libMesh
Public Member Functions | Static Public Member Functions | Public Attributes | Protected Types | Protected Member Functions | Protected Attributes | Static Protected Attributes | Private Member Functions | Private Attributes | List of all members
libMesh::QJacobi Class Referencefinal

This class implements two (for now) Jacobi-Gauss quadrature rules. More...

#include <quadrature_jacobi.h>

Inheritance diagram for libMesh::QJacobi:
[legend]

Public Member Functions

 QJacobi (unsigned int dim, Order order=INVALID_ORDER, unsigned int a=1, unsigned int b=0)
 Constructor. More...
 
 QJacobi (const QJacobi &)=default
 Copy/move ctor, copy/move assignment operator, and destructor are all explicitly defaulted for this simple class. More...
 
 QJacobi (QJacobi &&)=default
 
QJacobi & operator= (const QJacobi &)=default
 
QJacobi & operator= (QJacobi &&)=default
 
virtual ~QJacobi ()=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...
 
virtual void init_2D (const ElemType type=INVALID_ELEM, unsigned int p_level=0)
 Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate values. More...
 
virtual void init_3D (const ElemType type=INVALID_ELEM, unsigned int p_level=0)
 Initializes the 3D 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...
 

Private Attributes

unsigned int _alpha
 
unsigned int _beta
 

Detailed Description

This class implements two (for now) Jacobi-Gauss quadrature rules.

These rules have the same order of accuracy as the normal Gauss quadrature rules, but instead of integrating a weight function w(x)=1, they integrate w(x)=(1-x)^alpha * (1+x)^beta. The reason that they are useful is that they allow you to implement conical product rules for triangles and tetrahedra. Although these product rules are non-optimal (use more points than necessary) they are automatically constructable for high orders of accuracy where other formulae may not exist.

There is not much sense in using this class directly, since it only provides 1D rules, weighted, as described before. Still, this class is particularly helpful: check QGauss for triangles and tetrahedra, with orders beyond THIRTIETH.

Author
John W. Peterson
Date
2003

Implements 1D Gauss-Jacobi quadrature rules of various orders.

Definition at line 49 of file quadrature_jacobi.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

◆ QJacobi() [1/3]

libMesh::QJacobi::QJacobi ( unsigned int  dim,
Order  order = INVALID_ORDER,
unsigned int  a = 1,
unsigned int  b = 0 
)
inline

Constructor.

Currently, only one-dimensional rules provided.

Definition at line 56 of file quadrature_jacobi.h.

59  :
60  QBase(dim, order),
61  _alpha(a),
62  _beta(b)
63  {
64  if (_dim == 1)
65  init(EDGE2);
66  }

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

◆ QJacobi() [2/3]

libMesh::QJacobi::QJacobi ( const QJacobi &  )
default

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

◆ QJacobi() [3/3]

libMesh::QJacobi::QJacobi ( QJacobi &&  )
default

◆ ~QJacobi()

virtual libMesh::QJacobi::~QJacobi ( )
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.

55 {
56  switch (_qt)
57  {
58 
59  case QCLOUGH:
60  {
61 #ifdef DEBUG
62  if (_order > TWENTYTHIRD)
63  {
64  libMesh::out << "WARNING: Clough quadrature implemented" << std::endl
65  << " up to TWENTYTHIRD order." << std::endl;
66  }
67 #endif
68 
69  return libmesh_make_unique<QClough>(_dim, _order);
70  }
71 
72  case QGAUSS:
73  {
74 
75 #ifdef DEBUG
76  if (_order > FORTYTHIRD)
77  {
78  libMesh::out << "WARNING: Gauss quadrature implemented" << std::endl
79  << " up to FORTYTHIRD order." << std::endl;
80  }
81 #endif
82 
83  return libmesh_make_unique<QGauss>(_dim, _order);
84  }
85 
86  case QJACOBI_1_0:
87  {
88 
89 #ifdef DEBUG
90  if (_order > FORTYTHIRD)
91  {
92  libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
93  << " up to FORTYTHIRD order." << std::endl;
94  }
95 
96  if (_dim > 1)
97  {
98  libMesh::out << "WARNING: Jacobi(1,0) quadrature implemented" << std::endl
99  << " in 1D only." << std::endl;
100  }
101 #endif
102 
103  return libmesh_make_unique<QJacobi>(_dim, _order, 1, 0);
104  }
105 
106  case QJACOBI_2_0:
107  {
108 
109 #ifdef DEBUG
110  if (_order > FORTYTHIRD)
111  {
112  libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
113  << " up to FORTYTHIRD order." << std::endl;
114  }
115 
116  if (_dim > 1)
117  {
118  libMesh::out << "WARNING: Jacobi(2,0) quadrature implemented" << std::endl
119  << " in 1D only." << std::endl;
120  }
121 #endif
122 
123  return libmesh_make_unique<QJacobi>(_dim, _order, 2, 0);
124  }
125 
126  case QSIMPSON:
127  {
128 
129 #ifdef DEBUG
130  if (_order > THIRD)
131  {
132  libMesh::out << "WARNING: Simpson rule provides only" << std::endl
133  << " THIRD order!" << std::endl;
134  }
135 #endif
136 
137  return libmesh_make_unique<QSimpson>(_dim);
138  }
139 
140  case QTRAP:
141  {
142 
143 #ifdef DEBUG
144  if (_order > FIRST)
145  {
146  libMesh::out << "WARNING: Trapezoidal rule provides only" << std::endl
147  << " FIRST order!" << std::endl;
148  }
149 #endif
150 
151  return libmesh_make_unique<QTrap>(_dim);
152  }
153 
154  case QGRID:
155  return libmesh_make_unique<QGrid>(_dim, _order);
156 
157  case QGRUNDMANN_MOLLER:
158  return libmesh_make_unique<QGrundmann_Moller>(_dim, _order);
159 
160  case QMONOMIAL:
161  return libmesh_make_unique<QMonomial>(_dim, _order);
162 
163  case QGAUSS_LOBATTO:
164  return libmesh_make_unique<QGaussLobatto>(_dim, _order);
165 
166  case QCONICAL:
167  return libmesh_make_unique<QConical>(_dim, _order);
168 
169  case QNODAL:
170  return libmesh_make_unique<QNodal>(_dim, _order);
171 
172  default:
173  libmesh_error_msg("ERROR: Bad qt=" << _qt);
174  }
175 }

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.

44 {
45  return QBase::build (Utility::string_to_enum<QuadratureType> (type),
46  _dim,
47  _order);
48 }

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.

107 {
108  _enable_print_counter = false;
109  return;
110 }

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.

101 {
102  _enable_print_counter = true;
103  return;
104 }

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.

135 { 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.

116 { 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.

48 {
49 #if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
50 
51  std::ostringstream oss;
52 
53  oss << '\n'
54  << " ---------------------------------------------------------------------------- \n"
55  << "| Reference count information |\n"
56  << " ---------------------------------------------------------------------------- \n";
57 
58  for (const auto & pr : _counts)
59  {
60  const std::string name(pr.first);
61  const unsigned int creations = pr.second.first;
62  const unsigned int destructions = pr.second.second;
63 
64  oss << "| " << name << " reference count information:\n"
65  << "| Creations: " << creations << '\n'
66  << "| Destructions: " << destructions << '\n';
67  }
68 
69  oss << " ---------------------------------------------------------------------------- \n";
70 
71  return oss.str();
72 
73 #else
74 
75  return "";
76 
77 #endif
78 }

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.

211 { 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(), 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.

121 { 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.

147 { 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.

141 { 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(), libMesh::QGrundmann_Moller::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.

159 { 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.

153 { return _weights; }

References libMesh::QBase::_weights.

Referenced by libMesh::QClough::init_1D(), libMesh::QConical::init_1D(), libMesh::QNodal::init_1D(), libMesh::QMonomial::init_1D(), libMesh::QGrundmann_Moller::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().

◆ 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.

182 {
183  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
184  std::pair<unsigned int, unsigned int> & p = _counts[name];
185 
186  p.first++;
187 }

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.

195 {
196  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
197  std::pair<unsigned int, unsigned int> & p = _counts[name];
198 
199  p.second++;
200 }

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.

106 {
107  // dispatch generic implementation
108  this->init(elem.type(), p_level);
109 }

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.

61 {
62  // check to see if we have already
63  // done the work for this quadrature rule
64  if (t == _type && p == _p_level)
65  return;
66  else
67  {
68  _type = t;
69  _p_level = p;
70  }
71 
72 
73 
74  switch(_dim)
75  {
76  case 0:
77  this->init_0D();
78 
79  return;
80 
81  case 1:
82  this->init_1D();
83 
84  return;
85 
86  case 2:
87  this->init_2D();
88 
89  return;
90 
91  case 3:
92  this->init_3D();
93 
94  return;
95 
96  default:
97  libmesh_error_msg("Invalid dimension _dim = " << _dim);
98  }
99 }

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::QGrid::init_2D(), libMesh::QTrap::init_2D(), libMesh::QGauss::init_2D(), libMesh::QSimpson::init_2D(), libMesh::QNodal::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(), libMesh::QNodal::init_3D(), libMesh::QMonomial::init_3D(), libMesh::QGauss::QGauss(), libMesh::QGaussLobatto::QGaussLobatto(), 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.

114 {
115  _points.resize(1);
116  _weights.resize(1);
117  _points[0] = Point(0.);
118  _weights[0] = 1.0;
119 }

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

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

◆ init_1D()

void libMesh::QJacobi::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 26 of file quadrature_jacobi_1D.C.

