libMesh::QGrundmann_Moller Class Reference

This class implements the Grundmann-Moller quadrature rules for tetrahedra. More...

#include <quadrature_gm.h>

Inheritance diagram for libMesh::QGrundmann_Moller:

Public Member Functions
	QGrundmann_Moller (unsigned int dim, Order order=INVALID_ORDER)
	Constructor. More...
	QGrundmann_Moller (const QGrundmann_Moller &)=default
	Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class. More...
	QGrundmann_Moller (QGrundmann_Moller &&)=default
QGrundmann_Moller &	operator= (const QGrundmann_Moller &)=default
QGrundmann_Moller &	operator= (QGrundmann_Moller &&)=default
virtual	~QGrundmann_Moller ()=default
virtual QuadratureType	type () const override
ElemType	get_elem_type () const
unsigned int	get_p_level () const
unsigned int	n_points () const
unsigned int	get_dim () const
const std::vector< Point > &	get_points () const
std::vector< Point > &	get_points ()
const std::vector< Real > &	get_weights () const
std::vector< Real > &	get_weights ()
Point	qp (const unsigned int i) const
Real	w (const unsigned int i) const
virtual void	init (const ElemType type=INVALID_ELEM, unsigned int p_level=0)
	Initializes the data structures for a quadrature rule for an element of type type. More...
virtual void	init (const Elem &elem, const std::vector< Real > &vertex_distance_func, unsigned int p_level=0)
	Initializes the data structures for an element potentially "cut" by a signed distance function. More...
Order	get_order () const
void	print_info (std::ostream &os=libMesh::out) const
	Prints information relevant to the quadrature rule, by default to libMesh::out. More...
void	scale (std::pair< Real, Real > old_range, std::pair< Real, Real > new_range)
	Maps the points of a 1D quadrature rule defined by "old_range" to another 1D interval defined by "new_range" and scales the weights accordingly. More...
virtual bool	shapes_need_reinit ()

Static Public Member Functions
static std::unique_ptr< QBase >	build (const std::string &name, const unsigned int dim, const Order order=INVALID_ORDER)
	Builds a specific quadrature rule based on the name string. More...
static std::unique_ptr< QBase >	build (const QuadratureType qt, const unsigned int dim, const Order order=INVALID_ORDER)
	Builds a specific quadrature rule based on the QuadratureType. More...
static void	print_info (std::ostream &out=libMesh::out)
	Prints the reference information, by default to libMesh::out. More...
static std::string	get_info ()
	Gets a string containing the reference information. More...
static unsigned int	n_objects ()
	Prints the number of outstanding (created, but not yet destroyed) objects. More...
static void	enable_print_counter_info ()
	Methods to enable/disable the reference counter output from print_info() More...
static void	disable_print_counter_info ()

Public Attributes
bool	allow_rules_with_negative_weights
	Flag (default true) controlling the use of quadrature rules with negative weights. More...

Protected Types
typedef std::map< std::string, std::pair< unsigned int, unsigned int > >	Counts
	Data structure to log the information. More...

Protected Member Functions
virtual void	init_0D (const ElemType type=INVALID_ELEM, unsigned int p_level=0)
	Initializes the 0D quadrature rule by filling the points and weights vectors with the appropriate values. More...
void	tensor_product_quad (const QBase &q1D)
	Constructs a 2D rule from the tensor product of q1D with itself. More...
void	tensor_product_hex (const QBase &q1D)
	Computes the tensor product quadrature rule [q1D x q1D x q1D] from the 1D rule q1D. More...
void	tensor_product_prism (const QBase &q1D, const QBase &q2D)
	Computes the tensor product of a 1D quadrature rule and a 2D quadrature rule. More...
void	increment_constructor_count (const std::string &name)
	Increments the construction counter. More...
void	increment_destructor_count (const std::string &name)
	Increments the destruction counter. More...

Protected Attributes
unsigned int	_dim
	The spatial dimension of the quadrature rule. More...
Order	_order
	The polynomial order which the quadrature rule is capable of integrating exactly. More...
ElemType	_type
	The type of element for which the current values have been computed. More...
unsigned int	_p_level
	The p-level of the element for which the current values have been computed. More...
std::vector< Point >	_points
	The locations of the quadrature points in reference element space. More...
std::vector< Real >	_weights
	The quadrature weights. More...

Static Protected Attributes
static Counts	_counts
	Actually holds the data. More...
static Threads::atomic< unsigned int >	_n_objects
	The number of objects. More...
static Threads::spin_mutex	_mutex
	Mutual exclusion object to enable thread-safe reference counting. More...
static bool	_enable_print_counter = true
	Flag to control whether reference count information is printed when print_info is called. More...

Private Member Functions
virtual void	init_1D (const ElemType, unsigned int) override
	In 1D, use a Gauss rule. More...
virtual void	init_2D (const ElemType, unsigned int) override
	Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate values. More...
virtual void	init_3D (const ElemType, unsigned int) override
	Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate values. More...
void	gm_rule (unsigned int s, unsigned int dim)
	This routine is called from init_2D() and init_3D(). More...
void	compose_all (unsigned int s, unsigned int p, std::vector< std::vector< unsigned int >> &result)
	Routine which generates p-compositions of a given order, s, as well as permutations thereof. More...

Detailed Description

This class implements the Grundmann-Moller quadrature rules for tetrahedra.

The GM rules are well-defined for simplices of arbitrary dimension and to any order, but the rules by Dunavant for two-dimensional simplices are in general superior. This is primarily due to the fact that the GM rules contain a significant proportion of negative weights, making them susceptible to round-off error at high-order.

The GM rules are interesting in 3D because they overlap with the conical product rules at higher order while having significantly fewer evaluation points, making them potentially much more efficient. The table below gives a comparison between the number of points in a conical product (CP) rule and the GM rule of equivalent order. The GM rules are defined to be exact for polynomials of degree d=2*s+1, s=0,1,2,3,... The table also gives the percentage of each GM rule's weights which are negative. The percentage of negative weights appears to approach 50, and the amplification factor (a measure of the effect of round-off) defined as

amp. factor = \( \frac{1}{V} \sum \|w_i\|, \)

where V is the volume of the reference element, grows like exp(C*s). (A rule with all positive weights has an amplification factor of 1.0 by definition.)

* s   degree  n_pts(conical)  n_pts(GM)   % neg wts  amp. factor
* ------------------------------------------------------------------------
* 0   1       1               1            0.00      1.00e+00
* 1   3       8               5           20.00      2.60e+00
* 2   5       27              15          26.67      5.63e+00
* 3   7       64              35          31.43      1.19e+01
* 4   9       125             70          34.29      2.54e+01
* 5   11      216             126         36.51      5.41e+01
* 6   13      343             210         38.10      1.16e+02
* 7   15      512             330         39.39      2.51e+02
* 8   17      729             495         40.40      5.45e+02
* 9   19      1000            715         41.26      1.19e+03
* 10  21      1331            1001        41.96      2.59e+03
* 11  23      1728            1365        42.56      5.68e+03
* 12  25      2197            1820        43.08      1.25e+04
* 13  27      2744            2380        43.53      2.75e+04
* 14  29      3375            3060        43.92      6.07e+04
* 15  31      4096            3876        44.27      1.34e+05
* 16  33      4913            4845        44.58      2.97e+05
* 17  35      5832            5985        44.86      6.59e+05 <= Conical rule has fewer points for degree >= 34
* 18  37      6859            7315        45.11      1.46e+06
* 19  39      8000            8855        45.34      3.25e+06
* 20  41      9261            10626       45.55      7.23e+06
* 21  43      10648           12650       45.74      1.61e+07
* 

Reference: Axel Grundmann and Michael M"{o}ller, "Invariant Integration Formulas for the N-Simplex by Combinatorial Methods," SIAM Journal on Numerical Analysis, Volume 15, Number 2, April 1978, pages 282-290.

