index * (360.0 / (Real)_num_sides) - (180.0 - 180.0 / (Real)_num_sides));
      }
    }
  }
  std::vector<Real> ring_radii_corr;
  if (_has_rings)
  {
    if (_preserve_volumes)
    {
      Real corr_factor =
          PolygonalMeshGenerationUtils::radiusCorrectionFactor(azimuthal_list, true, _order);
      for (unsigned int i = 0; i < _ring_radii.size(); i++)
        ring_radii_corr.push_back(_ring_radii[i] * corr_factor);
    }
    else
      ring_radii_corr = _ring_radii;
    if (ring_radii_corr.back() >= _pitch / 2.0)
      paramError("ring_radii",
                 "Elements of this parameter must be smaller than polygon apothem (after volume "
                 "preserve correction if applicable).");
    setMeshProperty("max_radius_meta", ring_radii_corr.back());
  }
  // build the first slice of the polygon.
  auto mesh0 = buildSimpleSlice(ring_radii_corr,
                                _ring_intervals,
                                _ring_radial_biases,
                                _ring_inner_boundary_layer_params,
                                _ring_outer_boundary_layer_params,
                                _duct_sizes,
                                _duct_intervals,
                                _duct_radial_biases,
                                _duct_inner_boundary_layer_params,
                                _duct_outer_boundary_layer_params,
                                _pitch,
                                _num_sectors_per_side[0],
                                _background_intervals,
                                _background_radial_bias,
                                _background_inner_boundary_layer_params,
                                _background_outer_boundary_layer_params,
                                _node_id_background_meta,
                                _num_sides,
                                1,
                                _azimuthal_angles_array[0],
                                _block_id_shift,
                                _quad_center_elements,
                                _center_quad_factor,
                                _create_inward_interface_boundaries,
                                _create_outward_interface_boundaries,
                                _interface_boundary_id_shift,
                                _generate_side_specific_boundaries,
                                _tri_elem_type,
                                _quad_elem_type);
  // This loop builds add-on slices and stitches them to the first slice
  for (unsigned int mesh_index = 1; mesh_index < _num_sides; mesh_index++)
  {
    auto mesh_tmp = buildSimpleSlice(ring_radii_corr,
                                     _ring_intervals,
                                     _ring_radial_biases,
                                     _ring_inner_boundary_layer_params,
                                     _ring_outer_boundary_layer_params,
                                     _duct_sizes,
                                     _duct_intervals,
                                     _duct_radial_biases,
                                     _duct_inner_boundary_layer_params,
                                     _duct_outer_boundary_layer_params,
                                     _pitch,
                                     _num_sectors_per_side[mesh_index],
                                     _background_intervals,
                                     _background_radial_bias,
                                     _background_inner_boundary_layer_params,
                                     _background_outer_boundary_layer_params,
                                     _node_id_background_meta,
                                     _num_sides,
                                     mesh_index + 1,
                                     _azimuthal_angles_array[mesh_index],
                                     _block_id_shift,
                                     _quad_center_elements,
                                     _center_quad_factor,
                                     _create_inward_interface_boundaries,
                                     _create_outward_interface_boundaries,
                                     _interface_boundary_id_shift,
                                     _generate_side_specific_boundaries,
                                     _tri_elem_type,
                                     _quad_elem_type);
 
    ReplicatedMesh other_mesh(*mesh_tmp);
    MeshTools::Modification::rotate(other_mesh, 360.0 / _num_sides * mesh_index, 0, 0);
    mesh0->prepare_for_use();
    other_mesh.prepare_for_use();
    mesh0->stitch_meshes(other_mesh, SLICE_BEGIN, SLICE_END, TOLERANCE, true, false);
    other_mesh.clear();
  }
 
  // An extra step to stich the first and last slices together
  mesh0->stitch_surfaces(SLICE_BEGIN, SLICE_END, TOLERANCE, true, false);
 
  if (!_has_rings && !_has_ducts && _background_intervals == 1)
    MooseMesh::changeBoundaryId(*mesh0, 1 + _interface_boundary_id_shift, OUTER_SIDESET_ID, false);
 
  if (!_is_general_polygon)
  {
    setMeshProperty("azimuthal_angle_meta",
                    azimuthalAnglesCollector(*mesh0, -180.0, 180.0, ANGLE_DEGREE));
    setMeshProperty("pattern_pitch_meta", _pitch);
  }
 