27 {
28  //----------------------------------------------------------------------
29  // 1D quadrature rules
30  // Note that we need to check _alpha and _beta
31  // to determine which quadrature rule to implement.
32  // These rules have been pre-scaled based on their
33  // intended use. The weights of the (alpha=1,beta=0)
34  // rule sum to 0.5. The weights of the (alpha=2,beta=0)
35  // rule sum to 0.333333333333.
36 
37  if ((_alpha == 1) && (_beta == 0))
38  {
39  switch(get_order())
40  {
41  case CONSTANT:
42  case FIRST:
43  {
44  _points.resize (1);
45  _weights.resize(1);
46 
47  _points[0](0) = 1./3.;
48 
49  _weights[0] = 0.5;
50 
51  return;
52  }
53  case SECOND:
54  case THIRD:
55  {
56  _points.resize (2);
57  _weights.resize(2);
58 
59  _points[ 0](0)=Real(1.5505102572168219018027159252941e-01L);
60  _points[ 1](0)=Real(6.4494897427831780981972840747059e-01L);
61 
62  _weights[ 0]=Real(3.1804138174397716939436900207516e-01L);
63  _weights[ 1]=Real(1.8195861825602283060563099792484e-01L);
64 
65  return;
66  }
67  case FOURTH:
68  case FIFTH:
69  {
70  _points.resize (3);
71  _weights.resize(3);
72 
73  _points[ 0](0)=Real(8.8587959512703947395546143769456e-02L);
74  _points[ 1](0)=Real(4.0946686444073471086492625206883e-01L);
75  _points[ 2](0)=Real(7.8765946176084705602524188987600e-01L);
76 
77  _weights[ 0]=Real(2.0093191373895963077219813326460e-01L);
78  _weights[ 1]=Real(2.2924110635958624669392059455632e-01L);
79  _weights[ 2]=Real(6.9826979901454122533881272179077e-02L);
80 
81  return;
82  }
83  case SIXTH:
84  case SEVENTH:
85  {
86  _points.resize (4);
87  _weights.resize(4);
88 
89  _points[ 0](0)=Real(5.7104196114517682193121192554116e-02L);
90  _points[ 1](0)=Real(2.7684301363812382768004599768563e-01L);
91  _points[ 2](0)=Real(5.8359043236891682005669766866292e-01L);
92  _points[ 3](0)=Real(8.6024013565621944784791291887512e-01L);
93 
94  _weights[ 0]=Real(1.3550691343148811620826417407794e-01L);
95  _weights[ 1]=Real(2.0346456801027136079140447593585e-01L);
96  _weights[ 2]=Real(1.2984754760823244082645620288963e-01L);
97  _weights[ 3]=Real(3.1180970950008082173875147096575e-02L);
98 
99  return;
100  }
101  case EIGHTH:
102  case NINTH:
103  {
104  _points.resize (5);
105  _weights.resize(5);
106 
107  _points[ 0](0)=Real(3.9809857051468742340806690093333e-02L);
108  _points[ 1](0)=Real(1.9801341787360817253579213679530e-01L);
109  _points[ 2](0)=Real(4.3797481024738614400501252000523e-01L);
110  _points[ 3](0)=Real(6.9546427335363609451461482372117e-01L);
111  _points[ 4](0)=Real(9.0146491420117357387650110211225e-01L);
112 
113  _weights[ 0]=Real(9.6781590226651679274360971636151e-02L);
114  _weights[ 1]=Real(1.6717463809436956549167562309770e-01L);
115  _weights[ 2]=Real(1.4638698708466980869803786935596e-01L);
116  _weights[ 3]=Real(7.3908870072616670350633219341704e-02L);
117  _weights[ 4]=Real(1.5747914521692276185292316568488e-02L);
118 
119  return;
120  }
121  case TENTH:
122  case ELEVENTH:
123  {
124 
125  _points.resize (6);
126  _weights.resize(6);
127 
128  _points[ 0](0)=Real(2.9316427159784891972050276913165e-02L);
129  _points[ 1](0)=Real(1.4807859966848429184997685249598e-01L);
130  _points[ 2](0)=Real(3.3698469028115429909705297208078e-01L);
131  _points[ 3](0)=Real(5.5867151877155013208139334180552e-01L);
132  _points[ 4](0)=Real(7.6923386203005450091688336011565e-01L);
133  _points[ 5](0)=Real(9.2694567131974111485187396581968e-01L);
134 
135  _weights[ 0]=Real(7.2310330725508683655454326124832e-02L);
136  _weights[ 1]=Real(1.3554249723151861684069039663805e-01L);
137  _weights[ 2]=Real(1.4079255378819892811907683907093e-01L);
138  _weights[ 3]=Real(9.8661150890655264120584510548360e-02L);
139  _weights[ 4]=Real(4.3955165550508975508176624305430e-02L);
140  _weights[ 5]=Real(8.7383018136095317560173033123989e-03L);
141 
142  return;
143  }
144  case TWELFTH:
145  case THIRTEENTH:
146  {
147  _points.resize (7);
148  _weights.resize(7);
149 
150  _points[ 0](0)=Real(2.2479386438712498108825499570845e-02L);
151  _points[ 1](0)=Real(1.1467905316090423190964023706751e-01L);
152  _points[ 2](0)=Real(2.6578982278458946847678939169339e-01L);
153  _points[ 3](0)=Real(4.5284637366944461699855144234765e-01L);
154  _points[ 4](0)=Real(6.4737528288683036262609222982876e-01L);
155  _points[ 5](0)=Real(8.1975930826310763501242005719082e-01L);
156  _points[ 6](0)=Real(9.4373743946307785353434780896769e-01L);
157 
158  _weights[ 0]=Real(5.5967363423491051151562113429926e-02L);
159  _weights[ 1]=Real(1.1050925819087460242112073636961e-01L);
160  _weights[ 2]=Real(1.2739089729958832691873448577496e-01L);
161  _weights[ 3]=Real(1.0712506569587366999091225299986e-01L);
162  _weights[ 4]=Real(6.6384696465491469983647988763640e-02L);
163  _weights[ 5]=Real(2.7408356721873475444331048358226e-02L);
164  _weights[ 6]=Real(5.2143622028074040896913743037830e-03L);
165 
166  return;
167  }
168  case FOURTEENTH:
169  case FIFTEENTH:
170  {
171  _points.resize (8);
172  _weights.resize(8);
173 
174  _points[ 0](0)=Real(1.7779915147363451813205101037679e-02L);
175  _points[ 1](0)=Real(9.1323607899793956003741458074541e-02L);
176  _points[ 2](0)=Real(2.1430847939563075835754126758167e-01L);
177  _points[ 3](0)=Real(3.7193216458327230243085396048263e-01L);
178  _points[ 4](0)=Real(5.4518668480342664903227222995321e-01L);
179  _points[ 5](0)=Real(7.1317524285556948105131376025091e-01L);
180  _points[ 6](0)=Real(8.5563374295785442851478147977179e-01L);
181  _points[ 7](0)=Real(9.5536604471003014926687897814169e-01L);
182 
183  _weights[ 0]=Real(4.4550804361555931326215619533963e-02L);
184  _weights[ 1]=Real(9.1119023636373626345722461782880e-02L);
185  _weights[ 2]=Real(1.1250579947088736617177209860428e-01L);
186  _weights[ 3]=Real(1.0604735943593001070453109641116e-01L);
187  _weights[ 4]=Real(7.9199599492319160120408189359892e-02L);
188  _weights[ 5]=Real(4.5439319504698898083055421095694e-02L);
189  _weights[ 6]=Real(1.7842902655986208393552797201042e-02L);
190  _weights[ 7]=Real(3.2951914422487988547423160110891e-03L);
191 
192  return;
193  }
194  case SIXTEENTH:
195  case SEVENTEENTH:
196  {
197  _points.resize (9);
198  _weights.resize(9);
199 
200  _points[ 0](0)=Real(1.4412409648876548632826740810813e-02L);
201  _points[ 1](0)=Real(7.4387389709196044635918185955999e-02L);
202  _points[ 2](0)=Real(1.7611665616299528186317574607257e-01L);
203  _points[ 3](0)=Real(3.0966757992763781705962046722948e-01L);
204  _points[ 4](0)=Real(4.6197040108101093488314310868056e-01L);
205  _points[ 5](0)=Real(6.1811723469529402463922975160350e-01L);
206  _points[ 6](0)=Real(7.6282301518503961468269330714673e-01L);
207  _points[ 7](0)=Real(8.8192102121000129980771488800526e-01L);
208  _points[ 8](0)=Real(9.6374218711679053905883569923192e-01L);
209 
210  _weights[ 0]=Real(3.6278003523279871459649597941160e-02L);
211  _weights[ 1]=Real(7.6074255109308162580079303753964e-02L);
212  _weights[ 2]=Real(9.8533742172345705160173020369274e-02L);
213  _weights[ 3]=Real(1.0030880919336828965415022473259e-01L);
214  _weights[ 4]=Real(8.4358321844920349394250019958587e-02L);
215  _weights[ 5]=Real(5.8401195295165110565731522901640e-02L);
216  _weights[ 6]=Real(3.1804821491054001261690106935870e-02L);
217  _weights[ 7]=Real(1.2060004284785379051727152286900e-02L);
218  _weights[ 8]=Real(2.1808470857731308725490511200170e-03L);
219 
220  return;
221  }
222  case EIGHTTEENTH:
223  case NINETEENTH:
224  {
225  _points.resize (10);
226  _weights.resize(10);
227 
228  _points[ 0](0)=Real(1.1917613432415596909745586958986e-02L);
229  _points[ 1](0)=Real(6.1732071877148125522629367194250e-02L);
230  _points[ 2](0)=Real(1.4711144964307024042759943557982e-01L);
231  _points[ 3](0)=Real(2.6115967600845624026605165805485e-01L);
232  _points[ 4](0)=Real(3.9463984688578684296195210507761e-01L);
233  _points[ 5](0)=Real(5.3673876571566063287309517771189e-01L);
234  _points[ 6](0)=Real(6.7594446167666510735715050893476e-01L);
235  _points[ 7](0)=Real(8.0097892103689884513794630161724e-01L);
236  _points[ 8](0)=Real(9.0171098779014677034879897840977e-01L);
237  _points[ 9](0)=Real(9.6997096783851350295693564236559e-01L);