Reference LGPL Fortran90 code by John Burkardt can be found here: http://people.scs.fsu.edu/~burkardt/f_src/gm_rules/gm_rules.html

Author

John W. Peterson

Date

2008

Implements the quadrature rules of Grundmann and Moller in 2D and 3D.

Definition at line 96 of file quadrature_gm.h.

Member Typedef Documentation

Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts

protectedinherited

Data structure to log the information.

The log is identified by the class name.

Definition at line 117 of file reference_counter.h.

Constructor & Destructor Documentation

QGrundmann_Moller() [1/3]

libMesh::QGrundmann_Moller::QGrundmann_Moller ( unsigned int  dim, Order  order = INVALID_ORDER  )

inline

Constructor.

Declares the order of the quadrature rule.

Definition at line 103 of file quadrature_gm.h.

                                                :
    QBase(dim,order)
  {}

QGrundmann_Moller() [2/3]

libMesh::QGrundmann_Moller::QGrundmann_Moller ( const QGrundmann_Moller &  )

default

Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class.

QGrundmann_Moller() [3/3]

libMesh::QGrundmann_Moller::QGrundmann_Moller ( QGrundmann_Moller &&  )

default

~QGrundmann_Moller()

virtual libMesh::QGrundmann_Moller::~QGrundmann_Moller ( )

virtualdefault

Member Function Documentation

build() [1/2]

std::unique_ptr< QBase > libMesh::QBase::build ( const QuadratureType  qt, const unsigned int  dim, const Order  order = INVALID_ORDER  )

staticinherited

Builds a specific quadrature rule based on the QuadratureType.

This enables selection of the quadrature rule at run-time.

This function allocates memory, therefore a std::unique_ptr<QBase> is returned so that the user does not accidentally leak it.

Definition at line 52 of file quadrature_build.C.

{
  switch (_qt)
    {
 
    case QCLOUGH:
      {
#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            libMesh::out << "WARNING: Clough quadrature implemented" << std::endl
                         << " up to TWENTYTHIRD order." << std::endl;
          }
#endif
 
        return libmesh_make_unique<QClough>(_dim, _order);
      }
 
    case QGAUSS:
      {
 
#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Gauss quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }
#endif
 
        return libmesh_make_unique<QGauss>(_dim, _order);
      }
 
    case QJACOBI_1_0:
      {
 
#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }
 
        if (_dim > 1)
          {
            libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
                         << " in 1D only." << std::endl;
          }
#endif
 
        return libmesh_make_unique<QJacobi>(_dim, _order, 1, 0);
      }
 
    case QJACOBI_2_0:
      {
 
#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
                         << " up to FORTYTHIRD order." << std::endl;
          }
 
        if (_dim > 1)
          {
            libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
                         << " in 1D only." << std::endl;
          }
#endif
 
        return libmesh_make_unique<QJacobi>(_dim, _order, 2, 0);
      }
 
    case QSIMPSON:
      {
 
#ifdef DEBUG
        if (_order > THIRD)
          {
            libMesh::out << "WARNING: Simpson rule provides only" << std::endl
                         << " THIRD order!" << std::endl;
          }
#endif
 
        return libmesh_make_unique<QSimpson>(_dim);
      }
 
    case QTRAP:
      {
 
#ifdef DEBUG
        if (_order > FIRST)
          {
            libMesh::out << "WARNING: Trapezoidal rule provides only" << std::endl
                         << " FIRST order!" << std::endl;
          }
#endif
 
        return libmesh_make_unique<QTrap>(_dim);
      }
 
    case QGRID:
      return libmesh_make_unique<QGrid>(_dim, _order);
 
    case QGRUNDMANN_MOLLER:
      return libmesh_make_unique<QGrundmann_Moller>(_dim, _order);
 
    case QMONOMIAL:
      return libmesh_make_unique<QMonomial>(_dim, _order);
 
    case QGAUSS_LOBATTO:
      return libmesh_make_unique<QGaussLobatto>(_dim, _order);
 
    case QCONICAL:
      return libmesh_make_unique<QConical>(_dim, _order);
 
    case QNODAL:
      return libmesh_make_unique<QNodal>(_dim, _order);
 
    default:
      libmesh_error_msg("ERROR: Bad qt=" << _qt);
    }
}

References libMesh::QBase::_dim, libMesh::QBase::_order, libMesh::FIRST, libMesh::FORTYTHIRD, libMesh::out, libMesh::QCLOUGH, libMesh::QCONICAL, libMesh::QGAUSS, libMesh::QGAUSS_LOBATTO, libMesh::QGRID, libMesh::QGRUNDMANN_MOLLER, libMesh::QJACOBI_1_0, libMesh::QJACOBI_2_0, libMesh::QMONOMIAL, libMesh::QNODAL, libMesh::QSIMPSON, libMesh::QTRAP, libMesh::THIRD, and libMesh::TWENTYTHIRD.

build() [2/2]

std::unique_ptr< QBase > libMesh::QBase::build ( const std::string &  name, const unsigned int  dim, const Order  order = INVALID_ORDER  )

staticinherited

Builds a specific quadrature rule based on the name string.

This enables selection of the quadrature rule at run-time. The input parameter name must be mappable through the Utility::string_to_enum<>() function.

This function allocates memory, therefore a std::unique_ptr<QBase> is returned so that the user does not accidentally leak it.

Definition at line 41 of file quadrature_build.C.

{
  return QBase::build (Utility::string_to_enum<QuadratureType> (type),
                       _dim,
                       _order);
}

References libMesh::QBase::_dim, libMesh::QBase::_order, and libMesh::QBase::type().

Referenced by assemble_poisson(), libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::InfFE< Dim, T_radial, T_map >::reinit(), QuadratureTest::test1DWeights(), QuadratureTest::test2DWeights(), QuadratureTest::test3DWeights(), QuadratureTest::testBuild(), QuadratureTest::testJacobi(), QuadratureTest::testMonomialQuadrature(), QuadratureTest::testTetQuadrature(), and QuadratureTest::testTriQuadrature().

compose_all()

void libMesh::QGrundmann_Moller::compose_all ( unsigned int  s, unsigned int  p, std::vector< std::vector< unsigned int >> &  result  )

private

Routine which generates p-compositions of a given order, s, as well as permutations thereof.

This routine is called internally by the gm_rule() routine, you should not call this yourself!

Definition at line 150 of file quadrature_gm.C.

{
  // Clear out results remaining from previous calls
  result.clear();
 
  // Allocate storage for a workspace.  The workspace will periodically
  // be copied into the result container.
  std::vector<unsigned int> workspace(p);
 
  // The first result is always (s,0,...,0)
  workspace[0] = s;
  result.push_back(workspace);
 
  // the value of the first non-zero entry
  unsigned int head_value=s;
 
  // When head_index=-1, it refers to "off the front" of the array.  Therefore,
  // this needs to be a regular int rather than unsigned.  I initially tried to
  // do this with head_index unsigned and an else statement below, but then there
  // is the special case: (1,0,...,0) which does not work correctly.
  int head_index = -1;
 
  // At the end, all the entries will be in the final slot of workspace
  while (workspace.back() != s)
    {
      // If the previous head value is still larger than 1, reset the index
      // to "off the front" of the array
      if (head_value > 1)
        head_index = -1;
 
      // Either move the index onto the front of the array or on to
      // the next value.
      head_index++;
 
      // Get current value of the head entry
      head_value = workspace[head_index];
 
      // Put a zero into the head_index of the array.  If head_index==0,
      // this will be overwritten in the next line with head_value-1.
      workspace[head_index] = 0;
 
      // The initial entry gets the current head value, minus 1.
      // If head_value > 1, the next loop iteration will start back
      // at workspace[0] again.
      libmesh_assert_greater (head_value, 0);
      workspace[0] = head_value - 1;
 
      // Increment the head+1 value
      workspace[head_index+1] += 1;
 
      // Save this composition in the results
      result.push_back(workspace);
    }
}

Referenced by gm_rule().

disable_print_counter_info()

void libMesh::ReferenceCounter::disable_print_counter_info ( )

staticinherited

Definition at line 106 of file reference_counter.C.