  // Move nodes on the external boundary for force uniform spacing.
  if (_uniform_mesh_on_sides)
  {
    const Real angle_tol = 1.0e-5;
    std::vector<std::pair<Real, unsigned int>> node_azi_list;
    MeshTools::Modification::rotate(*mesh0, -(270.0 - 360.0 / (Real)_num_sides), 0.0, 0.0);
    std::vector<std::tuple<dof_id_type, unsigned short int, boundary_id_type>> side_list =
        mesh0->get_boundary_info().build_side_list();
    mesh0->get_boundary_info().build_node_list_from_side_list();
    std::vector<std::tuple<dof_id_type, boundary_id_type>> node_list =
        mesh0->get_boundary_info().build_node_list();
 
    for (unsigned int i = 0; i < node_list.size(); ++i)
    {
      if (std::get<1>(node_list[i]) == OUTER_SIDESET_ID)
      {
        node_azi_list.push_back(
            std::make_pair(atan2((*mesh0->node_ptr(std::get<0>(node_list[i])))(1),
                                 (*mesh0->node_ptr(std::get<0>(node_list[i])))(0)) *
                               180.0 / M_PI,
                           std::get<0>(node_list[i])));
        if (std::abs(node_azi_list.back().first + 180.0) <= angle_tol)
          node_azi_list.back().first = 180.0;
      }
    }
    std::sort(node_azi_list.begin(), node_azi_list.end());
    for (unsigned int i = 0; i < _num_sides; i++)
    {
      for (unsigned int j = 1; j <= _num_sectors_per_side[i]; j++)
      {
        Real azi_corr_tmp = atan2((Real)j * 2.0 / (Real)_num_sectors_per_side[i] - 1.0,
                                  1.0 / std::tan(M_PI / (Real)_num_sides));
        Real x_tmp = _pitch / 2.0;
        Real y_tmp = x_tmp * std::tan(azi_corr_tmp);
        nodeCoordRotate(
            x_tmp, y_tmp, (Real)i * 360.0 / (Real)_num_sides - (180.0 - 180.0 / (Real)_num_sides));
        Point p_tmp = Point(x_tmp, y_tmp, 0.0);
        mesh0->add_point(
            p_tmp,
            node_azi_list[std::accumulate(
                              _num_sectors_per_side.begin(), _num_sectors_per_side.begin() + i, 0) +
                          j - 1]
                .second);
      }
    }
    MeshTools::Modification::rotate(*mesh0, (270.0 - 360.0 / (Real)_num_sides), 0.0, 0.0);
  }
 
  setMeshProperty("background_intervals_meta", _background_intervals);
 
  if (!_has_ducts && _sides_to_adapt.empty())
  {
    libMesh::LaplaceMeshSmoother lms(*mesh0, _smoothing_max_it);
    lms.smooth();
  }
 
  // Set up customized Block Names and/or IDs
  unsigned int block_it = 0;
  unsigned ring_block_num = 0;
  std::vector<subdomain_id_type> block_ids_old;
  std::vector<subdomain_id_type> block_ids_new;
  std::vector<SubdomainName> block_names;
  if (_has_rings)
  {
    ringBlockIdsNamesPreparer(block_it, ring_block_num, block_ids_old, block_ids_new, block_names);
  }
  else
  {
    if (_background_intervals > 1)
    {
      block_ids_old.push_back(_block_id_shift + 1 + block_it);
      block_ids_new.push_back(_background_block_ids.empty() ? block_ids_old.back()
                                                            : _background_block_ids.front());
      block_names.push_back(_background_block_names.empty()
                                ? (SubdomainName)std::to_string(block_ids_new.back())
                                : _background_block_names.front());
      block_it++;
    }
  }
  block_ids_old.push_back(_block_id_shift + 1 + block_it);
  block_ids_new.push_back(_background_block_ids.empty() ? block_ids_old.back()
                                                        : _background_block_ids.back());
  block_names.push_back(_background_block_names.empty()
                            ? (SubdomainName)std::to_string(block_ids_new.back())
                            : _background_block_names.back());
  block_it++;
  if (_has_ducts)
  {
    for (unsigned int i = 0; i < _duct_intervals.size(); i++)
    {
      block_ids_old.push_back(_block_id_shift + 1 + block_it);
      block_ids_new.push_back(_duct_block_ids.empty() ? block_ids_old.back() : _duct_block_ids[i]);
      block_names.push_back(_duct_block_names.empty()
                                ? (SubdomainName)std::to_string(block_ids_new.back())
                                : _duct_block_names[i]);
      block_it++;
    }
  }
 