238 
239  _weights[ 0]=Real(3.0099508024037023300654755523879e-02L);
240  _weights[ 1]=Real(6.4287154509082572874826538628865e-02L);
241  _weights[ 2]=Real(8.6211300289176036428333360711914e-02L);
242  _weights[ 3]=Real(9.2696893677723415844756991929711e-02L);
243  _weights[ 4]=Real(8.4557109690827332430645582165501e-02L);
244  _weights[ 5]=Real(6.6053075563350379166074502504878e-02L);
245  _weights[ 6]=Real(4.3401906407150625922456117586384e-02L);
246  _weights[ 7]=Real(2.2774591453263032586487649426060e-02L);
247  _weights[ 8]=Real(8.4193197829831874175163655187011e-03L);
248  _weights[ 9]=Real(1.4991406024063940282481360041064e-03L);
249 
250  return;
251  }
252  case TWENTIETH:
253  case TWENTYFIRST:
254  {
255  _points.resize (11);
256  _weights.resize(11);
257 
258  _points[ 0](0)=Real(1.0018280461680405843024729867805e-02L);
259  _points[ 1](0)=Real(5.2035451127180552583542695772964e-02L);
260  _points[ 2](0)=Real(1.2461922514444307373529958726391e-01L);
261  _points[ 3](0)=Real(2.2284060704383785550783145345736e-01L);
262  _points[ 4](0)=Real(3.4000815791466518823360523389702e-01L);
263  _points[ 5](0)=Real(4.6813761308958404208311038075775e-01L);
264  _points[ 6](0)=Real(5.9849727976713918322772071367304e-01L);
265  _points[ 7](0)=Real(7.2220328489096792556332130780461e-01L);
266  _points[ 8](0)=Real(8.3082489962281857403056654390566e-01L);
267  _points[ 9](0)=Real(9.1695838655259485329313462701803e-01L);
268  _points[10](0)=Real(9.7472637960247965024666881353837e-01L);
269 
270  _weights[ 0]=Real(2.5367340688141426184944658517383e-02L);
271  _weights[ 1]=Real(5.4938091132871498258746681665651e-02L);
272  _weights[ 2]=Real(7.5620048057186998321377054841660e-02L);
273  _weights[ 3]=Real(8.4659422884017621219239388551910e-02L);
274  _weights[ 4]=Real(8.1879102988063470389586851943461e-02L);
275  _weights[ 5]=Real(6.9531875158183049799050889633934e-02L);
276  _weights[ 6]=Real(5.1591360672297580193086641744608e-02L);
277  _weights[ 7]=Real(3.2641546713833346017953865389764e-02L);
278  _weights[ 8]=Real(1.6663623451680692415747124573826e-02L);
279  _weights[ 9]=Real(6.0439209604797757927329621765769e-03L);
280  _weights[10]=Real(1.0636672932445414075338809612253e-03L);
281 
282  return;
283  }
284  case TWENTYSECOND:
285  case TWENTYTHIRD:
286  {
287  _points.resize (12);
288  _weights.resize(12);
289 
290  _points[ 0](0)=Real(8.5390549884274193686644608778398e-03L);
291  _points[ 1](0)=Real(4.4446463155407723025466798785553e-02L);
292  _points[ 2](0)=Real(1.0685449088347665763410677043250e-01L);
293  _points[ 3](0)=Real(1.9215105452985404099105725622861e-01L);
294  _points[ 4](0)=Real(2.9538088426258022162291683437601e-01L);
295  _points[ 5](0)=Real(4.1054508120145768248903435055933e-01L);
296  _points[ 6](0)=Real(5.3095084931281767062893024289682e-01L);
297  _points[ 7](0)=Real(6.4960065027725499276629172334298e-01L);
298  _points[ 8](0)=Real(7.5959888952522705374260257404342e-01L);
299  _points[ 9](0)=Real(8.5455254376493588079021191640562e-01L);
300  _points[10](0)=Real(9.2894210126441101784881015513432e-01L);
301  _points[11](0)=Real(9.7843793683414963909190691691700e-01L);
302 
303  _weights[ 0]=Real(2.1664860886871767324583472077976e-02L);
304  _weights[ 1]=Real(4.7427851980377470134309182197087e-02L);
305  _weights[ 2]=Real(6.6606750626673198130834485351975e-02L);
306  _weights[ 3]=Real(7.6896602680041006281204469112373e-02L);
307  _weights[ 4]=Real(7.7696316815531026628765631099760e-02L);
308  _weights[ 5]=Real(7.0109339997630094495921805029671e-02L);
309  _weights[ 6]=Real(5.6613843713667631943701105156121e-02L);
310  _weights[ 7]=Real(4.0451653706913616760646424250646e-02L);
311  _weights[ 8]=Real(2.4876780409265432012508172290016e-02L);
312  _weights[ 9]=Real(1.2436009166422265607483293056674e-02L);
313  _weights[10]=Real(4.4448077956684623227961458658283e-03L);
314  _weights[11]=Real(7.7518222093802835724581451187414e-04L);
315 
316  return;
317  }
318 
319  case TWENTYFOURTH:
320  case TWENTYFIFTH:
321  {
322  _points.resize (13);
323  _weights.resize(13);
324 
325  _points[ 0](0)=Real(7.3646510260893216506914984138223e-03L);
326  _points[ 1](0)=Real(3.8398138739678350376832524864142e-02L);
327  _points[ 2](0)=Real(9.2595224699002635282891375438616e-02L);
328  _points[ 3](0)=Real(1.6725101139155773149552247875936e-01L);
329  _points[ 4](0)=Real(2.5862354070576251658979073282269e-01L);
330  _points[ 5](0)=Real(3.6213139728223880040868129822732e-01L);
331  _points[ 6](0)=Real(4.7258438600411772517509464267860e-01L);
332  _points[ 7](0)=Real(5.8444396402134045550422084781091e-01L);
333  _points[ 8](0)=Real(6.9210100171960165689704195168767e-01L);
334  _points[ 9](0)=Real(7.9015702827343748555286333249938e-01L);
335  _points[10](0)=Real(8.7369482130668941936771456713174e-01L);
336  _points[11](0)=Real(9.3852445910073101239763338676530e-01L);
337  _points[12](0)=Real(9.8138963498901214856028062215971e-01L);
338 
339  _weights[ 0]=Real(1.8714731585615175193374408664994e-02L);
340  _weights[ 1]=Real(4.1320289419839298476611706952624e-02L);
341  _weights[ 2]=Real(5.8953937956647082536161503261961e-02L);
342  _weights[ 3]=Real(6.9713468282144398251416629950427e-02L);
343  _weights[ 4]=Real(7.2849696515818223079384033843973e-02L);
344  _weights[ 5]=Real(6.8815529487565417217837889436694e-02L);
345  _weights[ 6]=Real(5.9120481314092327419290155953032e-02L);
346  _weights[ 7]=Real(4.5995780676052393313259784530213e-02L);
347  _weights[ 8]=Real(3.1936787162203148842381371158461e-02L);
348  _weights[ 9]=Real(1.9213957164719820645895497863743e-02L);
349  _weights[10]=Real(9.4489244795927503661800865492413e-03L);
350  _weights[11]=Real(3.3383592507737718066104206420419e-03L);
351  _weights[12]=Real(5.7805670493619285159651119259460e-04L);
352 
353  return;
354  }
355 
356  case TWENTYSIXTH:
357  case TWENTYSEVENTH:
358  {
359  _points.resize (14);
360  _weights.resize(14);
361 
362  _points[ 0](0)=Real(6.4167607928184568108204640945072e-03L);
363  _points[ 1](0)=Real(3.3501404532013140035963928570572e-02L);
364  _points[ 2](0)=Real(8.0985499681955184392451307739982e-02L);
365  _points[ 3](0)=Real(1.4680486768121372992366016526080e-01L);
366  _points[ 4](0)=Real(2.2808427064925799153464409861994e-01L);
367  _points[ 5](0)=Real(3.2127174398893617440234039741304e-01L);
368  _points[ 6](0)=Real(4.2229465730757025784040898751810e-01L);
369  _points[ 7](0)=Real(5.2673786133987303205372694481288e-01L);
370  _points[ 8](0)=Real(6.3003668837040395788448059413143e-01L);
371  _points[ 9](0)=Real(7.2767645288926468543602672799033e-01L);
372  _points[10](0)=Real(8.1538973944347464197307421861206e-01L);
373  _points[11](0)=Real(8.8934280881951553969087166094649e-01L);
374  _points[12](0)=Real(9.4630270006027538353340594342472e-01L);
375  _points[13](0)=Real(9.8377523409860023828122800914100e-01L);
376 
377  _weights[ 0]=Real(1.6326754322596839819449429350767e-02L);
378  _weights[ 1]=Real(3.6296078055443693187652118821852e-02L);
379  _weights[ 2]=Real(5.2445953501916745591081806162678e-02L);
380  _weights[ 3]=Real(6.3213025574329203442529115357932e-02L);
381  _weights[ 4]=Real(6.7831659604182837102347339834146e-02L);
382  _weights[ 5]=Real(6.6392350626085425132821358651277e-02L);
383  _weights[ 6]=Real(5.9785559022531584222614059168587e-02L);
384  _weights[ 7]=Real(4.9519454523203004580936179335753e-02L);
385  _weights[ 8]=Real(3.7443096458985826655938301826886e-02L);
386  _weights[ 9]=Real(2.5423465407148762115069898757459e-02L);
387  _weights[10]=Real(1.5032303743928643503408714751315e-02L);
388  _weights[11]=Real(7.2964841332126214434099222674776e-03L);
389  _weights[12]=Real(2.5541013176876539479794996099427e-03L);
390  _weights[13]=Real(4.3971370874715925476225610392609e-04L);
391 
392  return;
393  }
394 
395  case TWENTYEIGHTH:
396  case TWENTYNINTH:
397  {
398  _points.resize (15);
399  _weights.resize(15);
400 
401  _points[ 0](0)=Real(5.6406889725117097575064665794442e-03L);
402  _points[ 1](0)=Real(2.9482298647942486631640984718004e-02L);
403  _points[ 2](0)=Real(7.1412953115158840054783901746735e-02L);
404  _points[ 3](0)=Real(1.2983102555359105597125453809429e-01L);