{
  _enable_print_counter = false;
  return;
}

References libMesh::ReferenceCounter::_enable_print_counter.

Referenced by libMesh::LibMeshInit::LibMeshInit().

enable_print_counter_info()

void libMesh::ReferenceCounter::enable_print_counter_info ( )

staticinherited

Methods to enable/disable the reference counter output from print_info()

Definition at line 100 of file reference_counter.C.

{
  _enable_print_counter = true;
  return;
}

References libMesh::ReferenceCounter::_enable_print_counter.

get_dim()

unsigned int libMesh::QBase::get_dim ( ) const

inlineinherited

Returns

The spatial dimension of the quadrature rule.

Definition at line 135 of file quadrature.h.

{ return _dim; }

References libMesh::QBase::_dim.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), and libMesh::QConical::conical_product_tri().

get_elem_type()

ElemType libMesh::QBase::get_elem_type ( ) const

inlineinherited

Returns

The element type we're currently using.

Definition at line 116 of file quadrature.h.

{ return _type; }

References libMesh::QBase::_type.

get_info()

std::string libMesh::ReferenceCounter::get_info ( )

staticinherited

Gets a string containing the reference information.

Definition at line 47 of file reference_counter.C.

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
 
  std::ostringstream oss;
 
  oss << '\n'
      << " ---------------------------------------------------------------------------- \n"
      << "| Reference count information                                                |\n"
      << " ---------------------------------------------------------------------------- \n";
 
  for (const auto & pr : _counts)
    {
      const std::string name(pr.first);
      const unsigned int creations    = pr.second.first;
      const unsigned int destructions = pr.second.second;
 
      oss << "| " << name << " reference count information:\n"
          << "|  Creations:    " << creations    << '\n'
          << "|  Destructions: " << destructions << '\n';
    }
 
  oss << " ---------------------------------------------------------------------------- \n";
 
  return oss.str();
 
#else
 
  return "";
 
#endif
}

References libMesh::ReferenceCounter::_counts, and libMesh::Quality::name().

Referenced by libMesh::ReferenceCounter::print_info().

get_order()

Order libMesh::QBase::get_order ( ) const

inlineinherited

Returns

The current "total" order of the quadrature rule which can vary element by element, depending on the Elem::p_level(), which gets passed to us during init().

Each additional power of p increases the quadrature order required to integrate the mass matrix by 2, hence the formula below.

Definition at line 211 of file quadrature.h.

{ return static_cast<Order>(_order + 2 * _p_level); }

References libMesh::QBase::_order, and libMesh::QBase::_p_level.

Referenced by libMesh::InfFE< Dim, T_radial, T_map >::attach_quadrature_rule(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QGaussLobatto::init_1D(), libMesh::QConical::init_1D(), libMesh::QGauss::init_1D(), libMesh::QJacobi::init_1D(), init_1D(), libMesh::QGauss::init_2D(), libMesh::QMonomial::init_2D(), init_2D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), and init_3D().

get_p_level()

unsigned int libMesh::QBase::get_p_level ( ) const

inlineinherited

Returns

The p-refinement level we're currently using.

Definition at line 121 of file quadrature.h.

{ return _p_level; }

References libMesh::QBase::_p_level.

get_points() [1/2]

std::vector<Point>& libMesh::QBase::get_points ( )

inlineinherited

Returns

A std::vector containing the quadrature point locations in reference element space as a writable reference.

Definition at line 147 of file quadrature.h.

{ return _points; }

References libMesh::QBase::_points.

get_points() [2/2]

const std::vector<Point>& libMesh::QBase::get_points ( ) const

inlineinherited

Returns

A std::vector containing the quadrature point locations in reference element space.

Definition at line 141 of file quadrature.h.

{ return _points; }

References libMesh::QBase::_points.

Referenced by assemble_ellipticdg(), libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), init_1D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), EIM_F::interior_assembly(), and AssemblyEIM::interior_assembly().

get_weights() [1/2]

std::vector<Real>& libMesh::QBase::get_weights ( )

inlineinherited

Returns

A writable references to a std::vector containing the quadrature weights.

Definition at line 159 of file quadrature.h.

{ return _weights; }

References libMesh::QBase::_weights.

get_weights() [2/2]

const std::vector<Real>& libMesh::QBase::get_weights ( ) const

inlineinherited

Returns

A constant reference to a std::vector containing the quadrature weights.

Definition at line 153 of file quadrature.h.

{ return _weights; }

References libMesh::QBase::_weights.

Referenced by libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), init_1D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), and libMesh::QMonomial::init_3D().

gm_rule()

void libMesh::QGrundmann_Moller::gm_rule ( unsigned int  s, unsigned int  dim  )

private

This routine is called from init_2D() and init_3D().

It actually fills the _points and _weights vectors for a given rule index, s and dimension, dim.

Definition at line 52 of file quadrature_gm.C.

{
  // Only dim==2 or dim==3 is allowed
  libmesh_assert(dim==2 || dim==3);
 
  // A GM rule of index s can integrate polynomials of degree 2*s+1 exactly
  const unsigned int degree = 2*s+1;
 
  // The number of points for rule of index s is
  // (dim+1+s)! / (dim+1)! / s!
  // In 3D, this is = 1/24 * Pi_{i=1}^4 (s+i)
  // In 2D, this is =  1/6 * Pi_{i=1}^3 (s+i)
  const unsigned int n_pts = dim==2 ? (s+3)*(s+2)*(s+1) / 6 : (s+4)*(s+3)*(s+2)*(s+1) / 24;
  //libMesh::out << "n_pts=" << n_pts << std::endl;
 
  // Allocate space for points and weights
  _points.resize(n_pts);
  _weights.resize(n_pts);
 
  // (-1)^i -> This one flips sign at each iteration of the i-loop below.
  int one_pm=1;
 
  // Where we store all the integer point compositions/permutations
  std::vector<std::vector<unsigned int>> permutations;
 
  // Index into the vector where we should start adding the next round of points/weights
  std::size_t offset=0;
 
  // Implement the GM formula 4.1 on page 286 of the paper
  for (unsigned int i=0; i<=s; ++i)
    {
      // Get all the ordered compositions (and their permutations)
      // of |beta| = s-i into dim+1 parts
      compose_all(s-i, dim+1, permutations);
      //libMesh::out << "n. permutations=" << permutations.size() << std::endl;
 
      for (auto p : index_range(permutations))
        {
          // We use the first dim entries of each permutation to
          // construct an integration point.
          for (unsigned int j=0; j<dim; ++j)
            _points[offset+p](j) =
              static_cast<Real>(2.*permutations[p][j] + 1.) /
              static_cast<Real>(  degree + dim - 2.*i     );
        }
 
      // Compute the weight for this i, being careful to avoid overflow.
      // This technique is borrowed from Burkardt's code as well.
      // Use once for each of the points obtained from the permutations array.
      Real weight = one_pm;
 