  assignBlockIdsNames(
      *mesh0, block_ids_old, block_ids_new, block_names, "ConcentricCircleMeshGenerator");
 
  if (_external_boundary_id > 0)
    MooseMesh::changeBoundaryId(*mesh0, OUTER_SIDESET_ID, _external_boundary_id, false);
  if (!_external_boundary_name.empty())
  {
    mesh0->get_boundary_info().sideset_name(
        _external_boundary_id > 0 ? _external_boundary_id : (boundary_id_type)OUTER_SIDESET_ID) =
        _external_boundary_name;
    mesh0->get_boundary_info().nodeset_name(
        _external_boundary_id > 0 ? _external_boundary_id : (boundary_id_type)OUTER_SIDESET_ID) =
        _external_boundary_name;
  }
 
  assignInterfaceBoundaryNames(*mesh0);
 
  // add sector ids
  if (isParamValid("sector_id_name"))
    setSectorExtraIDs(
        *mesh0, getParam<std::string>("sector_id_name"), _num_sides, _num_sectors_per_side);
 
  // add ring ids
  if (isParamValid("ring_id_name"))
    setRingExtraIDs(*mesh0,
                    getParam<std::string>("ring_id_name"),
                    _num_sides,
                    _num_sectors_per_side,
                    _ring_intervals,
                    getParam<MooseEnum>("ring_id_assign_type") == "ring_wise",
                    _quad_center_elements);
 
  // add internal side set info to metadata
  if (_create_inward_interface_boundaries || _create_outward_interface_boundaries)
  {
    setMeshProperty("interface_boundaries", true);
    // lists boundary ids assigned to interfaces
    std::set<boundary_id_type> boundary_ids = mesh0->get_boundary_info().get_boundary_ids();
    std::set<boundary_id_type> interface_boundary_ids;
    if (_create_outward_interface_boundaries)
    {
      const unsigned int num_boundary_ids = boundary_ids.size();
      for (const auto i : make_range(num_boundary_ids))
      {
        const unsigned int id = i * 2 + 1 + _interface_boundary_id_shift;
        auto it = boundary_ids.find(id);
        if (it != boundary_ids.end())
        {
          boundary_ids.erase(it);
          interface_boundary_ids.insert(id);
        }
      }
    }
    if (_create_inward_interface_boundaries)
    {
      const unsigned int num_boundary_ids = boundary_ids.size();
      for (const auto i : make_range(num_boundary_ids))
      {
        const unsigned int id = i * 2 + 2 + _interface_boundary_id_shift;
        auto it = boundary_ids.find(id);
        if (it != boundary_ids.end())
        {
          boundary_ids.erase(it);
          interface_boundary_ids.insert(id);
        }
      }
    }
    setMeshProperty("interface_boundary_ids", interface_boundary_ids);
  }
 
  bool flat_side_up = getMeshProperty<bool>("flat_side_up", name());
  if (flat_side_up)
    MeshTools::Modification::rotate(*mesh0, 180.0 / (Real)_num_sides, 0.0, 0.0);
  mesh0->unset_is_prepared();
 
  if (_has_rings && getParam<bool>("replace_inner_ring_with_delaunay_mesh"))
  {
    if (isParamSetByUser("quad_center_elements"))
      paramError("quad_center_elements",
                 "Should not be set because the center elements of the inner ring will be replaced "
                 "by a Delaunay mesh with 'replace_inner_ring_with_delaunay_mesh=true'");
 