405  _points[ 4](0)=Real(2.0249275505010404756821998832023e-01L);
406  _points[ 5](0)=Real(2.8660608625752705998402604548440e-01L);
407  _points[ 6](0)=Real(3.7893868864697803810652900914277e-01L);
408  _points[ 7](0)=Real(4.7594230846323486057258899201585e-01L);
409  _points[ 8](0)=Real(5.7388916090668588067145385523753e-01L);
410  _points[ 9](0)=Real(6.6901519502995987653869563905314e-01L);
411  _points[10](0)=Real(7.5766473903134271199707427774029e-01L);
412  _points[11](0)=Real(8.3643096060561012397555908565418e-01L);
413  _points[12](0)=Real(9.0228670067937802663123850466201e-01L);
414  _points[13](0)=Real(9.5270040990583331433804420752426e-01L);
415  _points[14](0)=Real(9.8573054526317422526590063305913e-01L);
416 
417  _weights[ 0]=Real(1.4367069621712523019113300206269e-02L);
418  _weights[ 1]=Real(3.2119044874965915878547666076448e-02L);
419  _weights[ 2]=Real(4.6891639944059925679345570546797e-02L);
420  _weights[ 3]=Real(5.7398825506941289374618916116414e-02L);
421  _weights[ 4]=Real(6.2918106648596909592665349230551e-02L);
422  _weights[ 5]=Real(6.3343955161511392519350738069297e-02L);
423  _weights[ 6]=Real(5.9174192059712931565021168664588e-02L);
424  _weights[ 7]=Real(5.1412362311886468530400169371359e-02L);
425  _weights[ 8]=Real(4.1400735184422578228813150524935e-02L);
426  _weights[ 9]=Real(3.0609769586468540804291808789747e-02L);
427  _weights[10]=Real(2.0416309272619835691190995270654e-02L);
428  _weights[11]=Real(1.1904190355097578843030186960250e-02L);
429  _weights[12]=Real(5.7172223947211761716246502974268e-03L);
430  _weights[13]=Real(1.9862346931450380410338051145760e-03L);
431  _weights[14]=Real(3.4034238413789606095252476068833e-04L);
432 
433  return;
434  }
435 
436 
437  case THIRTIETH:
438  case THIRTYFIRST:
439  {
440  _points.resize (16);
441  _weights.resize(16);
442 
443  _points[ 0](0)=Real(4.9972996637719210426511496015207e-03L);
444  _points[ 1](0)=Real(2.6143513681394051978549323380543e-02L);
445  _points[ 2](0)=Real(6.3430945583836745492528222770701e-02L);
446  _points[ 3](0)=Real(1.1559843757981594017892362824740e-01L);
447  _points[ 4](0)=Real(1.8087055965788366624757339125570e-01L);
448  _points[ 5](0)=Real(2.5702480784517085992294423955927e-01L);
449  _points[ 6](0)=Real(3.4146792754782306862589929793869e-01L);
450  _points[ 7](0)=Real(4.3132434359562537508359226958274e-01L);
451  _points[ 8](0)=Real(5.2353411602516832051747016507566e-01L);
452  _points[ 9](0)=Real(6.1495715187648951748964083381908e-01L);
453  _points[10](0)=Real(7.0248013792504104445480697553762e-01L);
454  _points[11](0)=Real(7.8312255396486808385218178256205e-01L);
455  _points[12](0)=Real(8.5413814777521063366511368381932e-01L);
456  _points[13](0)=Real(9.1310837653714127462958554670327e-01L);
457  _points[14](0)=Real(9.5802441769047545454495934455429e-01L);
458  _points[15](0)=Real(9.8735302062604161803115590316790e-01L);
459 
460  _weights[ 0]=Real(1.2739310657334184747549845879578e-02L);
461  _weights[ 1]=Real(2.8612452590143149357558068987418e-02L);
462  _weights[ 2]=Real(4.2129431157428284757515740541878e-02L);
463  _weights[ 3]=Real(5.2228594403959147363509678893029e-02L);
464  _weights[ 4]=Real(5.8254240209855835379301779422393e-02L);
465  _weights[ 5]=Real(6.0000854888113507055385942002166e-02L);
466  _weights[ 6]=Real(5.7718879609267823617681995467969e-02L);
467  _weights[ 7]=Real(5.2064137843806583754973352189273e-02L);
468  _weights[ 8]=Real(4.3997382189243923173481417304490e-02L);
469  _weights[ 9]=Real(3.4647816579285799103084877873731e-02L);
470  _weights[10]=Real(2.5159233106470040585653957496918e-02L);
471  _weights[11]=Real(1.6539584355635793501225242083105e-02L);
472  _weights[12]=Real(9.5341678846659366549669638207733e-03L);
473  _weights[13]=Real(4.5392323861386350682211111786128e-03L);
474  _weights[14]=Real(1.5671884735958197030724006964051e-03L);
475  _weights[15]=Real(2.6749366505553617681762616226073e-04L);
476 
477  return;
478  }
479 
480 
481  case THIRTYSECOND:
482  case THIRTYTHIRD:
483  {
484  _points.resize (17);
485  _weights.resize(17);
486 
487  _points[ 0](0)=Real(4.4579935677873917545062291115464e-03L);
488  _points[ 1](0)=Real(2.3340094123774273967021528207683e-02L);
489  _points[ 2](0)=Real(5.6707968769078239532713331556521e-02L);
490  _points[ 3](0)=Real(1.0355543293519706341349122696131e-01L);
491  _points[ 4](0)=Real(1.6246000342813654998162954391410e-01L);
492  _points[ 5](0)=Real(2.3163212577717218294679722573836e-01L);
493  _points[ 6](0)=Real(3.0897011775219590331752426128626e-01L);
494  _points[ 7](0)=Real(3.9212413472209565803361946333190e-01L);
495  _points[ 8](0)=Real(4.7856759685307958878371046285937e-01L);
496  _points[ 9](0)=Real(5.6567396688663433190330697600965e-01L);
497  _points[10](0)=Real(6.5079655845338226473148740732315e-01L);
498  _points[11](0)=Real(7.3134895273405138213302149556298e-01L);
499  _points[12](0)=Real(8.0488357852496649199917770139703e-01L);
500  _points[13](0)=Real(8.6916605956741361920444649801116e-01L);
501  _points[14](0)=Real(9.2224303459229840848710732823038e-01L);
502  _points[15](0)=Real(9.6250119782335004125046077538851e-01L);
503  _points[16](0)=Real(9.8871404063224375141712140225296e-01L);
504 
505  _weights[ 0]=Real(1.1372703113196894148880104403419e-02L);
506  _weights[ 1]=Real(2.5642427920205179185750205247311e-02L);
507  _weights[ 2]=Real(3.8025728825742400201474917006665e-02L);
508  _weights[ 3]=Real(4.7641869374618441920575209265709e-02L);
509  _weights[ 4]=Real(5.3907931667527480191616020246527e-02L);
510  _weights[ 5]=Real(5.6573611382471512986991034182850e-02L);
511  _weights[ 6]=Real(5.5734917923560549577129019490753e-02L);
512  _weights[ 7]=Real(5.1809741929296333255214704762820e-02L);
513  _weights[ 8]=Real(4.5477790399142277497438924164211e-02L);
514  _weights[ 9]=Real(3.7592325487112238031431998524319e-02L);
515  _weights[10]=Real(2.9074524087705050563187355467924e-02L);
516  _weights[11]=Real(2.0803278010295362060012866375773e-02L);
517  _weights[12]=Real(1.3513697452300780909638958310491e-02L);
518  _weights[13]=Real(7.7164222148059386958884227660543e-03L);
519  _weights[14]=Real(3.6472304834214064450344565237838e-03L);
520  _weights[15]=Real(1.2526834393912207489106525201067e-03L);
521  _weights[16]=Real(2.1311628920693358082515074128342e-04L);
522 
523  return;
524  }
525 
526  case THIRTYFOURTH:
527  case THIRTYFIFTH:
528  {
529  _points.resize (18);
530  _weights.resize(18);
531 
532  _points[ 0](0)=Real(4.0014793838673867970427199102708e-03L);
533  _points[ 1](0)=Real(2.0963648393766477995135600986561e-02L);
534  _points[ 2](0)=Real(5.0994041587890553966774921299853e-02L);
535  _points[ 3](0)=Real(9.3280395928544950777609058826066e-02L);
536  _points[ 4](0)=Real(1.4667010367761795715160882973461e-01L);
537  _points[ 5](0)=Real(2.0970703958884296672188171145203e-01L);
538  _points[ 6](0)=Real(2.8067179006017169910681926203455e-01L);
539  _points[ 7](0)=Real(3.5762864997663462939832714298390e-01L);
540  _points[ 8](0)=Real(4.3847844922413811765185426038741e-01L);
541  _points[ 9](0)=Real(5.2101582087077614731981479158547e-01L);
542  _points[10](0)=Real(6.0298936055983207213748070418747e-01L);
543  _points[11](0)=Real(6.8216303911365156501882207998153e-01L);
544  _points[12](0)=Real(7.5637719340615062679816733590978e-01L);
545  _points[13](0)=Real(8.2360742977486956587394885462062e-01L);
546  _points[14](0)=Real(8.8201982536207914673124120886230e-01L);
547  _points[15](0)=Real(9.3002088969969321648195850472769e-01L);
548  _points[16](0)=Real(9.6630075194563254241150674649068e-01L);
549  _points[17](0)=Real(9.8986684820259713441676302277596e-01L);
550 
551  _weights[ 0]=Real(1.0214339435040633872267566728543e-02L);
552  _weights[ 1]=Real(2.3106350163377066931289331193145e-02L);
553  _weights[ 2]=Real(3.4471118921922024965038695158493e-02L);
554  _weights[ 3]=Real(4.3573907074643088262181650935306e-02L);
555  _weights[ 4]=Real(4.9902226917702713891102223856106e-02L);
556  _weights[ 5]=Real(5.3192334631835660026223777017865e-02L);
557  _weights[ 6]=Real(5.3445287802814027020361560753181e-02L);
558  _weights[ 7]=Real(5.0916928856374093181562996165432e-02L);
559  _weights[ 8]=Real(4.6082400990241280762086995392822e-02L);
