This class defines alternate quadrature rules on "tensor-product" elements (quadrilaterals and hexahedra) which can be useful when integrating monomial finite element bases. More...

#include <quadrature_monomial.h>

Inheritance diagram for libMesh::QMonomial:

[legend]

Public Member Functions
	QMonomial (unsigned int dim, Order order=INVALID_ORDER)
	Constructor. More...

	QMonomial (const QMonomial &)=default
	Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class. More...

	QMonomial (QMonomial &&)=default

QMonomial &	operator= (const QMonomial &)=default

QMonomial &	operator= (QMonomial &&)=default

virtual	~QMonomial ()=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
	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=0) override
	Just uses a Gauss rule in 1D. More...

virtual void	init_2D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0) override
	More efficient rules for quadrilaterals. More...

virtual void	init_3D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0) override
	More efficient rules for hexahedra. More...

void	wissmann_rule (const Real rule_data[][3], const unsigned int n_pts)
	Wissmann published three interesting "partially symmetric" rules for integrating degree 4, 6, and 8 polynomials exactly on QUADs. More...

void	stroud_rule (const Real rule_data[][3], const unsigned int *rule_symmetry, const unsigned int n_pts)
	Stroud's rules for quads and hexes can have one of several different types of symmetry. More...

void	kim_rule (const Real rule_data[][4], const unsigned int *rule_id, const unsigned int n_pts)
	Rules from Kim and Song, Comm. More...

Detailed Description

This class defines alternate quadrature rules on "tensor-product" elements (quadrilaterals and hexahedra) which can be useful when integrating monomial finite element bases.

While tensor product rules are optimal for integrating bi/tri-linear, bi/tri-quadratic, etc. (i.e. tensor product) bases (which consist of incomplete polynomials up to degree=dim*p) they are not optimal for the MONOMIAL or FEXYZ bases, which consist of complete polynomials of degree=p.

This class provides quadrature rules which are more efficient than tensor product rules when they are available, and falls back on Gaussian quadrature rules otherwise.

A number of these rules have been helpfully collected in electronic form by: Prof. Ronald Cools Katholieke Universiteit Leuven, Dept. Computerwetenschappen http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html A username and password to access the tables is available by request.

We also provide the original reference for each rule when it is available.

Author: John W. Peterson

Date: 2008 Implements quadrature rules for non-tensor polynomials.

Definition at line 58 of file quadrature_monomial.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

◆ QMonomial() [1/3]

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

Constructor.

Declares the order of the quadrature rule.

Definition at line 65 of file quadrature_monomial.h.

                                         :
     QBase(dim,order)
   {}

◆ QMonomial() [2/3]

libMesh::QMonomial::QMonomial ( const QMonomial & )

default

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

◆ QMonomial() [3/3]

libMesh::QMonomial::QMonomial ( QMonomial && )

default

◆ ~QMonomial()

virtual libMesh::QMonomial::~QMonomial ( )

virtualdefault

Member Function Documentation

◆ build() [1/2]

static 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.

◆ build() [2/2]

static 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.

◆ disable_print_counter_info()

static void libMesh::ReferenceCounter::disable_print_counter_info ( )

staticinherited

◆ enable_print_counter_info()

static void libMesh::ReferenceCounter::enable_print_counter_info ( )

staticinherited

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

◆ get_dim()

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

inherited

Returns: The spatial dimension of the quadrature rule.

Definition at line 136 of file quadrature.h.

References libMesh::QBase::_dim.

136 { return _dim; }

libMesh::QBase::_dim

unsigned int _dim

The spatial dimension of the quadrature rule.

Definition: quadrature.h:325

◆ get_elem_type()

ElemType libMesh::QBase::get_elem_type ( ) const

inherited

Returns: The element type we're currently using.

Definition at line 117 of file quadrature.h.

References libMesh::QBase::_type.

117 { return _type; }

libMesh::QBase::_type

ElemType _type

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

Definition: quadrature.h:337

◆ get_info()

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

staticinherited

Gets a string containing the reference information.

◆ get_order()

Order libMesh::QBase::get_order ( ) const

inherited

Returns: The order of the quadrature rule.

Definition at line 203 of file quadrature.h.

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

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

libMesh::Order

Order

defines an enum for polynomial orders.

