libMesh::QNodal Class Reference

This class implements nodal quadrature rules for various element types. More...

#include <quadrature_nodal.h>

Inheritance diagram for libMesh::QNodal:

Public Member Functions
	QNodal (unsigned int dim, Order order=FIRST)
	Constructor. More...
	QNodal (const QNodal &)=default
	Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class. More...
	QNodal (QNodal &&)=default
QNodal &	operator= (const QNodal &)=default
QNodal &	operator= (QNodal &&)=default
virtual	~QNodal ()=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
	Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate values. 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...

Detailed Description

This class implements nodal quadrature rules for various element types.

For some element types, this corresponds to well-known quadratures such as the trapezoidal rule and Simpson's rule. For other element types (e.g. the serendipity QUAD8/HEX20/PRISM15) it implements a lower-order-accurate nodal quadrature which still generates a strictly positive definite (diagonal) mass matrix. Since the main purpose of this class is provide appropriate nodal quadrature rules, "order" arguments passed during initialization are ignored.

Author

John W. Peterson

Date

2019

Implements nodal quadrature for various element types.

Definition at line 44 of file quadrature_nodal.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

QNodal() [1/3]

libMesh::QNodal::QNodal ( unsigned int  dim, Order  order = FIRST  )

inlineexplicit

Constructor.

Declares the order of the quadrature rule. We explicitly call the init function in 1D since the other tensor-product rules require this one.

Note

The element type, EDGE2, will not be used internally, however if we called the function with INVALID_ELEM it would try to be smart and return, thinking it had already done the work.

Definition at line 58 of file quadrature_nodal.h.

                            :
    QBase(dim,order)
  {
    if (_dim == 1)
      init(EDGE2);
  }

References libMesh::QBase::_dim, libMesh::EDGE2, and libMesh::QBase::init().

QNodal() [2/3]

libMesh::QNodal::QNodal ( const QNodal &  )

default

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

QNodal() [3/3]

libMesh::QNodal::QNodal ( QNodal &&  )

default

~QNodal()

virtual libMesh::QNodal::~QNodal ( )

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().

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(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QGauss::init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrundmann_Moller::init_2D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::QGrundmann_Moller::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(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGauss::init_3D(), 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(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QClough::init_2D(), libMesh::QGauss::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGauss::init_3D(), init_3D(), and libMesh::QMonomial::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(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QGrid::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGauss::QGauss(), libMesh::QGaussLobatto::QGaussLobatto(), libMesh::QJacobi::QJacobi(), 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::QNodal::init_1D ( const  type, unsigned int  p_level  )

overrideprivatevirtual

Initializes the 1D 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. It is assumed that derived quadrature rules will at least define the init_1D function, therefore it is pure virtual.

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.

Implements libMesh::QBase.

Definition at line 29 of file quadrature_nodal_1D.C.

{
  switch (_type)
    {
    case EDGE2:
      {
        // Nodal quadrature on an Edge2 is QTrap
        QTrap rule(/*dim=*/1, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
    case EDGE3:
      {
        // Nodal quadrature on an Edge3 is QSimpson
        QSimpson rule(/*dim=*/1, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
    case EDGE4:
      {
        // The 4-point variant of Simpson's rule. The quadrature
        // points are in the same order as the reference element
        // nodes.
        _points = {Point(-1,0.,0.), Point(+1,0.,0.),
                   Point(-Real(1)/3,0.,0.), Point(Real(1)/3,0.,0.)};
        _weights = {0.25, 0.25, 0.75, 0.75};
        return;
      }
    default:
      libmesh_error_msg("Element type not supported:" << Utility::enum_to_string(_type));
    }
}

References libMesh::QBase::_order, libMesh::QBase::_p_level, libMesh::QBase::_points, libMesh::QBase::_type, libMesh::QBase::_weights, libMesh::EDGE2, libMesh::EDGE3, libMesh::EDGE4, libMesh::Utility::enum_to_string(), libMesh::QBase::get_points(), libMesh::QBase::get_weights(), libMesh::QBase::init(), and libMesh::Real.

init_2D()

void libMesh::QNodal::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 29 of file quadrature_nodal_2D.C.