560  _weights[ 9]=Real(3.9579162288607878726422969126448e-02L);
561  _weights[10]=Real(3.2134806127628549240737903166505e-02L);
562  _weights[11]=Real(2.4487590001291716597869859208141e-02L);
563  _weights[12]=Real(1.7308300480899289815470186505791e-02L);
564  _weights[13]=Real(1.1131870097409362452892993478578e-02L);
565  _weights[14]=Real(6.3060388823805337332782426625400e-03L);
566  _weights[15]=Real(2.9624430644328375036535062298419e-03L);
567  _weights[16]=Real(1.0130251793010471252471709101709e-03L);
568  _weights[17]=Real(1.7186908409819589231237151109171e-04L);
569 
570  return;
571  }
572 
573  case THIRTYSIXTH:
574  case THIRTYSEVENTH:
575  {
576  _points.resize (19);
577  _weights.resize(19);
578 
579  _points[ 0](0)=Real(3.6116428185568930344532101262520e-03L);
580  _points[ 1](0)=Real(1.8931837031588217250264524316949e-02L);
581  _points[ 2](0)=Real(4.6097933048431083573924770835459e-02L);
582  _points[ 3](0)=Real(8.4447222784209820599847900451170e-02L);
583  _points[ 4](0)=Real(1.3303618855809877542408742397522e-01L);
584  _points[ 5](0)=Real(1.9066859490476335108747466488719e-01L);
585  _points[ 6](0)=Real(2.5592540348210296025204739729528e-01L);
586  _points[ 7](0)=Real(3.2719980076381171572842996527566e-01L);
587  _points[ 8](0)=Real(4.0273678616507709512304701110488e-01L);
588  _points[ 9](0)=Real(4.8067639357855190263322135248271e-01L);
589  _points[10](0)=Real(5.5909949264903198784692797587908e-01L);
590  _points[11](0)=Real(6.3607504487927089469109105709816e-01L);
591  _points[12](0)=Real(7.0970765165390239884374678311164e-01L);
592  _points[13](0)=Real(7.7818422297676161420929964704208e-01L);
593  _points[14](0)=Real(8.3981861570871107783863629442929e-01L);
594  _points[15](0)=Real(8.9309313498184497075098115456491e-01L);
595  _points[16](0)=Real(9.3669584807436508054390550208195e-01L);
596  _points[17](0)=Real(9.6955263708022088547192878623227e-01L);
597  _points[18](0)=Real(9.9085180527095568535309483522012e-01L);
598 
599  _weights[ 0]=Real(9.2240377250330766917668248692203e-03L);
600  _weights[ 1]=Real(2.0924651751979890481445228332988e-02L);
601  _weights[ 2]=Real(3.1376275285732898854356814457609e-02L);
602  _weights[ 3]=Real(3.9962370048991741940293076442317e-02L);
603  _weights[ 4]=Real(4.6234928168578411765380785132191e-02L);
604  _weights[ 5]=Real(4.9934138240419379553284105838773e-02L);
605  _weights[ 6]=Real(5.1004186626719396295755229568486e-02L);
606  _weights[ 7]=Real(4.9591046468706580141316052533532e-02L);
607  _weights[ 8]=Real(4.6021985716138412908362881060678e-02L);
608  _weights[ 9]=Real(4.0768870871836685572301729841664e-02L);
609  _weights[10]=Real(3.4398957951907391429559705435925e-02L);
610  _weights[11]=Real(2.7518058144347978141481142479516e-02L);
611  _weights[12]=Real(2.0711672562757804879837159838775e-02L);
612  _weights[13]=Real(1.4489847112109724657001233005036e-02L);
613  _weights[14]=Real(9.2410919293165977626976877702861e-03L);
614  _weights[15]=Real(5.1997813282783796868055465441831e-03L);
615  _weights[16]=Real(2.4300917120432807075681660438661e-03L);
616  _weights[17]=Real(8.2788076092398219334600301771448e-04L);
617  _weights[18]=Real(1.4012759417838633744062778723898e-04L);
618 
619  return;
620  }
621 
622  case THIRTYEIGHTH:
623  case THIRTYNINTH:
624  {
625  _points.resize (20);
626  _weights.resize(20);
627 
628  _points[ 0](0)=Real(3.2761066690500989752646761128711e-03L);
629  _points[ 1](0)=Real(1.7181218145255713738247704631582e-02L);
630  _points[ 2](0)=Real(4.1871431117765195244234634143709e-02L);
631  _points[ 3](0)=Real(7.6800837089621970481870523019947e-02L);
632  _points[ 4](0)=Real(1.2118986732367606561768615229454e-01L);
633  _points[ 5](0)=Real(1.7404711263554216522415793419966e-01L);
634  _points[ 6](0)=Real(2.3419188631359219089445571283230e-01L);
635  _points[ 7](0)=Real(3.0028067683595016436625841871717e-01L);
636  _points[ 8](0)=Real(3.7083718058439689644532207953771e-01L);
637  _points[ 9](0)=Real(4.4428528696301116212882391783598e-01L);
638  _points[10](0)=Real(5.1898428870357372961841176083024e-01L);
639  _points[11](0)=Real(5.9326553348350648796739308654437e-01L);
640  _points[12](0)=Real(6.6546969890551364795372958813385e-01L);
641  _points[13](0)=Real(7.3398385823565944973202719329584e-01L);
642  _points[14](0)=Real(7.9727750833659468770218885137527e-01L);
643  _points[15](0)=Real(8.5393675303589045708900439161802e-01L);
644  _points[16](0)=Real(9.0269587179345369227634694169967e-01L);
645  _points[17](0)=Real(9.4246554236318633869089187742766e-01L);
646  _points[18](0)=Real(9.7235694664743691118470187166465e-01L);
647  _points[19](0)=Real(9.9169995579293273076654365969470e-01L);
648 
649  _weights[ 0]=Real(8.3708441762725569742347797346057e-03L);
650  _weights[ 1]=Real(1.9034969463701666952317752319364e-02L);
651  _weights[ 2]=Real(2.8668237379130596303519483134423e-02L);
652  _weights[ 3]=Real(3.6750239836647855880170014918540e-02L);
653  _weights[ 4]=Real(4.2890295837978204214146023790200e-02L);
654  _weights[ 5]=Real(4.6841691862557827847492882468251e-02L);
655  _weights[ 6]=Real(4.8516105059854090810181874268668e-02L);
656  _weights[ 7]=Real(4.7985461609943912515256158210751e-02L);
657  _weights[ 8]=Real(4.5470588941353475125260875269943e-02L);
658  _weights[ 9]=Real(4.1317706816665737825832945172262e-02L);
659  _weights[10]=Real(3.5964919153862747854063187859799e-02L);
660  _weights[11]=Real(2.9901741842629013049082489189589e-02L);
661  _weights[12]=Real(2.3625296173548892813066360441583e-02L);
662  _weights[13]=Real(1.7597066879206016267686128655074e-02L);
663  _weights[14]=Real(1.2204046126680104278798703245791e-02L);
664  _weights[15]=Real(7.7276679300514628735780671415898e-03L);
665  _weights[16]=Real(4.3232191126901531337390520742896e-03L);
666  _weights[17]=Real(2.0114576139640780069071394684122e-03L);
667  _weights[18]=Real(6.8306227608592198451771987553801e-04L);
668  _weights[19]=Real(1.1538190717568529014836276132844e-04L);
669 
670  return;
671  }
672 
673  case FORTIETH:
674  case FORTYFIRST:
675  {
676  _points.resize (21);
677  _weights.resize(21);
678 
679  _points[ 0](0)=Real(2.9852372832130627418887840757498e-03L);
680  _points[ 1](0)=Real(1.5662280557573547332895610655678e-02L);
681  _points[ 2](0)=Real(3.8198288245073553344832819395658e-02L);
682  _points[ 3](0)=Real(7.0139619062325798139842656763758e-02L);
683  _points[ 4](0)=Real(1.1083667332036350223762530758616e-01L);
684  _points[ 5](0)=Real(1.5946112944406525026381380836555e-01L);
685  _points[ 6](0)=Real(2.1502318535802028508091216764592e-01L);
686  _points[ 7](0)=Real(2.7639177909378317240968620976306e-01L);
687  _points[ 8](0)=Real(3.4231763295873079372348132371246e-01L);
688  _points[ 9](0)=Real(4.1145869156190519892697533612651e-01L);
689  _points[10](0)=Real(4.8240744461243888053531852185958e-01L);
690  _points[11](0)=Real(5.5371958072829359140036561243486e-01L);
691  _points[12](0)=Real(6.2394338972128194749630581474409e-01L);
692  _points[13](0)=Real(6.9164931501296225721944667896925e-01L);
693  _points[14](0)=Real(7.5545905444968698626584997281486e-01L);
694  _points[15](0)=Real(8.1407361651269741678894410957934e-01L);
695  _points[16](0)=Real(8.6629975897095659707636330435792e-01L);
696  _points[17](0)=Real(9.1107426580261577477966643276619e-01L);
697  _points[18](0)=Real(9.4748554440639734668609897166113e-01L);
698  _points[19](0)=Real(9.7479197566036565307915209128675e-01L);
699  _points[20](0)=Real(9.9243549072562147749379027938900e-01L);
700 
701  _weights[ 0]=Real(7.6306059065231890951709176867159e-03L);
702  _weights[ 1]=Real(1.7387926076195012545310092581185e-02L);
703  _weights[ 2]=Real(2.6287260083203306468723755830943e-02L);
704  _weights[ 3]=Real(3.3886790344403175515158905218748e-02L);
705  _weights[ 4]=Real(3.9845977571398966444570950002831e-02L);
706  _weights[ 5]=Real(4.3935570635150377464859835729052e-02L);
707  _weights[ 6]=Real(4.6050270723257502074077985626262e-02L);
708  _weights[ 7]=Real(4.6212552611022412660350368837561e-02L);
709  _weights[ 8]=Real(4.4566874686154606866984823191992e-02L);
710  _weights[ 9]=Real(4.1364760396997617354403702904192e-02L);