Definition: enum_order.h:40

libMesh::QBase::_p_level

unsigned int _p_level

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

Definition: quadrature.h:343

libMesh::QBase::_order

Order _order

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

Definition: quadrature.h:331

◆ get_p_level()

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

inherited

Returns: The p-refinement level we're currently using.

Definition at line 122 of file quadrature.h.

References libMesh::QBase::_p_level.

122 { return _p_level; }

libMesh::QBase::_p_level

unsigned int _p_level

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

Definition: quadrature.h:343

◆ get_points() [1/2]

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

inherited

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

Definition at line 142 of file quadrature.h.

References libMesh::QBase::_points.

Referenced by EIM_F::interior_assembly(), and AssemblyEIM::interior_assembly().

142 { return _points; }

libMesh::QBase::_points

std::vector< Point > _points

The locations of the quadrature points in reference element space.

Definition: quadrature.h:349

◆ get_points() [2/2]

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

inherited

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

Definition at line 148 of file quadrature.h.

References libMesh::QBase::_points.

148 { return _points; }

libMesh::QBase::_points

std::vector< Point > _points

The locations of the quadrature points in reference element space.

Definition: quadrature.h:349

◆ get_weights() [1/2]

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

inherited

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

Definition at line 154 of file quadrature.h.

References libMesh::QBase::_weights.

154 { return _weights; }

libMesh::QBase::_weights

std::vector< Real > _weights

The quadrature weights.

Definition: quadrature.h:355

◆ get_weights() [2/2]

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

inherited

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

Definition at line 160 of file quadrature.h.

References libMesh::QBase::_weights.

160 { return _weights; }

libMesh::QBase::_weights

std::vector< Real > _weights

The quadrature weights.

Definition: quadrature.h:355

◆ increment_constructor_count()

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

protectedinherited

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.

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

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

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

◆ increment_destructor_count()

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

protectedinherited

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.

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

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

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

◆ init() [1/2]

virtual 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.

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

◆ init() [2/2]

virtual 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.

◆ init_0D()

virtual 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.

◆ init_1D()

virtual void libMesh::QMonomial::init_1D	(	const ElemType	,
		unsigned	int = `0`
	)

overrideprivatevirtual

Just uses a Gauss rule in 1D.

Implements libMesh::QBase.

◆ init_2D()

virtual void libMesh::QMonomial::init_2D	(	const ElemType	_type = `INVALID_ELEM`,
		unsigned int	p_level = `0`
	)

overrideprivatevirtual

More efficient rules for quadrilaterals.

Reimplemented from libMesh::QBase.

◆ init_3D()

virtual void libMesh::QMonomial::init_3D	(	const ElemType	_type = `INVALID_ELEM`,
		unsigned int	p_level = `0`
	)

overrideprivatevirtual

More efficient rules for hexahedra.

Reimplemented from libMesh::QBase.

◆ kim_rule()

void libMesh::QMonomial::kim_rule	(	const Real	rule_data[][4],
		const unsigned int *	rule_id,
		const unsigned int	n_pts
	)

private

Rules from Kim and Song, Comm.

Korean Math. Soc vol. 13, no. 4, 1998, pp. 913-931. The rules are obtained by considering the group G^{rot} of rotations of the reference hex, and the invariant polynomials of this group.

In Kim and Song's rules, quadrature points are described by the following points and their unique permutations under the G^{rot} group:

0.) (0,0,0) ( 1 perm ) -> [0, 0, 0] 1.) (x,0,0) ( 6 perms) -> [x, 0, 0], [0, -x, 0], [-x, 0, 0], [0, x, 0], [0, 0, -x], [0, 0, x] 2.) (x,x,0) (12 perms) -> [x, x, 0], [x, -x, 0], [-x, -x, 0], [-x, x, 0], [x, 0, -x], [x, 0, x], [0, x, -x], [0, x, x], [0, -x, -x], [-x, 0, -x], [0, -x, x], [-x, 0, x] 3.) (x,y,0) (24 perms) -> [x, y, 0], [y, -x, 0], [-x, -y, 0], [-y, x, 0], [x, 0, -y], [x, -y, 0], [x, 0, y], [0, y, -x], [-x, y, 0], [0, y, x], [y, 0, -x], [0, -y, -x], [-y, 0, -x], [y, x, 0], [-y, -x, 0], [y, 0, x], [0, -y, x], [-y, 0, x], [-x, 0, y], [0, -x, -y], [0, -x, y], [-x, 0, -y], [0, x, y], [0, x, -y] 4.) (x,x,x) ( 8 perms) -> [x, x, x], [x, -x, x], [-x, -x, x], [-x, x, x], [x, x, -x], [x, -x, -x], [-x, x, -x], [-x, -x, -x] 5.) (x,x,z) (24 perms) -> [x, x, z], [x, -x, z], [-x, -x, z], [-x, x, z], [x, z, -x], [x, -x, -z], [x, -z, x], [z, x, -x], [-x, x, -z], [-z, x, x], [x, -z, -x], [-z, -x, -x], [-x, z, -x], [x, x, -z], [-x, -x, -z], [x, z, x], [z, -x, x], [-x, -z, x], [-x, z, x], [z, -x, -x], [-z, -x, x], [-x, -z, -x], [z, x, x], [-z, x, -x] 6.) (x,y,z) (24 perms) -> [x, y, z], [y, -x, z], [-x, -y, z], [-y, x, z], [x, z, -y], [x, -y, -z], [x, -z, y], [z, y, -x], [-x, y, -z], [-z, y, x], [y, -z, -x], [-z, -y, -x], [-y, z, -x], [y, x, -z], [-y, -x, -z], [y, z, x], [z, -y, x], [-y, -z, x], [-x, z, y], [z, -x, -y], [-z, -x, y], [-x, -z, -y], [z, x, y], [-z, x, -y]

Only two of Kim and Song's rules are particularly useful for FEM calculations: the degree 7, 38-point rule and their degree 8, 47-point rule. The others either contain negative weights or points outside the reference interval. The points and weights, to 32 digits, were obtained from: Ronald Cools' website (http://www.cs.kuleuven.ac.be/~nines/research/ecf/ecf.html) and the unique permutations of G^{rot} were computed by me [JWP] using Maple.

◆ n_objects()

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

staticinherited

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

Definition at line 83 of file reference_counter.h.

References libMesh::ReferenceCounter::_n_objects.

84 { return _n_objects; }

libMesh::ReferenceCounter::_n_objects

static Threads::atomic< unsigned int > _n_objects

The number of objects.

Definition: reference_counter.h:130

◆ n_points()

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

inherited

Returns: The number of points associated with the quadrature rule.

Definition at line 127 of file quadrature.h.

References libMesh::QBase::_points.

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

◆ operator=() [1/2]

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

default

◆ operator=() [2/2]

QMonomial& libMesh::QMonomial::operator= ( QMonomial && )

default

◆ print_info() [1/2]

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

staticinherited

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

◆ print_info() [2/2]

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 378 of file quadrature.h.

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

 {
   libmesh_assert(!_points.empty());
   libmesh_assert(!_weights.empty());
 
   Real summed_weights=0;
   os << "N_Q_Points=" << this->n_points() << std::endl << std::endl;
   for (unsigned int qpoint=0; qpoint<this->n_points(); qpoint++)
     {
       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;
 }

◆ qp()

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

inherited

Returns: The $i^{th}$ quadrature point in reference element space.

Definition at line 165 of file quadrature.h.

References libMesh::QBase::_points.

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

◆ 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.

◆ shapes_need_reinit()

virtual bool libMesh::QBase::shapes_need_reinit ( )

virtualinherited

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 231 of file quadrature.h.

231 { return false; }

◆ stroud_rule()

void libMesh::QMonomial::stroud_rule	(	const Real	rule_data[][3],
		const unsigned int *	rule_symmetry,
		const unsigned int	n_pts
	)

private

Stroud's rules for quads and hexes can have one of several different types of symmetry.

The rule_symmetry array describes how the different lines of the rule_data array are to be applied. The different rule_symmetry possibilities are: 0) Origin or single-point: (x,y) Fully-symmetric, 3 cases: 1) (x,y) -> (x,y), (-x,y), (x,-y), (-x,-y) (y,x), (-y,x), (y,-x), (-y,-x) 2) (x,x) -> (x,x), (-x,x), (x,-x), (-x,-x) 3) (x,0) -> (x,0), (-x,0), (0, x), ( 0,-x) 4) Rotational Invariant, (x,y) -> (x,y), (-x,-y), (-y, x), (y,-x) 5) Partial Symmetry, (x,y) -> (x,y), (-x, y) [x!=0] 6) Rectangular Symmetry, (x,y) -> (x,y), (-x, y), (-x,-y), (x,-y) 7) Central Symmetry, (0,y) -> (0,y), ( 0,-y)

Not all rules with these symmetries are due to Stroud, however, his book is probably the most frequently-cited compendium of quadrature rules and later authors certainly built upon his work.