      // This for loop needs to run for dim, degree, or dim+degree-i iterations,
      // whichever is largest.
      const unsigned int weight_loop_index =
        std::max(dim, std::max(degree, degree+dim-i))+1;
 
      for (unsigned int j=1; j<weight_loop_index; ++j)
        {
          if (j <= degree) // Accumulate (d+n-2i)^d term
            weight *= static_cast<Real>(degree+dim-2*i);
 
          if (j <= 2*s) // Accumulate 2^{-2s}
            weight *= 0.5;
 
          if (j <= i) // Accumulate (i!)^{-1}
            weight /= static_cast<Real>(j);
 
          if (j <= degree+dim-i) // Accumulate ( (d+n-i)! )^{-1}
            weight /= static_cast<Real>(j);
        }
 
      // This is the weight for each of the points computed previously
      for (auto j : index_range(permutations))
        _weights[offset+j] = weight;
 
      // Change sign for next iteration
      one_pm = -one_pm;
 
      // Update offset for the next set of points
      offset += permutations.size();
    }
}

References libMesh::QBase::_points, libMesh::QBase::_weights, compose_all(), dim, libMesh::index_range(), libMesh::libmesh_assert(), libMesh::Real, and libMesh::MeshTools::weight().

Referenced by init_2D(), and init_3D().

increment_constructor_count()

void libMesh::ReferenceCounter::increment_constructor_count ( const std::string &  name )

inlineprotectedinherited

Increments the construction counter.

Should be called in the constructor of any derived class that will be reference counted.

Definition at line 181 of file reference_counter.h.

{
  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
  std::pair<unsigned int, unsigned int> & p = _counts[name];
 
  p.first++;
}

References libMesh::ReferenceCounter::_counts, libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::ReferenceCountedObject().

increment_destructor_count()

void libMesh::ReferenceCounter::increment_destructor_count ( const std::string &  name )

inlineprotectedinherited

Increments the destruction counter.

Should be called in the destructor of any derived class that will be reference counted.

Definition at line 194 of file reference_counter.h.

{
  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
  std::pair<unsigned int, unsigned int> & p = _counts[name];
 
  p.second++;
}

References libMesh::ReferenceCounter::_counts, libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::~ReferenceCountedObject().

init() [1/2]

void libMesh::QBase::init ( const Elem &  elem, const std::vector< Real > &  vertex_distance_func, unsigned int  p_level = 0  )

virtualinherited

Initializes the data structures for an element potentially "cut" by a signed distance function.

The array vertex_distance_func contains vertex values of the signed distance function. If the signed distance function changes sign on the vertices, then the element is considered to be cut.) This interface can be extended by derived classes in order to subdivide the element and construct a composite quadrature rule.

Definition at line 103 of file quadrature.C.

{
  // dispatch generic implementation
  this->init(elem.type(), p_level);
}

References libMesh::QBase::init(), and libMesh::Elem::type().

init() [2/2]

void libMesh::QBase::init ( const ElemType  type = INVALID_ELEM, unsigned int  p_level = 0  )

virtualinherited

Initializes the data structures for a quadrature rule for an element of type type.

Definition at line 59 of file quadrature.C.

{
  // check to see if we have already
  // done the work for this quadrature rule
  if (t == _type && p == _p_level)
    return;
  else
    {
      _type = t;
      _p_level = p;
    }
 
 
 
  switch(_dim)
    {
    case 0:
      this->init_0D();
 
      return;
 
    case 1:
      this->init_1D();
 
      return;
 
    case 2:
      this->init_2D();
 
      return;
 
    case 3:
      this->init_3D();
 
      return;
 
    default:
      libmesh_error_msg("Invalid dimension _dim = " << _dim);
    }
}

References libMesh::QBase::_dim, libMesh::QBase::_p_level, libMesh::QBase::_type, libMesh::QBase::init_0D(), libMesh::QBase::init_1D(), libMesh::QBase::init_2D(), and libMesh::QBase::init_3D().

Referenced by libMesh::QBase::init(), libMesh::QClough::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGrid::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGauss::QGauss(), libMesh::QGaussLobatto::QGaussLobatto(), libMesh::QJacobi::QJacobi(), libMesh::QNodal::QNodal(), libMesh::QSimpson::QSimpson(), and libMesh::QTrap::QTrap().

init_0D()

void libMesh::QBase::init_0D ( const ElemType  type = INVALID_ELEM, unsigned int  p_level = 0  )

protectedvirtualinherited

Initializes the 0D quadrature rule by filling the points and weights vectors with the appropriate values.

Generally this is just one point with weight 1.

Note

The arguments should no longer be used for anything in derived classes, they are only maintained for backwards compatibility and will eventually be removed.

Definition at line 113 of file quadrature.C.

{
  _points.resize(1);
  _weights.resize(1);
  _points[0] = Point(0.);
  _weights[0] = 1.0;
}

References libMesh::QBase::_points, and libMesh::QBase::_weights.

Referenced by libMesh::QBase::init().

init_1D()

void libMesh::QGrundmann_Moller::init_1D ( const  ElemType, unsigned int    )

overrideprivatevirtual

In 1D, use a Gauss rule.

In 2D, the GM product rule is only defined for Tris. In 3D, the GM product rule is only defined for Tets.

Implements libMesh::QBase.

Definition at line 39 of file quadrature_gm.C.

{
  QGauss gauss1D(1, get_order());
 
  // Swap points and weights with the about-to-be destroyed rule.
  _points.swap(gauss1D.get_points());
  _weights.swap(gauss1D.get_weights());
}

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::get_order(), libMesh::QBase::get_points(), and libMesh::QBase::get_weights().

init_2D()

void libMesh::QGrundmann_Moller::init_2D ( const  type, unsigned int  p_level  )

overrideprivatevirtual

Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate values.

The order of the rule will be defined by the implementing class. Should not be pure virtual since a derived quadrature rule may only be defined in 1D. If not overridden, throws an error.

Note

The arguments should no longer be used for anything in derived classes, they are only maintained for backwards compatibility and will eventually be removed.

Reimplemented from libMesh::QBase.

Definition at line 27 of file quadrature_gm_2D.C.

{
  // Nearly all GM rules contain negative weights, so if you are not
  // allowing rules with negative weights, we cannot continue!
  if (!allow_rules_with_negative_weights)
    libmesh_error_msg("You requested a Grundmann-Moller rule but\n"        \
                      << "are not allowing rules with negative weights!\n" \
                      << "Either select a different quadrature class or\n" \
                      << "set allow_rules_with_negative_weights==true.");
 
  switch (_type)
    {
    case TRI3:
    case TRISHELL3:
    case TRI3SUBDIVISION:
    case TRI6:
      {
        switch(get_order())
          {
 
          default:
            {
              // Untested above _order=23 but should work...
              gm_rule(get_order()/2, /*dim=*/2);
              return;
            }
          } // end switch (order)
      } // end case TRI3, TRI6
 
    default:
      libmesh_error_msg("ERROR: Unsupported element type: " << Utility::enum_to_string(_type));
    } // end switch (_type)
}

References libMesh::QBase::_type, libMesh::QBase::allow_rules_with_negative_weights, libMesh::Utility::enum_to_string(), libMesh::QBase::get_order(), gm_rule(), libMesh::TRI3, libMesh::TRI3SUBDIVISION, libMesh::TRI6, and libMesh::TRISHELL3.

init_3D()

void libMesh::QGrundmann_Moller::init_3D ( const  type, unsigned int  p_level  )

overrideprivatevirtual

Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate values.

The order of the rule will be defined by the implementing class. Should not be pure virtual since a derived quadrature rule may only be defined in 1D. If not overridden, throws an error.

Note

The arguments should no longer be used for anything in derived classes, they are only maintained for backwards compatibility and will eventually be removed.