711  _weights[10]=Real(3.6942012648499385551903205764287e-02L);
712  _weights[11]=Real(3.1689953050127340376763333466278e-02L);
713  _weights[12]=Real(2.6023046795895555117823162899995e-02L);
714  _weights[13]=Real(2.0345549389821508292035088652126e-02L);
715  _weights[14]=Real(1.5019872613192784763520392446339e-02L);
716  _weights[15]=Real(1.0339209757970312663832726410241e-02L);
717  _weights[16]=Real(6.5065974236456053354067512991831e-03L);
718  _weights[17]=Real(3.6220528697449398652362737797211e-03L);
719  _weights[18]=Real(1.6787560215669155362763365937815e-03L);
720  _weights[19]=Real(5.6849852669976417861179123569953e-04L);
721  _weights[20]=Real(9.5861868529721828979599842865244e-05L);
722 
723  return;
724  }
725 
726  case FORTYSECOND:
727  case FORTYTHIRD:
728  {
729  _points.resize (22);
730  _weights.resize(22);
731 
732  _points[ 0](0)=Real(2.7314460088842296840089704503200e-03L);
733  _points[ 1](0)=Real(1.4335933483699706185308039285053e-02L);
734  _points[ 2](0)=Real(3.4986328351216449387218814071085e-02L);
735  _points[ 3](0)=Real(6.4302641132158882531275071395686e-02L);
736  _points[ 4](0)=Real(1.0173934345216392401258226593794e-01L);
737  _points[ 5](0)=Real(1.4659920015766541692656584266952e-01L);
738  _points[ 6](0)=Real(1.9804660411818261484660504028001e-01L);
739  _points[ 7](0)=Real(2.5512320697168696957682873507625e-01L);
740  _points[ 8](0)=Real(3.1676578871044727183421117602379e-01L);
741  _points[ 9](0)=Real(3.8182606925675020305095127628112e-01L);
742  _points[10](0)=Real(4.4909210098681733251387195042393e-01L);
743  _points[11](0)=Real(5.1731084595099112005136286684174e-01L);
744  _points[12](0)=Real(5.8521151795129912975524533467408e-01L);
745  _points[13](0)=Real(6.5152925489581447403580682231185e-01L);
746  _points[14](0)=Real(7.1502868047476240261215783933800e-01L);
747  _points[15](0)=Real(7.7452691606482263532020273841099e-01L);
748  _points[16](0)=Real(8.2891561362172651235400549854277e-01L);
749  _points[17](0)=Real(8.7718159746542002099358323827803e-01L);
750  _points[18](0)=Real(9.1842572498984926327926994425432e-01L);
751  _points[19](0)=Real(9.5187959322971991452332541323047e-01L);
752  _points[20](0)=Real(9.7691966323712886717816657113704e-01L);
753  _points[21](0)=Real(9.9307748504434821490300210664154e-01L);
754 
755  _weights[ 0]=Real(6.9842561136978136538216549700282e-03L);
756  _weights[ 1]=Real(1.5944053454778496864565929126309e-02L);
757  _weights[ 2]=Real(2.4184236671890499758870393233781e-02L);
758  _weights[ 3]=Real(3.1327596999375227892408958559682e-02L);
759  _weights[ 4]=Real(3.7077054093202864483217335909271e-02L);
760  _weights[ 5]=Real(4.1222404906411452577079119693783e-02L);
761  _weights[ 6]=Real(4.3651203786303462995293138094828e-02L);
762  _weights[ 7]=Real(4.4353370900419806188626977124445e-02L);
763  _weights[ 8]=Real(4.3418750145417827908334525766667e-02L);
764  _weights[ 9]=Real(4.1027795781940901638265438618895e-02L);
765  _weights[10]=Real(3.7436116466930019239662981188891e-02L);
766  _weights[11]=Real(3.2954058785385534039887856528676e-02L);
767  _weights[12]=Real(2.7922870823442631249079662456458e-02L);
768  _weights[13]=Real(2.2689228598160995380212860776143e-02L);
769  _weights[14]=Real(1.7580017560152292742735027157072e-02L);
770  _weights[15]=Real(1.2879230281365339696348205046681e-02L);
771  _weights[16]=Real(8.8086724401109070881737532508054e-03L);
772  _weights[17]=Real(5.5138751021276410109163746634529e-03L);
773  _weights[18]=Real(3.0562141131504037344643025112362e-03L);
774  _weights[19]=Real(1.4117668531394242829582650189559e-03L);
775  _weights[20]=Real(4.7692790565900675904839748933142e-04L);
776  _weights[21]=Real(8.0298216937450816028842814607537e-05L);
777 
778  return;
779  }
780 
781  default:
782  libmesh_error_msg("Quadrature rule " << _order << " not supported!");
783  } // end switch(_order + 2*p)
784  } // end if ((_alpha == 1) && (_beta == 0))
785 
786 
787 
788  else if ((_alpha == 2) && (_beta == 0))
789  {
790 
791  switch(get_order())
792  {
793  case CONSTANT:
794  case FIRST:
795  {
796  _points.resize (1);
797  _weights.resize(1);
798 
799  _points[0](0) = 0.25;
800 
801  _weights[0] = 1./3.;
802 
803  return;
804  }
805  case SECOND:
806  case THIRD:
807  {
808  _points.resize (2);
809  _weights.resize(2);
810 
811  _points[ 0](0)=Real(1.2251482265544137786674043037115e-01L);
812  _points[ 1](0)=Real(5.4415184401122528879992623629551e-01L);
813 
814  _weights[ 0]=Real(2.3254745125350790274997694884235e-01L);
815  _weights[ 1]=Real(1.0078588207982543058335638449099e-01L);
816 
817  return;
818  }
819  case FOURTH:
820  case FIFTH:
821  {
822  _points.resize (3);
823  _weights.resize(3);
824 
825  _points[ 0](0)=Real(7.2994024073149732155837979012003e-02L);
826  _points[ 1](0)=Real(3.4700376603835188472176354340395e-01L);
827  _points[ 2](0)=Real(7.0500220988849838312239847758405e-01L);
828 
829  _weights[ 0]=Real(1.5713636106488661331834482221327e-01L);
830  _weights[ 1]=Real(1.4624626925986602200351202036424e-01L);
831  _weights[ 2]=Real(2.9950703008580698011476490755827e-02L);
832 
833  return;
834  }
835  case SIXTH:
836  case SEVENTH:
837  {
838  _points.resize (4);
839  _weights.resize(4);
840 
841  _points[ 0](0)=Real(4.8500549446997329297067257098986e-02L);
842  _points[ 1](0)=Real(2.3860073755186230505898141272470e-01L);
843  _points[ 2](0)=Real(5.1704729510436750234057336938307e-01L);
844  _points[ 3](0)=Real(7.9585141789677286330337796079324e-01L);
845 
846  _weights[ 0]=Real(1.1088841561127798368323131746895e-01L);
847  _weights[ 1]=Real(1.4345878979921420904832801427594e-01L);
848  _weights[ 2]=Real(6.8633887172923075317376345041811e-02L);
849  _weights[ 3]=Real(1.0352240749918065284397656546639e-02L);
850 
851  return;
852  }
853  case EIGHTH:
854  case NINTH:
855  {
856  _points.resize (5);
857  _weights.resize(5);
858 
859  _points[ 0](0)=Real(3.4578939918215091524457428631527e-02L);
860  _points[ 1](0)=Real(1.7348032077169572310459241798618e-01L);
861  _points[ 2](0)=Real(3.8988638706551932824089541038499e-01L);
862  _points[ 3](0)=Real(6.3433347263088677234716388892062e-01L);
863  _points[ 4](0)=Real(8.5105421294701641811622418741001e-01L);
864 
865  _weights[ 0]=Real(8.1764784285770917904880732922352e-02L);
866  _weights[ 1]=Real(1.2619896189991148802883293516467e-01L);
867  _weights[ 2]=Real(8.9200161221590000186254493070384e-02L);
868  _weights[ 3]=Real(3.2055600722961919254748930556633e-02L);
869  _weights[ 4]=Real(4.1138252030990079586162416192983e-03L);
870 
871  return;
872  }
873  case TENTH:
874  case ELEVENTH:
875  {
876  _points.resize (6);
877  _weights.resize(6);
878 
879  _points[ 0](0)=Real(2.5904555093667192754643606997235e-02L);
880  _points[ 1](0)=Real(1.3156394165798513398691085074097e-01L);
881  _points[ 2](0)=Real(3.0243691802289123274990557791855e-01L);
882  _points[ 3](0)=Real(5.0903641316475208401103990516772e-01L);
883  _points[ 4](0)=Real(7.1568112731171391876766262459361e-01L);
884  _points[ 5](0)=Real(8.8680561617756186630126600601049e-01L);
885 
886  _weights[ 0]=Real(6.2538702726580937878526556468332e-02L);
887  _weights[ 1]=Real(1.0737649973678063260575568234795e-01L);
888  _weights[ 2]=Real(9.4577186748541203568292051720052e-02L);
889  _weights[ 3]=Real(5.1289571129616210220129325076919e-02L);
890  _weights[ 4]=Real(1.5720297184945051327851262130020e-02L);
891  _weights[ 5]=Real(1.8310758068692977327784555900562e-03L);
892 
893  return;
894  }
895  case TWELFTH:
896  case THIRTEENTH:
897  {
898  _points.resize (7);
899  _weights.resize(7);
900 
901  _points[ 0](0)=Real(2.0132773773400507230501687117472e-02L);
902  _points[ 1](0)=Real(1.0308902914804901475222678600595e-01L);
903  _points[ 2](0)=Real(2.4055412604805753665369914150100e-01L);
904  _points[ 3](0)=Real(4.1400214459705974641828724885057e-01L);
905  _points[ 4](0)=Real(6.0002151327899293019396877288994e-01L);
906  _points[ 5](0)=Real(7.7351724659143750111199899642603e-01L);
907  _points[ 6](0)=Real(9.1118316656300276363931736720905e-01L);
908 
909  _weights[ 0]=Real(4.9276501776438120823429129084905e-02L);
910  _weights[ 1]=Real(9.0698824612686144536967479972374e-02L);