◆ 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.

◆ 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.

◆ 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.

◆ type()

virtual QuadratureType libMesh::QMonomial::type ( ) const

overridevirtual

Returns: QMONOMIAL.

Implements libMesh::QBase.

◆ w()

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

inherited

Returns: The $i^{th}$ quadrature weight.

Definition at line 174 of file quadrature.h.

References libMesh::QBase::_weights.

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

◆ wissmann_rule()

void libMesh::QMonomial::wissmann_rule	(	const Real	rule_data[][3],
		const unsigned int	n_pts
	)

private

Wissmann published three interesting "partially symmetric" rules for integrating degree 4, 6, and 8 polynomials exactly on QUADs.

These rules have all positive weights, all points inside the reference element, and have fewer points than tensor-product rules of equivalent order, making them superior to those rules for monomial bases.

J. W. Wissman and T. Becker, Partially symmetric cubature formulas for even degrees of exactness, SIAM J. Numer. Anal. 23 (1986), 676–685.

Member Data Documentation

◆ _counts

Counts libMesh::ReferenceCounter::_counts

staticprotectedinherited

Actually holds the data.

Definition at line 122 of file reference_counter.h.

Referenced by 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 325 of file quadrature.h.

Referenced by libMesh::QBase::get_dim(), libMesh::QJacobi::QJacobi(), libMesh::QSimpson::QSimpson(), and libMesh::QTrap::QTrap().

◆ _enable_print_counter

bool libMesh::ReferenceCounter::_enable_print_counter

staticprotectedinherited

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

Definition at line 141 of file reference_counter.h.

◆ _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 331 of file quadrature.h.

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

◆ _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 343 of file quadrature.h.

Referenced by libMesh::QBase::get_order(), and libMesh::QBase::get_p_level().

◆ _points

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

protectedinherited

The locations of the quadrature points in reference element space.

Definition at line 349 of file quadrature.h.

Referenced by libMesh::QBase::get_points(), libMesh::QBase::n_points(), libMesh::QBase::print_info(), and libMesh::QBase::qp().

◆ _type

ElemType libMesh::QBase::_type

protectedinherited

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

Definition at line 337 of file quadrature.h.

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

◆ _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 355 of file quadrature.h.

Referenced by libMesh::QBase::get_weights(), libMesh::QBase::print_info(), and libMesh::QBase::w().

◆ 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 246 of file quadrature.h.

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

include/quadrature/quadrature_monomial.h

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Types

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ Counts

Constructor & Destructor Documentation

◆ QMonomial() [1/3]

◆ QMonomial() [2/3]

◆ QMonomial() [3/3]

◆ ~QMonomial()

Member Function Documentation

◆ build() [1/2]

◆ build() [2/2]

◆ disable_print_counter_info()

◆ enable_print_counter_info()

◆ get_dim()

◆ get_elem_type()

◆ get_info()

◆ get_order()

◆ get_p_level()

◆ get_points() [1/2]

◆ get_points() [2/2]

◆ get_weights() [1/2]

◆ get_weights() [2/2]

◆ increment_constructor_count()

◆ increment_destructor_count()

◆ init() [1/2]

◆ init() [2/2]

◆ init_0D()

◆ init_1D()

◆ init_2D()

◆ init_3D()

◆ kim_rule()

◆ n_objects()

◆ n_points()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ print_info() [1/2]

◆ print_info() [2/2]

◆ qp()

◆ scale()

◆ shapes_need_reinit()

◆ stroud_rule()

◆ tensor_product_hex()

◆ tensor_product_prism()

◆ tensor_product_quad()

◆ type()

◆ w()

◆ wissmann_rule()

Member Data Documentation

◆ _counts

◆ _dim

◆ _enable_print_counter

◆ _mutex

◆ _n_objects

◆ _order

◆ _p_level

◆ _points

◆ _type

◆ _weights

◆ allow_rules_with_negative_weights