Reimplemented from libMesh::QBase.

Definition at line 27 of file quadrature_gm_3D.C.

{
  // Nearly all GM rules contain negative weights, so if you are not
  // allowing rules with negative weights, we cannot continue!
  if (!allow_rules_with_negative_weights)
    libmesh_error_msg("You requested a Grundmann-Moller rule but\n"        \
                      << "are not allowing rules with negative weights!\n" \
                      << "Either select a different quadrature class or\n" \
                      << "set allow_rules_with_negative_weights==true.");
 
  switch (_type)
    {
    case TET4:
    case TET10:
      {
        switch(get_order())
          {
            // We hard-code the first few orders based on output from
            // the mp-quadrature library:
            //
            // https://code.google.com/p/mp-quadrature
            //
            // The points are ordered in such a way that the amount of
            // round-off error in the quadrature calculations is
            // (hopefully) minimized.  These orderings were obtained
            // via a simple permutation optimization strategy designed
            // to produce the smallest overall average error while
            // integrating all polynomials of degree <= d.
          case CONSTANT:
          case FIRST:
            {
              _points.resize(1);
              _weights.resize(1);
 
              _points[0](0) = Real(1)/4;
              _points[0](1) = Real(1)/4;
              _points[0](2) = Real(1)/4;
 
              _weights[0] = Real(1)/6;
              return;
            }
 
          case SECOND:
          case THIRD:
            {
              _points.resize(5);
              _weights.resize(5);
 
              _points[0](0) = Real(1)/6;  _points[0](1) = Real(1)/6;  _points[0](2) = Real(1)/2;  _weights[0] =  Real(3)/40;
              _points[1](0) = Real(1)/6;  _points[1](1) = Real(1)/6;  _points[1](2) = Real(1)/6;  _weights[1] =  Real(3)/40;
              _points[2](0) = Real(1)/4;  _points[2](1) = Real(1)/4;  _points[2](2) = Real(1)/4;  _weights[2] = -Real(2)/15;
              _points[3](0) = Real(1)/2;  _points[3](1) = Real(1)/6;  _points[3](2) = Real(1)/6;  _weights[3] =  Real(3)/40;
              _points[4](0) = Real(1)/6;  _points[4](1) = Real(1)/2;  _points[4](2) = Real(1)/6;  _weights[4] =  Real(3)/40;
              return;
            }
 
          case FOURTH:
          case FIFTH:
            {
              _points.resize(15);
              _weights.resize(15);
 
              _points[ 0](0) = Real(1)/8;  _points[ 0](1) = Real(3)/8;  _points[ 0](2) = Real(1)/8;  _weights[ 0] =  Real(16)/315;
              _points[ 1](0) = Real(1)/8;  _points[ 1](1) = Real(1)/8;  _points[ 1](2) = Real(5)/8;  _weights[ 1] =  Real(16)/315;
              _points[ 2](0) = Real(3)/8;  _points[ 2](1) = Real(1)/8;  _points[ 2](2) = Real(1)/8;  _weights[ 2] =  Real(16)/315;
              _points[ 3](0) = Real(1)/6;  _points[ 3](1) = Real(1)/2;  _points[ 3](2) = Real(1)/6;  _weights[ 3] = -Real(27)/280;
              _points[ 4](0) = Real(3)/8;  _points[ 4](1) = Real(1)/8;  _points[ 4](2) = Real(3)/8;  _weights[ 4] =  Real(16)/315;
              _points[ 5](0) = Real(1)/8;  _points[ 5](1) = Real(3)/8;  _points[ 5](2) = Real(3)/8;  _weights[ 5] =  Real(16)/315;
              _points[ 6](0) = Real(1)/6;  _points[ 6](1) = Real(1)/6;  _points[ 6](2) = Real(1)/6;  _weights[ 6] = -Real(27)/280;
              _points[ 7](0) = Real(1)/6;  _points[ 7](1) = Real(1)/6;  _points[ 7](2) = Real(1)/2;  _weights[ 7] = -Real(27)/280;
              _points[ 8](0) = Real(1)/8;  _points[ 8](1) = Real(1)/8;  _points[ 8](2) = Real(1)/8;  _weights[ 8] =  Real(16)/315;
              _points[ 9](0) = Real(1)/4;  _points[ 9](1) = Real(1)/4;  _points[ 9](2) = Real(1)/4;  _weights[ 9] =    Real(2)/45;
              _points[10](0) = Real(1)/8;  _points[10](1) = Real(5)/8;  _points[10](2) = Real(1)/8;  _weights[10] =  Real(16)/315;
              _points[11](0) = Real(1)/2;  _points[11](1) = Real(1)/6;  _points[11](2) = Real(1)/6;  _weights[11] = -Real(27)/280;
              _points[12](0) = Real(1)/8;  _points[12](1) = Real(1)/8;  _points[12](2) = Real(3)/8;  _weights[12] =  Real(16)/315;
              _points[13](0) = Real(5)/8;  _points[13](1) = Real(1)/8;  _points[13](2) = Real(1)/8;  _weights[13] =  Real(16)/315;
              _points[14](0) = Real(3)/8;  _points[14](1) = Real(3)/8;  _points[14](2) = Real(1)/8;  _weights[14] =  Real(16)/315;
              return;
            }
 
          case SIXTH:
          case SEVENTH:
            {
              _points.resize(35);
              _weights.resize(35);
 