911  _weights[ 2]=Real(9.1733803279795254111416595896867e-02L);
912  _weights[ 3]=Real(6.3146378708891297709533940481199e-02L);
913  _weights[ 4]=Real(2.9422211289528614840745351985011e-02L);
914  _weights[ 5]=Real(8.1629256323046945072318090687213e-03L);
915  _weights[ 6]=Real(8.9268803368920680400902684425561e-04L);
916 
917  return;
918  }
919  case FOURTEENTH:
920  case FIFTEENTH:
921  {
922  _points.resize (8);
923  _weights.resize(8);
924 
925  _points[ 0](0)=Real(1.6097759551921033532013550096618e-02L);
926  _points[ 1](0)=Real(8.2900617485651102700366353380388e-02L);
927  _points[ 2](0)=Real(1.9547516848873991732426660953061e-01L);
928  _points[ 3](0)=Real(3.4165199147720222027296226216240e-01L);
929  _points[ 4](0)=Real(5.0559707818448917194006186500608e-01L);
930  _points[ 5](0)=Real(6.6955227182436145183011451055437e-01L);
931  _points[ 6](0)=Real(8.1577170358328376075475178697587e-01L);
932  _points[ 7](0)=Real(9.2850896495990689720101861784923e-01L);
933 
934  _weights[ 0]=Real(3.9778957806690559830106455926398e-02L);
935  _weights[ 1]=Real(7.6818093267222624804506735068290e-02L);
936  _weights[ 2]=Real(8.5284769171938765209441226265186e-02L);
937  _weights[ 3]=Real(6.8447183421653272247027200610852e-02L);
938  _weights[ 4]=Real(4.0814426388544023186461596152148e-02L);
939  _weights[ 5]=Real(1.7246863780234982804243655774862e-02L);
940  _weights[ 6]=Real(4.4745217130144079957565210032836e-03L);
941  _weights[ 7]=Real(4.6851778403469725578994253231334e-04L);
942 
943  return;
944  }
945  case SIXTEENTH:
946  case SEVENTEENTH:
947  {
948  _points.resize (9);
949  _weights.resize(9);
950 
951  _points[ 0](0)=Real(1.3165885597114490545190537817972e-02L);
952  _points[ 1](0)=Real(6.8084529593767587476505856986822e-02L);
953  _points[ 2](0)=Real(1.6175951676407464206981091232919e-01L);
954  _points[ 3](0)=Real(2.8589108833922039772798956691264e-01L);
955  _points[ 4](0)=Real(4.2945364538781279250924800228659e-01L);
956  _points[ 5](0)=Real(5.7969405635116312626577241331199e-01L);
957  _points[ 6](0)=Real(7.2326857174033543181796015820021e-01L);
958  _points[ 7](0)=Real(8.4743684201323732017318042501962e-01L);
959  _points[ 8](0)=Real(9.4124586421327421141434212713498e-01L);
960 
961  _weights[ 0]=Real(3.2760145111039721461819540084274e-02L);
962  _weights[ 1]=Real(6.5489537033396631781939107203912e-02L);
963  _weights[ 2]=Real(7.7673569160555504078595170478444e-02L);
964  _weights[ 3]=Real(6.9284395689804709215727785348892e-02L);
965  _weights[ 4]=Real(4.8540627864506507959528062424865e-02L);
966  _weights[ 5]=Real(2.6343280902549835737974696002673e-02L);
967  _weights[ 6]=Real(1.0406116579352237052426337235938e-02L);
968  _weights[ 7]=Real(2.5743986456087231023317159056037e-03L);
969  _weights[ 8]=Real(2.6126234651946294299091864873302e-04L);
970 
971  return;
972  }
973  case EIGHTTEENTH:
974  case NINETEENTH:
975  {
976  _points.resize (10);
977  _weights.resize(10);
978 
979  _points[ 0](0)=Real(1.0968452456174134250281032990432e-02L);
980  _points[ 1](0)=Real(5.6898150533657920711434859379121e-02L);
981  _points[ 2](0)=Real(1.3595023405022895426576342938519e-01L);
982  _points[ 3](0)=Real(2.4228119613252356111139455536509e-01L);
983  _points[ 4](0)=Real(3.6800785044933771760476956625017e-01L);
984  _points[ 5](0)=Real(5.0380712641487390700553064205723e-01L);
985  _points[ 6](0)=Real(6.3960948865470970932853650616696e-01L);
986  _points[ 7](0)=Real(7.6534767954810789620953312724460e-01L);
987  _points[ 8](0)=Real(8.7171007457440848761186134200542e-01L);
988  _points[ 9](0)=Real(9.5087429264052316644634948461033e-01L);
989 
990  _weights[ 0]=Real(2.7434088710097496960451648584485e-02L);
991  _weights[ 1]=Real(5.6272936402808126282415832152709e-02L);
992  _weights[ 2]=Real(7.0069507708666334086372455308183e-02L);
993  _weights[ 3]=Real(6.7452219381437824970525794313691e-02L);
994  _weights[ 4]=Real(5.2883788766964158209884838942421e-02L);
995  _weights[ 5]=Real(3.3854565016814116044101071309373e-02L);
996  _weights[ 6]=Real(1.7197575046553008079137502323978e-02L);
997  _weights[ 7]=Real(6.4698890685585292297306065609276e-03L);
998  _weights[ 8]=Real(1.5455231947365786285853268147186e-03L);
999  _weights[ 9]=Real(1.5324003669716084212825702284675e-04L);
1000 
1001  return;
1002  }
1003  case TWENTIETH:
1004  case TWENTYFIRST:
1005  {
1006  _points.resize (11);
1007  _weights.resize(11);
1008 
1009  _points[ 0](0)=Real(9.2789738313488342029466103013448e-03L);
1010  _points[ 1](0)=Real(4.8249692094286258286483723731132e-02L);
1011  _points[ 2](0)=Real(1.1578862662939522596030591825565e-01L);
1012  _points[ 3](0)=Real(2.0766834159705988244389542530053e-01L);
1013  _points[ 4](0)=Real(3.1811795190623396637744646657914e-01L);
1014  _points[ 5](0)=Real(4.4019839985886246708268132217632e-01L);
1015  _points[ 6](0)=Real(5.6623983915456831356751247193488e-01L);
1016  _points[ 7](0)=Real(6.8832423986295668569553397580809e-01L);
1017  _points[ 8](0)=Real(7.9878435859091464197460872800735e-01L);
1018  _points[ 9](0)=Real(8.9069109935439218915081289990608e-01L);
1019  _points[10](0)=Real(9.5832514378664820192443912466615e-01L);
1020 
1021  _weights[ 0]=Real(2.3300850051388377415061404350855e-02L);
1022  _weights[ 1]=Real(4.8745861030664491864450329028080e-02L);
1023  _weights[ 2]=Real(6.2979543000367394338333998811129e-02L);
1024  _weights[ 3]=Real(6.4183559349755944992539371306173e-02L);
1025  _weights[ 4]=Real(5.4632222321044926070678715192708e-02L);
1026  _weights[ 5]=Real(3.9290217798435612246535835921329e-02L);
1027  _weights[ 6]=Real(2.3589663538806928649316661943808e-02L);
1028  _weights[ 7]=Real(1.1414590918097618249921262806781e-02L);
1029  _weights[ 8]=Real(4.1400042632190223547676874553245e-03L);
1030  _weights[ 9]=Real(9.6302057554323908320037373956771e-04L);
1031  _weights[10]=Real(9.3800486009778068527692777578977e-05L);
1032 
1033  return;
1034  }
1035  case TWENTYSECOND:
1036  case TWENTYTHIRD:
1037  {
1038  _points.resize (12);
1039  _weights.resize(12);
1040 
1041  _points[ 0](0)=Real(7.9520457026384368762190933400404e-03L);
1042  _points[ 1](0)=Real(4.1427810454294590790770165194795e-02L);
1043  _points[ 2](0)=Real(9.9757625542614157066081703480300e-02L);
1044  _points[ 3](0)=Real(1.7981078905242324954164334430721e-01L);
1045  _points[ 4](0)=Real(2.7727345779931511981753891831052e-01L);
1046  _points[ 5](0)=Real(3.8689200999768979166563470380544e-01L);
1047  _points[ 6](0)=Real(5.0275736044903220327930927843912e-01L);
1048  _points[ 7](0)=Real(6.1862386345845604629354886189114e-01L);
1049  _points[ 8](0)=Real(7.2824645295307268642888033006114e-01L);
1050  _points[ 9](0)=Real(8.2571851421478690176408336295370e-01L);
1051  _points[10](0)=Real(9.0579507354454372680179647039974e-01L);
1052  _points[11](0)=Real(9.6420653529267155121295530627839e-01L);
1053 
1054  _weights[ 0]=Real(2.0031112584748752943807724216722e-02L);
1055  _weights[ 1]=Real(4.2556615367405637772968490900760e-02L);
1056  _weights[ 2]=Real(5.6584184749474069646478036154467e-02L);
1057  _weights[ 3]=Real(6.0250607487604518170935343500906e-02L);
1058  _weights[ 4]=Real(5.4573941164231582825558709780290e-02L);
1059  _weights[ 5]=Real(4.2764763570188902317265936785879e-02L);
1060  _weights[ 6]=Real(2.8908051838727360494403492180206e-02L);
1061  _weights[ 7]=Real(1.6547343644609412101387213540038e-02L);
1062  _weights[ 8]=Real(7.7163670238864266187877366246530e-03L);
1063  _weights[ 9]=Real(2.7208421441038393545415361663513e-03L);
1064  _weights[10]=Real(6.1995339854451942336673117135933e-04L);
1065  _weights[11]=Real(5.9550359808311663832382311702501e-05L);
1066 
1067  return;
1068  }
1069 
1070  case TWENTYFOURTH:
1071  case TWENTYFIFTH:
1072  {
1073  _points.resize (13);
1074  _weights.resize(13);
1075 
1076  _points[ 0](0)=Real(6.8908313099587313966815341534070e-03L);
1077  _points[ 1](0)=Real(3.5953362700170095501132811969521e-02L);
1078  _points[ 2](0)=Real(8.6811780157585433284280307690601e-02L);
1079  _points[ 3](0)=Real(1.5709997419650927473052206555148e-01L);
1080  _points[ 4](0)=Real(2.4353289958712844441903410356775e-01L);
1081  _points[ 5](0)=Real(3.4206951264607532347450799656627e-01L);
1082  _points[ 6](0)=Real(4.4810263890570985362873430879398e-01L);