{
#if LIBMESH_DIM > 1
 
  switch (_type)
    {
 
    case QUAD4:
    case QUADSHELL4:
    case TRI3:
    case TRISHELL3:
      {
        QTrap rule(/*dim=*/2, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
 
    case QUAD8:
    case QUADSHELL8:
      {
        // A rule with 8 points which is exact for linears, and
        // naturally produces a lumped approximation to the mass
        // matrix. The quadrature points are numbered the same way as
        // the reference element nodes.
        _points =
          {
            Point(-1,-1), Point(+1,-1), Point(+1,+1), Point(-1,+1),
            Point(0.,-1), Point(+1,0.), Point(0.,+1), Point(-1,0.)
          };
 
        // The weights for the Quad8 nodal quadrature rule are
        // obtained from the following specific steps. Other
        // "serendipity" type rules are obtained similarly.
        //
        // 1.) Due to the symmetry of the bi-unit square domain, we
        // first note that there are only two "classes" of node in the
        // Quad8: vertices (with associated weight wv) and edges (with
        // associated weight we).
        //
        // 2.) In order for such a nodal quadrature rule to be exact
        // for constants, the weights must sum to the area of the
        // reference element, and therefore we must have:
        // 4*wv + 4*we = 4 --> wv + we = 1
        //
        // 3.) Due to symmetry (once again), such a rule is then
        // automatically exact for the linear polynomials "x" and "y",
        // regardless of the values of wv and we.
        //
        // 4.) We therefore still have two unknowns and one equation.
        // Attempting to additionally make the nodal quadrature rule
        // exact for the quadratic polynomials "x^2" and "y^2" leads
        // to a rule with negative weights, namely:
        // wv = -1/3
        // we = 4/3
        // Note: these are the same values one obtains by integrating
        // the corresponding Quad8 Lagrange basis functions over the
        // reference element.
        //
        // Since the weights appear on the diagonal of the nodal
        // quadrature rule's approximation to the mass matrix, rules
        // with negative weights yield an indefinite mass matrix,
        // i.e. one with both positive and negative eigenvalues. Rules
        // with negative weights can also produce a negative integral
        // approximation to a strictly positive integrand, which may
        // be unacceptable in some situations.
        //
        // 5.) Requiring all positive weights therefore restricts the
        // nodal quadrature rule to only be exact for linears. But
        // there is still one free parameter remaining, and thus we
        // need some other criterion in order to complete the
        // description of the rule.
        //
        // Here, we have decided to choose the quadrature weights in
        // such a way that the resulting nodal quadrature mass matrix
        // approximation is "proportional" to the true mass matrix's
        // diagonal entries for the reference element. We therefore
        // pose the following constrained optimization problem:
        //
        //     { min_{wv, we} |diag(M) - C*diag(W)|^2
        // (O) {
        //     { subject to wv + we = 1
        //
        // where:
        // * M is the true mass matrix
        // * W is the nodal quadrature approximation to the mass
        //   matrix. In this particular case:
        //   diag(W) = [wv,wv,wv,wv,we,we,we,we]
        // * C = tr(M) / vol(E) is the ratio between the trace of the
        //   true mass matrix and the volume of the reference
        //   element. For all Lagrange finite elements, we have C<1.
        //
        // 6.) The optimization problem (O) is solved directly by
        // substituting the algebraic constraint into the functional
        // which is to be minimized, then setting the derivative with
        // respect to the remaining parameter equal to zero and
        // solving. In the Quad8 and Hex20 cases, there is only one
        // free parameter, while in the Prism15 case there are two
        // free parameters, so a 2x2 system of linear equations must
        // be solved.
        Real wv = Real(12) / 79;
        Real we = Real(67) / 79;
 
        _weights = {wv, wv, wv, wv, we, we, we, we};
 
        return;
      }
 
    case QUAD9:
    case TRI6:
      {
        QSimpson rule(/*dim=*/2, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
 
    default:
      libmesh_error_msg("Element type not supported!:" << Utility::enum_to_string(_type));
    }
#endif
}

References libMesh::QBase::_order, libMesh::QBase::_p_level, libMesh::QBase::_points, libMesh::QBase::_type, libMesh::QBase::_weights, libMesh::Utility::enum_to_string(), libMesh::QBase::get_points(), libMesh::QBase::get_weights(), libMesh::QBase::init(), libMesh::QUAD4, libMesh::QUAD8, libMesh::QUAD9, libMesh::QUADSHELL4, libMesh::QUADSHELL8, libMesh::Real, libMesh::TRI3, libMesh::TRI6, and libMesh::TRISHELL3.

init_3D()

void libMesh::QNodal::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 29 of file quadrature_nodal_3D.C.

{
#if LIBMESH_DIM == 3
 
  switch (_type)
    {
    case TET4:
    case PRISM6:
    case HEX8:
      {
        QTrap rule(/*dim=*/3, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
 
    case PRISM15:
      {
        // A rule with 15 points which is exact for linears, and
        // naturally produces a lumped approximation to the mass
        // matrix. The quadrature points are numbered the same way as
        // the reference element nodes.
        _points =
          {
            Point(0.,0.,-1), Point(+1,0.,-1), Point(0.,+1,-1),
            Point(0.,0.,+1), Point(+1,0.,+1), Point(0.,+1,+1),
            Point(.5,0.,-1), Point(.5,.5,-1), Point(0.,.5,-1),
            Point(0.,0.,0.), Point(+1,0.,0.), Point(0.,+1,0.),
            Point(.5,0.,+1), Point(.5,.5,+1), Point(0.,.5,+1),
          };
 