              _points[ 0](0) = Real(3)/10;  _points[ 0](1) = Real(1)/10;  _points[ 0](2) = Real(3)/10;  _weights[ 0] = Real(3125)/72576;
              _points[ 1](0) =  Real(1)/6;  _points[ 1](1) =  Real(1)/2;  _points[ 1](2) =  Real(1)/6;  _weights[ 1] =   Real(243)/4480;
              _points[ 2](0) =  Real(1)/6;  _points[ 2](1) =  Real(1)/6;  _points[ 2](2) =  Real(1)/2;  _weights[ 2] =   Real(243)/4480;
              _points[ 3](0) =  Real(1)/2;  _points[ 3](1) = Real(1)/10;  _points[ 3](2) = Real(1)/10;  _weights[ 3] = Real(3125)/72576;
              _points[ 4](0) = Real(3)/10;  _points[ 4](1) = Real(1)/10;  _points[ 4](2) = Real(1)/10;  _weights[ 4] = Real(3125)/72576;
              _points[ 5](0) = Real(3)/10;  _points[ 5](1) = Real(3)/10;  _points[ 5](2) = Real(1)/10;  _weights[ 5] = Real(3125)/72576;
              _points[ 6](0) =  Real(1)/2;  _points[ 6](1) =  Real(1)/6;  _points[ 6](2) =  Real(1)/6;  _weights[ 6] =   Real(243)/4480;
              _points[ 7](0) = Real(3)/10;  _points[ 7](1) = Real(1)/10;  _points[ 7](2) =  Real(1)/2;  _weights[ 7] = Real(3125)/72576;
              _points[ 8](0) = Real(7)/10;  _points[ 8](1) = Real(1)/10;  _points[ 8](2) = Real(1)/10;  _weights[ 8] = Real(3125)/72576;
              _points[ 9](0) =  Real(3)/8;  _points[ 9](1) =  Real(1)/8;  _points[ 9](2) =  Real(1)/8;  _weights[ 9] =  -Real(256)/2835;
              _points[10](0) = Real(3)/10;  _points[10](1) = Real(3)/10;  _points[10](2) = Real(3)/10;  _weights[10] = Real(3125)/72576;
              _points[11](0) = Real(1)/10;  _points[11](1) =  Real(1)/2;  _points[11](2) = Real(3)/10;  _weights[11] = Real(3125)/72576;
              _points[12](0) = Real(1)/10;  _points[12](1) = Real(1)/10;  _points[12](2) = Real(7)/10;  _weights[12] = Real(3125)/72576;
              _points[13](0) =  Real(1)/2;  _points[13](1) = Real(1)/10;  _points[13](2) = Real(3)/10;  _weights[13] = Real(3125)/72576;
              _points[14](0) = Real(1)/10;  _points[14](1) = Real(7)/10;  _points[14](2) = Real(1)/10;  _weights[14] = Real(3125)/72576;
              _points[15](0) = Real(1)/10;  _points[15](1) =  Real(1)/2;  _points[15](2) = Real(1)/10;  _weights[15] = Real(3125)/72576;
              _points[16](0) =  Real(1)/6;  _points[16](1) =  Real(1)/6;  _points[16](2) =  Real(1)/6;  _weights[16] =   Real(243)/4480;
              _points[17](0) =  Real(3)/8;  _points[17](1) =  Real(1)/8;  _points[17](2) =  Real(3)/8;  _weights[17] =  -Real(256)/2835;
              _points[18](0) =  Real(1)/8;  _points[18](1) =  Real(1)/8;  _points[18](2) =  Real(5)/8;  _weights[18] =  -Real(256)/2835;
              _points[19](0) = Real(1)/10;  _points[19](1) = Real(1)/10;  _points[19](2) = Real(3)/10;  _weights[19] = Real(3125)/72576;
              _points[20](0) =  Real(1)/8;  _points[20](1) =  Real(3)/8;  _points[20](2) =  Real(3)/8;  _weights[20] =  -Real(256)/2835;
              _points[21](0) =  Real(5)/8;  _points[21](1) =  Real(1)/8;  _points[21](2) =  Real(1)/8;  _weights[21] =  -Real(256)/2835;
              _points[22](0) =  Real(1)/8;  _points[22](1) =  Real(5)/8;  _points[22](2) =  Real(1)/8;  _weights[22] =  -Real(256)/2835;
              _points[23](0) = Real(1)/10;  _points[23](1) = Real(3)/10;  _points[23](2) = Real(1)/10;  _weights[23] = Real(3125)/72576;
              _points[24](0) =  Real(1)/4;  _points[24](1) =  Real(1)/4;  _points[24](2) =  Real(1)/4;  _weights[24] =     -Real(8)/945;
              _points[25](0) =  Real(1)/8;  _points[25](1) =  Real(1)/8;  _points[25](2) =  Real(3)/8;  _weights[25] =  -Real(256)/2835;
              _points[26](0) =  Real(3)/8;  _points[26](1) =  Real(3)/8;  _points[26](2) =  Real(1)/8;  _weights[26] =  -Real(256)/2835;
              _points[27](0) =  Real(1)/8;  _points[27](1) =  Real(3)/8;  _points[27](2) =  Real(1)/8;  _weights[27] =  -Real(256)/2835;
              _points[28](0) = Real(1)/10;  _points[28](1) = Real(3)/10;  _points[28](2) =  Real(1)/2;  _weights[28] = Real(3125)/72576;
              _points[29](0) = Real(3)/10;  _points[29](1) =  Real(1)/2;  _points[29](2) = Real(1)/10;  _weights[29] = Real(3125)/72576;
              _points[30](0) = Real(1)/10;  _points[30](1) = Real(1)/10;  _points[30](2) =  Real(1)/2;  _weights[30] = Real(3125)/72576;
              _points[31](0) =  Real(1)/2;  _points[31](1) = Real(3)/10;  _points[31](2) = Real(1)/10;  _weights[31] = Real(3125)/72576;
              _points[32](0) =  Real(1)/8;  _points[32](1) =  Real(1)/8;  _points[32](2) =  Real(1)/8;  _weights[32] =  -Real(256)/2835;
              _points[33](0) = Real(1)/10;  _points[33](1) = Real(3)/10;  _points[33](2) = Real(3)/10;  _weights[33] = Real(3125)/72576;
              _points[34](0) = Real(1)/10;  _points[34](1) = Real(1)/10;  _points[34](2) = Real(1)/10;  _weights[34] = Real(3125)/72576;
              return;
            }
 
          default:
            {
              // Untested above _order=23 but should work...
              gm_rule(get_order()/2, /*dim=*/3);
              return;
            }
          } // end switch (order)
      } // end case TET4, TET10
 
    default:
      libmesh_error_msg("ERROR: Unsupported element type: " << Utility::enum_to_string(_type));
    } // end switch (_type)
}

References libMesh::QBase::_points, libMesh::QBase::_type, libMesh::QBase::_weights, libMesh::QBase::allow_rules_with_negative_weights, libMesh::CONSTANT, libMesh::Utility::enum_to_string(), libMesh::FIFTH, libMesh::FIRST, libMesh::FOURTH, libMesh::QBase::get_order(), gm_rule(), libMesh::Real, libMesh::SECOND, libMesh::SEVENTH, libMesh::SIXTH, libMesh::TET10, libMesh::TET4, and libMesh::THIRD.

n_objects()

static unsigned int libMesh::ReferenceCounter::n_objects ( )

inlinestaticinherited

Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 83 of file reference_counter.h.

  { return _n_objects; }

References libMesh::ReferenceCounter::_n_objects.

n_points()

unsigned int libMesh::QBase::n_points ( ) const

inlineinherited

Returns

The number of points associated with the quadrature rule.

Definition at line 126 of file quadrature.h.

  {
    libmesh_assert (!_points.empty());
    return cast_int<unsigned int>(_points.size());
  }

References libMesh::QBase::_points, and libMesh::libmesh_assert().

Referenced by libMesh::ExactSolution::_compute_error(), assemble(), assemble_1D(), assemble_ellipticdg(), assemble_helmholtz(), assemble_poisson(), assemble_shell(), assemble_wave(), assembly_with_dg_fem_context(), AssemblyA0::boundary_assembly(), AssemblyF0::boundary_assembly(), AssemblyA1::boundary_assembly(), AssemblyF1::boundary_assembly(), AssemblyF2::boundary_assembly(), A2::boundary_assembly(), AssemblyA2::boundary_assembly(), A3::boundary_assembly(), F0::boundary_assembly(), Output0::boundary_assembly(), libMesh::System::calculate_norm(), libMesh::FirstOrderUnsteadySolver::compute_second_order_eqns(), libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), SecondOrderScalarSystemSecondOrderTimeSolverBase::damping_residual(), SecondOrderScalarSystemFirstOrderTimeSolverBase::damping_residual(), NavierSystem::element_constraint(), CoupledSystem::element_constraint(), PoissonSystem::element_postprocess(), LaplaceSystem::element_postprocess(), LaplaceQoI::element_qoi(), LaplaceQoI::element_qoi_derivative(), LaplaceSystem::element_qoi_derivative(), HeatSystem::element_qoi_derivative(), NavierSystem::element_time_derivative(), SolidSystem::element_time_derivative(), PoissonSystem::element_time_derivative(), LaplaceSystem::element_time_derivative(), CurlCurlSystem::element_time_derivative(), ElasticitySystem::element_time_derivative(), L2System::element_time_derivative(), CoupledSystem::element_time_derivative(), FirstOrderScalarSystemBase::element_time_derivative(), SecondOrderScalarSystemFirstOrderTimeSolverBase::element_time_derivative(), libMesh::RBEIMConstruction::enrich_RB_space(), A0::interior_assembly(), B::interior_assembly(), M0::interior_assembly(), A1::interior_assembly(), AssemblyA0::interior_assembly(), EIM_IP_assembly::interior_assembly(), AcousticsInnerProduct::interior_assembly(), AssemblyA1::interior_assembly(), A2::interior_assembly(), AssemblyA2::interior_assembly(), EIM_F::interior_assembly(), F0::interior_assembly(), OutputAssembly::interior_assembly(), InnerProductAssembly::interior_assembly(), AssemblyEIM::interior_assembly(), AssemblyF0::interior_assembly(), AssemblyF1::interior_assembly(), Ex6InnerProduct::interior_assembly(), Ex6EIMInnerProduct::interior_assembly(), LaplaceYoung::jacobian(), NavierSystem::mass_residual(), ElasticitySystem::mass_residual(), libMesh::FEMPhysics::mass_residual(), FirstOrderScalarSystemBase::mass_residual(), SecondOrderScalarSystemSecondOrderTimeSolverBase::mass_residual(), SecondOrderScalarSystemFirstOrderTimeSolverBase::mass_residual(), libMesh::QBase::print_info(), LaplaceYoung::residual(), LaplaceSystem::side_constraint(), LaplaceSystem::side_postprocess(), CoupledSystemQoI::side_qoi(), CoupledSystemQoI::side_qoi_derivative(), LaplaceSystem::side_qoi_derivative(), SolidSystem::side_time_derivative(), CurlCurlSystem::side_time_derivative(), ElasticitySystem::side_time_derivative(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and libMesh::RBEIMConstruction::truth_solve().