    // remove elements of the inner ring and create an inner-ring external boundary side set
    std::set<Elem *> deleteable_elems;
    for (auto & elem : mesh0->element_ptr_range())
      if (elem->vertex_average().norm() < ring_radii_corr[0])
        deleteable_elems.insert(elem);
 
    const boundary_id_type boundary_id = MooseMeshUtils::getBoundaryIDs(*mesh0, {"_foo"}, true)[0];
    BoundaryInfo & boundary_info = mesh0->get_boundary_info();
    for (auto & elem : deleteable_elems)
    {
      unsigned int n_sides = elem->n_sides();
      for (unsigned int n = 0; n != n_sides; ++n)
      {
        Elem * neighbor = elem->neighbor_ptr(n);
        if (!neighbor)
          continue;
 
        const unsigned int return_side = neighbor->which_neighbor_am_i(elem);
 
        if (neighbor->neighbor_ptr(return_side) == elem)
        {
          neighbor->set_neighbor(return_side, nullptr);
          boundary_info.add_side(neighbor, return_side, boundary_id);
        }
      }
 
      mesh0->delete_elem(elem);
    }
 
    // build the 1d mesh from the new boundary
    auto poly_mesh = MooseMeshUtils::buildBoundaryMesh(*mesh0, boundary_id);
    Real min_side = std::numeric_limits<Real>::max();
    for (auto & elem : poly_mesh->element_ptr_range())
    {
      Real l = elem->volume();
      if (l < min_side)
        min_side = l;
    }
 
    // triangulate with the 1d mesh
    libMesh::Poly2TriTriangulator poly2tri(*poly_mesh);
    poly2tri.triangulation_type() = libMesh::TriangulatorInterface::PSLG;
    poly2tri.set_interpolate_boundary_points(0);
    poly2tri.set_refine_boundary_allowed(false);
    poly2tri.set_verify_hole_boundaries(false);
    const auto desired_area = getParam<std::string>("inner_ring_desired_area");
    if (desired_area != "")
    {
      poly2tri.desired_area() = 0;
      libMesh::ParsedFunction<Real> area_func{desired_area};
      poly2tri.set_desired_area_function(&area_func);
    }
    else
      poly2tri.desired_area() = min_side * min_side;
    poly2tri.minimum_angle() = 0;
    poly2tri.smooth_after_generating() = true;
    // poly2tri.elem_type() is TRI3 by default
    if (_tri_elem_type == TRI_ELEM_TYPE::TRI6)
      poly2tri.elem_type() = libMesh::ElemType::TRI6;
    else if (_tri_elem_type == TRI_ELEM_TYPE::TRI7)
      poly2tri.elem_type() = libMesh::ElemType::TRI7;
    // let us keep the center point
    poly_mesh->add_point(libMesh::Point());
    poly2tri.triangulate();
    // keep the old subdomain id
    for (auto elem : poly_mesh->element_ptr_range())
      elem->subdomain_id() = block_ids_new[0];
 
    if (isParamValid("ring_id_name"))
    {
      if (_ring_intervals[0] != 1 && getParam<MooseEnum>("ring_id_assign_type") == "ring_wise")
        paramError("replace_inner_ring_with_delaunay_mesh",
                   "Inner ring has multple intervals with each being assigned with a different "
                   "ring id, replacing inner ring with Delaunay mesh will remove this ring id "
                   "assign type. Either change 'ring_id_assign_type' to block_wise or set the "
                   "first element of 'ring_intervals' to 1 or set "
                   "'replace_inner_ring_with_delaunay_mesh' to false to avoid this error.");
      auto id_name = getParam<std::string>("ring_id_name");
      const auto extra_id_index = poly_mesh->add_elem_integer(id_name);
      for (auto elem : poly_mesh->element_ptr_range())
        elem->set_extra_integer(extra_id_index, 1);
    }
    if (isParamValid("sector_id_name"))
    {
      // we will assign all elements in the inner ring with zero sector id
      auto id_name = getParam<std::string>("sector_id_name");
      const auto extra_id_index = poly_mesh->add_elem_integer(id_name);
      for (auto elem : poly_mesh->element_ptr_range())
        elem->set_extra_integer(extra_id_index, 0);
    }
 
    // stitch the triangulated mesh and the original mesh without the inner ring
    mesh0->stitch_meshes(*poly_mesh, boundary_id, 0, TOLERANCE, true, false);
  }
 
  return dynamic_pointer_cast<MeshBase>(mesh0);
}