        // vertex (wv), tri edge (wt), and quad edge (wq) weights are
        // obtained using the same approach that was used for the Quad8,
        // see quadrature_nodal_2D.C for details.
        Real wv = Real(1) / 34;
        Real wt = Real(4) / 51;
        Real wq = Real(2) / 17;
 
        _weights = {wv, wv, wv, wv, wv, wv,
                    wt, wt, wt,
                    wq, wq, wq,
                    wt, wt, wt};
 
        return;
      }
 
    case HEX20:
      {
        // A rule with 20 points which is exact for linears, and
        // naturally produces a lumped approximation to the mass
        // matrix. The quadrature points are numbered the same way as
        // the reference element nodes.
        _points =
          {
            Point(-1,-1,-1), Point(+1,-1,-1), Point(+1,+1,-1), Point(-1,+1,-1),
            Point(-1,-1,+1), Point(+1,-1,+1), Point(+1,+1,+1), Point(-1,+1,+1),
            Point(0.,-1,-1), Point(+1,0.,-1), Point(0.,+1,-1), Point(-1,0.,-1),
            Point(-1,-1,0.), Point(+1,-1,0.), Point(+1,+1,0.), Point(-1,+1,0.),
            Point(0.,-1,+1), Point(+1,0.,+1), Point(0.,+1,+1), Point(-1,0.,+1)
          };
 
        // vertex (wv), and edge (we) weights are obtained using the
        // same approach that was used for the Quad8, see
        // quadrature_nodal_2D.C for details.
        Real wv = Real(7) / 31;
        Real we = Real(16) / 31;
 
        _weights = {wv, wv, wv, wv, wv, wv, wv, wv,
                    we, we, we, we, we, we, we, we, we, we, we, we};
 
        return;
      }
 
    case TET10:
    case PRISM18:
    case HEX27:
      {
        QSimpson rule(/*dim=*/3, /*ignored*/_order);
        rule.init(_type, /*ignored*/_p_level);
        _points.swap (rule.get_points());
        _weights.swap(rule.get_weights());
        return;
      }
 
    default:
      libmesh_error_msg("ERROR: Unsupported type: " << Utility::enum_to_string(_type));
    }
#endif
}

References libMesh::QBase::_order, libMesh::QBase::_p_level, libMesh::QBase::_points, libMesh::QBase::_type, libMesh::QBase::_weights, libMesh::Utility::enum_to_string(), libMesh::QBase::get_points(), libMesh::QBase::get_weights(), libMesh::HEX20, libMesh::HEX27, libMesh::HEX8, libMesh::QBase::init(), libMesh::PRISM15, libMesh::PRISM18, libMesh::PRISM6, libMesh::Real, libMesh::TET10, and libMesh::TET4.

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(), B::interior_assembly(), A0::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]

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

default

operator=() [2/2]

QNodal& libMesh::QNodal::operator= ( QNodal &&  )

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::QNodal::type ( ) const

overridevirtual

Returns

QNODAL.

Implements libMesh::QBase.

Definition at line 26 of file quadrature_nodal.C.

{
  return QNODAL;
}

References libMesh::QNODAL.

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(), 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(), 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(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGrid::init_3D(), libMesh::QGauss::init_3D(), 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(), init_1D(), libMesh::QMonomial::init_1D(), libMesh::QClough::init_2D(), libMesh::QGaussLobatto::init_2D(), libMesh::QGauss::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGaussLobatto::init_3D(), libMesh::QGauss::init_3D(), 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(), libMesh::QGrundmann_Moller::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(), init_1D(), libMesh::QJacobi::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QClough::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QGauss::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGrundmann_Moller::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(), 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(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrundmann_Moller::init_2D(), libMesh::QClough::init_3D(), libMesh::QGaussLobatto::init_3D(), libMesh::QTrap::init_3D(), libMesh::QGrid::init_3D(), libMesh::QConical::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), init_3D(), libMesh::QMonomial::init_3D(), and libMesh::QGrundmann_Moller::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(), libMesh::QGrundmann_Moller::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(), init_1D(), libMesh::QJacobi::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::init_1D(), libMesh::QClough::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGrid::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), init_2D(), libMesh::QMonomial::init_2D(), libMesh::QGrid::init_3D(), libMesh::QTrap::init_3D(), libMesh::QSimpson::init_3D(), libMesh::QGauss::init_3D(), init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGrundmann_Moller::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 libMesh::QGrundmann_Moller::init_2D(), libMesh::QGauss::init_3D(), libMesh::QMonomial::init_3D(), and libMesh::QGrundmann_Moller::init_3D().

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

• include/quadrature/quadrature_nodal.h
• src/quadrature/quadrature_nodal.C
• src/quadrature/quadrature_nodal_1D.C
• src/quadrature/quadrature_nodal_2D.C
• src/quadrature/quadrature_nodal_3D.C