operator=() [1/2]

QGrundmann_Moller& libMesh::QGrundmann_Moller::operator= ( const QGrundmann_Moller &  )

default

operator=() [2/2]

QGrundmann_Moller& libMesh::QGrundmann_Moller::operator= ( QGrundmann_Moller &&  )

default

print_info() [1/2]

void libMesh::QBase::print_info ( std::ostream &  os = libMesh::out ) const

inherited

Prints information relevant to the quadrature rule, by default to libMesh::out.

Definition at line 37 of file quadrature.C.

{
  libmesh_assert(!_points.empty());
  libmesh_assert(!_weights.empty());
 
  Real summed_weights=0;
  os << "N_Q_Points=" << this->n_points() << std::endl << std::endl;
  for (auto qpoint: index_range(_points))
    {
      os << " Point " << qpoint << ":\n"
         << "  "
         << _points[qpoint]
         << "\n Weight:\n "
         << "  w=" << _weights[qpoint] << "\n" << std::endl;
 
      summed_weights += _weights[qpoint];
    }
  os << "Summed Weights: " << summed_weights << std::endl;
}

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::index_range(), libMesh::libmesh_assert(), libMesh::QBase::n_points(), and libMesh::Real.

Referenced by libMesh::operator<<().

print_info() [2/2]

void libMesh::ReferenceCounter::print_info ( std::ostream &  out = libMesh::out )

staticinherited

Prints the reference information, by default to libMesh::out.

Definition at line 87 of file reference_counter.C.

{
  if (_enable_print_counter)
    out_stream << ReferenceCounter::get_info();
}

References libMesh::ReferenceCounter::_enable_print_counter, and libMesh::ReferenceCounter::get_info().

qp()

Point libMesh::QBase::qp ( const unsigned int  i ) const

inlineinherited

Returns

The \( i^{th} \) quadrature point in reference element space.

Definition at line 164 of file quadrature.h.

  {
    libmesh_assert_less (i, _points.size());
    return _points[i];
  }

References libMesh::QBase::_points.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), and libMesh::QBase::tensor_product_quad().

scale()

void libMesh::QBase::scale ( std::pair< Real, Real >  old_range, std::pair< Real, Real >  new_range  )

inherited

Maps the points of a 1D quadrature rule defined by "old_range" to another 1D interval defined by "new_range" and scales the weights accordingly.

Definition at line 137 of file quadrature.C.

{
  // Make sure we are in 1D
  libmesh_assert_equal_to (_dim, 1);
 
  Real
    h_new = new_range.second - new_range.first,
    h_old = old_range.second - old_range.first;
 
  // Make sure that we have sane ranges
  libmesh_assert_greater (h_new, 0.);
  libmesh_assert_greater (h_old, 0.);
 
  // Make sure there are some points
  libmesh_assert_greater (_points.size(), 0);
 
  // Compute the scale factor
  Real scfact = h_new/h_old;
 
  // We're mapping from old_range -> new_range
  for (auto i : index_range(_points))
    {
      _points[i](0) = new_range.first +
        (_points[i](0) - old_range.first) * scfact;
 
      // Scale the weights
      _weights[i] *= scfact;
    }
}

References libMesh::QBase::_dim, libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::index_range(), and libMesh::Real.

Referenced by libMesh::QConical::conical_product_tet(), and libMesh::QConical::conical_product_tri().

shapes_need_reinit()

virtual bool libMesh::QBase::shapes_need_reinit ( )

inlinevirtualinherited

Returns

true if the shape functions need to be recalculated, false otherwise.

This may be required if the number of quadrature points or their position changes.

Definition at line 239 of file quadrature.h.

{ return false; }

tensor_product_hex()

void libMesh::QBase::tensor_product_hex ( const QBase &  q1D )

protectedinherited

Computes the tensor product quadrature rule [q1D x q1D x q1D] from the 1D rule q1D.

Used in the init_3D routines for hexahedral element types.

Definition at line 198 of file quadrature.C.

{
  const unsigned int np = q1D.n_points();
 
  _points.resize(np * np * np);
 
  _weights.resize(np * np * np);
 
  unsigned int q=0;
 
  for (unsigned int k=0; k<np; k++)
    for (unsigned int j=0; j<np; j++)
      for (unsigned int i=0; i<np; i++)
        {
          _points[q](0) = q1D.qp(i)(0);
          _points[q](1) = q1D.qp(j)(0);
          _points[q](2) = q1D.qp(k)(0);
 
          _weights[q] = q1D.w(i) * q1D.w(j) * q1D.w(k);
 
          q++;
        }
}

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGrid::init_3D(), libMesh::QSimpson::init_3D(), and libMesh::QGauss::init_3D().

tensor_product_prism()

void libMesh::QBase::tensor_product_prism ( const QBase &  q1D, const QBase &  q2D  )

protectedinherited

Computes the tensor product of a 1D quadrature rule and a 2D quadrature rule.

Used in the init_3D routines for prismatic element types.

Definition at line 225 of file quadrature.C.

{
  const unsigned int n_points1D = q1D.n_points();
  const unsigned int n_points2D = q2D.n_points();
 
  _points.resize  (n_points1D * n_points2D);
  _weights.resize (n_points1D * n_points2D);
 
  unsigned int q=0;
 
  for (unsigned int j=0; j<n_points1D; j++)
    for (unsigned int i=0; i<n_points2D; i++)
      {
        _points[q](0) = q2D.qp(i)(0);
        _points[q](1) = q2D.qp(i)(1);
        _points[q](2) = q1D.qp(j)(0);
 
        _weights[q] = q2D.w(i) * q1D.w(j);
 
        q++;
      }
 
}

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), and libMesh::QGauss::init_3D().

tensor_product_quad()

void libMesh::QBase::tensor_product_quad ( const QBase &  q1D )

protectedinherited

Constructs a 2D rule from the tensor product of q1D with itself.

Used in the init_2D() routines for quadrilateral element types.

Definition at line 171 of file quadrature.C.

{
 
  const unsigned int np = q1D.n_points();
 
  _points.resize(np * np);
 
  _weights.resize(np * np);
 
  unsigned int q=0;
 
  for (unsigned int j=0; j<np; j++)
    for (unsigned int i=0; i<np; i++)
      {
        _points[q](0) = q1D.qp(i)(0);
        _points[q](1) = q1D.qp(j)(0);
 
        _weights[q] = q1D.w(i)*q1D.w(j);
 
        q++;
      }
}

References libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::QBase::n_points(), libMesh::QBase::qp(), and libMesh::QBase::w().

Referenced by libMesh::QGaussLobatto::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QSimpson::init_2D(), and libMesh::QGauss::init_2D().

type()

QuadratureType libMesh::QGrundmann_Moller::type ( ) const

overridevirtual

Returns

QGRUNDMANN_MOLLER.

Implements libMesh::QBase.

Definition at line 32 of file quadrature_gm.C.

{
  return QGRUNDMANN_MOLLER;
}

References libMesh::QGRUNDMANN_MOLLER.

w()

Real libMesh::QBase::w ( const unsigned int  i ) const

inlineinherited

Returns

The \( i^{th} \) quadrature weight.

Definition at line 173 of file quadrature.h.

  {
    libmesh_assert_less (i, _weights.size());
    return _weights[i];
  }

References libMesh::QBase::_weights.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), and libMesh::QBase::tensor_product_quad().

Member Data Documentation

_counts

ReferenceCounter::Counts libMesh::ReferenceCounter::_counts

staticprotectedinherited

Actually holds the data.

Definition at line 122 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::get_info(), libMesh::ReferenceCounter::increment_constructor_count(), and libMesh::ReferenceCounter::increment_destructor_count().

_dim

unsigned int libMesh::QBase::_dim

protectedinherited

The spatial dimension of the quadrature rule.

Definition at line 339 of file quadrature.h.

Referenced by libMesh::QBase::build(), libMesh::QBase::get_dim(), libMesh::QBase::init(), libMesh::QGaussLobatto::QGaussLobatto(), libMesh::QJacobi::QJacobi(), libMesh::QNodal::QNodal(), libMesh::QSimpson::QSimpson(), libMesh::QTrap::QTrap(), and libMesh::QBase::scale().

_enable_print_counter

bool libMesh::ReferenceCounter::_enable_print_counter = true

staticprotectedinherited

Flag to control whether reference count information is printed when print_info is called.

Definition at line 141 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::disable_print_counter_info(), libMesh::ReferenceCounter::enable_print_counter_info(), and libMesh::ReferenceCounter::print_info().

_mutex

Threads::spin_mutex libMesh::ReferenceCounter::_mutex

staticprotectedinherited

Mutual exclusion object to enable thread-safe reference counting.

Definition at line 135 of file reference_counter.h.

_n_objects

Threads::atomic< unsigned int > libMesh::ReferenceCounter::_n_objects

staticprotectedinherited

The number of objects.

Print the reference count information when the number returns to 0.

Definition at line 130 of file reference_counter.h.

Referenced by libMesh::ReferenceCounter::n_objects(), libMesh::ReferenceCounter::ReferenceCounter(), and libMesh::ReferenceCounter::~ReferenceCounter().

_order

Order libMesh::QBase::_order

protectedinherited

The polynomial order which the quadrature rule is capable of integrating exactly.

Definition at line 345 of file quadrature.h.

Referenced by libMesh::QBase::build(), libMesh::QBase::get_order(), libMesh::QClough::init_1D(), libMesh::QGaussLobatto::init_1D(), libMesh::QGrid::init_1D(), libMesh::QGauss::init_1D(), libMesh::QNodal::init_1D(), libMesh::QJacobi::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QGrid::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGrid::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), and libMesh::QMonomial::init_3D().

_p_level

unsigned int libMesh::QBase::_p_level

protectedinherited

The p-level of the element for which the current values have been computed.

Definition at line 357 of file quadrature.h.

Referenced by libMesh::QBase::get_order(), libMesh::QBase::get_p_level(), libMesh::QBase::init(), libMesh::QClough::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), and libMesh::QMonomial::init_3D().

_points

std::vector<Point> libMesh::QBase::_points

protectedinherited

The locations of the quadrature points in reference element space.

Definition at line 363 of file quadrature.h.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QGauss::dunavant_rule(), libMesh::QGauss::dunavant_rule2(), libMesh::QBase::get_points(), gm_rule(), libMesh::QBase::init_0D(), libMesh::QClough::init_1D(), libMesh::QGaussLobatto::init_1D(), libMesh::QTrap::init_1D(), libMesh::QConical::init_1D(), libMesh::QGrid::init_1D(), libMesh::QGauss::init_1D(), libMesh::QSimpson::init_1D(), libMesh::QNodal::init_1D(), libMesh::QJacobi::init_1D(), libMesh::QMonomial::init_1D(), init_1D(), libMesh::QClough::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QGauss::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), init_3D(), libMesh::QGauss::keast_rule(), libMesh::QMonomial::kim_rule(), libMesh::QBase::n_points(), libMesh::QBase::print_info(), libMesh::QBase::qp(), libMesh::QBase::scale(), libMesh::QMonomial::stroud_rule(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), and libMesh::QMonomial::wissmann_rule().

_type

ElemType libMesh::QBase::_type

protectedinherited

The type of element for which the current values have been computed.

Definition at line 351 of file quadrature.h.

Referenced by libMesh::QBase::get_elem_type(), libMesh::QBase::init(), libMesh::QClough::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QConical::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), init_2D(), libMesh::QClough::init_3D(), libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGrid::init_3D(), libMesh::QConical::init_3D(), libMesh::QGauss::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), and init_3D().

_weights

std::vector<Real> libMesh::QBase::_weights

protectedinherited

The quadrature weights.

The order of the weights matches the ordering of the _points vector.

Definition at line 369 of file quadrature.h.

Referenced by libMesh::QConical::conical_product_pyramid(), libMesh::QConical::conical_product_tet(), libMesh::QConical::conical_product_tri(), libMesh::QGauss::dunavant_rule(), libMesh::QGauss::dunavant_rule2(), libMesh::QBase::get_weights(), gm_rule(), libMesh::QBase::init_0D(), libMesh::QClough::init_1D(), libMesh::QGaussLobatto::init_1D(), libMesh::QConical::init_1D(), libMesh::QTrap::init_1D(), libMesh::QGrid::init_1D(), libMesh::QGauss::init_1D(), libMesh::QSimpson::init_1D(), libMesh::QNodal::init_1D(), libMesh::QJacobi::init_1D(), libMesh::QMonomial::init_1D(), init_1D(), libMesh::QClough::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QNodal::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), init_3D(), libMesh::QGauss::keast_rule(), libMesh::QMonomial::kim_rule(), libMesh::QBase::print_info(), libMesh::QBase::scale(), libMesh::QMonomial::stroud_rule(), libMesh::QBase::tensor_product_hex(), libMesh::QBase::tensor_product_prism(), libMesh::QBase::tensor_product_quad(), libMesh::QBase::w(), and libMesh::QMonomial::wissmann_rule().

allow_rules_with_negative_weights

bool libMesh::QBase::allow_rules_with_negative_weights

inherited

Flag (default true) controlling the use of quadrature rules with negative weights.

Set this to false to require rules with all positive weights.

Rules with negative weights can be unsuitable for some problems. For example, it is possible for a rule with negative weights to obtain a negative result when integrating a positive function.

A particular example: if rules with negative weights are not allowed, a request for TET,THIRD (5 points) will return the TET,FIFTH (14 points) rule instead, nearly tripling the computational effort required!

Definition at line 254 of file quadrature.h.

Referenced by init_2D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), and init_3D().

---

The documentation for this class was generated from the following files:

• include/quadrature/quadrature_gm.h
• src/quadrature/quadrature_gm.C
• src/quadrature/quadrature_gm_2D.C
• src/quadrature/quadrature_gm_3D.C