1083  _points[ 7](0)=Real(5.5667462262945501069694664236208e-01L);
1084  _points[ 8](0)=Real(6.6270931356038854232146315212326e-01L);
1085  _points[ 9](0)=Real(7.6124976630827697227665952639343e-01L);
1086  _points[10](0)=Real(8.4769104394723239091031404895142e-01L);
1087  _points[11](0)=Real(9.1799964553720667953362597028835e-01L);
1088  _points[12](0)=Real(9.6892889422858896211181181730274e-01L);
1089 
1090  _weights[ 0]=Real(1.7401228610061845488081141733526e-02L);
1091  _weights[ 1]=Real(3.7426708168844039953666298186474e-02L);
1092  _weights[ 2]=Real(5.0909830712695019092906847187640e-02L);
1093  _weights[ 3]=Real(5.6111537130827396185039872203667e-02L);
1094  _weights[ 4]=Real(5.3340021605871745725401666422880e-02L);
1095  _weights[ 5]=Real(4.4624600755614954430566337477243e-02L);
1096  _weights[ 6]=Real(3.2940451678432790083648445397381e-02L);
1097  _weights[ 7]=Real(2.1254996714756613031113108888658e-02L);
1098  _weights[ 8]=Real(1.1728259593101880662970381149369e-02L);
1099  _weights[ 9]=Real(5.3135693388326384480559144318474e-03L);
1100  _weights[10]=Real(1.8323911392393785873485644191745e-03L);
1101  _weights[11]=Real(4.1072089179088541678428389490865e-04L);
1102  _weights[12]=Real(3.9016993264146227750471940564101e-05L);
1103 
1104  return;
1105  }
1106 
1107  case TWENTYSIXTH:
1108  case TWENTYSEVENTH:
1109  {
1110  _points.resize (14);
1111  _weights.resize(14);
1112 
1113  _points[ 0](0)=Real(6.0288088710666481700887477121600e-03L);
1114  _points[ 1](0)=Real(3.1494259818657590707306712766317e-02L);
1115  _points[ 2](0)=Real(7.6213622474853867586406786340023e-02L);
1116  _points[ 3](0)=Real(1.3836652595947406914513833295825e-01L);
1117  _points[ 4](0)=Real(2.1540975706889557490069553208515e-01L);
1118  _points[ 5](0)=Real(3.0418952814165630963236635490440e-01L);
1119  _points[ 6](0)=Real(4.0107137869715435758118603205199e-01L);
1120  _points[ 7](0)=Real(5.0208913974997841006932539804960e-01L);
1121  _points[ 8](0)=Real(6.0310739672759678368189556654036e-01L);
1122  _points[ 9](0)=Real(6.9999091716990649741073666393849e-01L);
1123  _points[10](0)=Real(7.8877423843456071534030488559891e-01L);
1124  _points[11](0)=Real(8.6582490073159695367114083518102e-01L);
1125  _points[12](0)=Real(9.2799573874675232498377812203940e-01L);
1126  _points[13](0)=Real(9.7277712074118323045296336316727e-01L);
1127 
1128  _weights[ 0]=Real(1.5255206119448295373511341972378e-02L);
1129  _weights[ 1]=Real(3.3139595469960559875930225836517e-02L);
1130  _weights[ 2]=Real(4.5914772114671178911403799944693e-02L);
1131  _weights[ 3]=Real(5.2025865410701701832827358849471e-02L);
1132  _weights[ 4]=Real(5.1389924039471503273808065266413e-02L);
1133  _weights[ 5]=Real(4.5253432254460881465122373566022e-02L);
1134  _weights[ 6]=Real(3.5739010292514612984162525810346e-02L);
1135  _weights[ 7]=Real(2.5216183536839055034306220202219e-02L);
1136  _weights[ 8]=Real(1.5694332285072957184930434798487e-02L);
1137  _weights[ 9]=Real(8.4129767371364622096077152778570e-03L);
1138  _weights[10]=Real(3.7248756752828588215538124784652e-03L);
1139  _weights[11]=Real(1.2617838951574880413283334197260e-03L);
1140  _weights[12]=Real(2.7909934094687847008945560658272e-04L);
1141  _weights[13]=Real(2.6276161668899854751670304157309e-05L);
1142 
1143  return;
1144  }
1145 
1146  case TWENTYEIGHTH:
1147  case TWENTYNINTH:
1148  {
1149  _points.resize (15);
1150  _weights.resize(15);
1151 
1152  _points[ 0](0)=Real(5.3190520028437405909978402739774e-03L);
1153  _points[ 1](0)=Real(2.7814561918260051571980709238074e-02L);
1154  _points[ 2](0)=Real(6.7431865838998613384568577571818e-02L);
1155  _points[ 3](0)=Real(1.2274828621549783933958732401303e-01L);
1156  _points[ 4](0)=Real(1.9176570627765362550282684505042e-01L);
1157  _points[ 5](0)=Real(2.7198996592948620305633800793026e-01L);
1158  _points[ 6](0)=Real(3.6052169358705764815778444077840e-01L);
1159  _points[ 7](0)=Real(4.5416123575447709916009624996188e-01L);
1160  _points[ 8](0)=Real(5.4952435559355131365468962196031e-01L);
1161  _points[ 9](0)=Real(6.4316460176878493853949400884187e-01L);
1162  _points[10](0)=Real(7.3169797305252320629933948467521e-01L);
1163  _points[11](0)=Real(8.1192547727500966668969312120195e-01L);
1164  _points[12](0)=Real(8.8094952871531360238808055493652e-01L);
1165  _points[13](0)=Real(9.3628182173551874210251937228715e-01L);
1166  _points[14](0)=Real(9.7595387433502370956200384127912e-01L);
1167 
1168  _weights[ 0]=Real(1.3481662725134304090265733542410e-02L);
1169  _weights[ 1]=Real(2.9527650756798205089388266870014e-02L);
1170  _weights[ 2]=Real(4.1531307651604265373799456795289e-02L);
1171  _weights[ 3]=Real(4.8132057668529815888404876719886e-02L);
1172  _weights[ 4]=Real(4.9041267894409180565196427508457e-02L);
1173  _weights[ 5]=Real(4.4991555820615933365730152800755e-02L);
1174  _weights[ 6]=Real(3.7473875792101303095319296790068e-02L);
1175  _weights[ 7]=Real(2.8326553174241247644068974123766e-02L);
1176  _weights[ 8]=Real(1.9293416585274520485988288429744e-02L);
1177  _weights[ 9]=Real(1.1668582484776638563534331197891e-02L);
1178  _weights[10]=Real(6.1110501102060490412153142922240e-03L);
1179  _weights[11]=Real(2.6556629857743191811282114211333e-03L);
1180  _weights[12]=Real(8.8657363523409667398227745346013e-04L);
1181  _weights[13]=Real(1.9398726306394554934013378631178e-04L);
1182  _weights[14]=Real(1.8128785569508725971591601924058e-05L);
1183 
1184  return;
1185  }
1186 
1187 
1188  case THIRTIETH:
1189  case THIRTYFIRST:
1190  {
1191  _points.resize (16);
1192  _weights.resize(16);
1193 
1194  _points[ 0](0)=Real(4.7276871229345922061506104450645e-03L);
1195  _points[ 1](0)=Real(2.4742967619434984512603456269536e-02L);
1196  _points[ 2](0)=Real(6.0076437716637992275242255328112e-02L);
1197  _points[ 3](0)=Real(1.0960060925877060286789758461950e-01L);
1198  _points[ 4](0)=Real(1.7172475948300210790307417791270e-01L);
1199  _points[ 5](0)=Real(2.4445243174451137730207656160275e-01L);
1200  _points[ 6](0)=Real(3.2544621002412961482683685190181e-01L);
1201  _points[ 7](0)=Real(4.1210296411685959691728421362251e-01L);
1202  _points[ 8](0)=Real(5.0163755615318759370013043235084e-01L);
1203  _points[ 9](0)=Real(5.9117238531650308897076051877634e-01L);
1204  _points[10](0)=Real(6.7782991741456081130251277264148e-01L);
1205  _points[11](0)=Real(7.5882525794914141335427940535114e-01L);
1206  _points[12](0)=Real(8.3155588302646195188920635482406e-01L);
1207  _points[13](0)=Real(8.9368597454880401881486969876816e-01L);
1208  _points[14](0)=Real(9.4322428571224559352545066239296e-01L);
1209  _points[15](0)=Real(9.7860643749869701257280091378128e-01L);
1210 
1211  _weights[ 0]=Real(1.1999405624691969586506695404143e-02L);
1212  _weights[ 1]=Real(2.6460842517339527040437264564557e-02L);
1213  _weights[ 2]=Real(3.7685824681918572833315081444311e-02L);
1214  _weights[ 3]=Real(4.4496573472543214976151049587710e-02L);
1215  _weights[ 4]=Real(4.6506239397362658797012521100333e-02L);
1216  _weights[ 5]=Real(4.4112657675899371113911374089320e-02L);
1217  _weights[ 6]=Real(3.8348046951185955673582690910292e-02L);
1218  _weights[ 7]=Real(3.0612037917837609541948834407964e-02L);
1219  _weights[ 8]=Real(2.2357185649529930223334734263644e-02L);
1220  _weights[ 9]=Real(1.4803776657751738340239250997704e-02L);
1221  _weights[10]=Real(8.7475454956120699745801506391282e-03L);
1222  _weights[11]=Real(4.4948488514798588832066397608164e-03L);
1223  _weights[12]=Real(1.9235319260667742273824398535627e-03L);
1224  _weights[13]=Real(6.3445999956883686801084896849641e-04L);
1225  _weights[14]=Real(1.3757810397555175246959527906570e-04L);
1226  _weights[15]=Real(1.2778410569693501244162062287056e-05L);
1227 
1228  return;
1229  }
1230 
1231 
1232  case THIRTYSECOND:
1233  case THIRTYTHIRD:
1234  {
1235  _points.resize (17);
1236  _weights.resize(17);
1237 
1238  _points[ 0](0)=Real(4.2297654864907678749919877813007e-03L);
1239  _points[ 1](0)=Real(2.2152705311830232294209002101573e-02L);
1240  _points[ 2](0)=Real(5.3856014827184829566760322013645e-02L);
1241  _points[ 3](0)=Real(9.8434936830541362494246924237098e-02L);
1242  _points[ 4](0)=Real(1.5460792826588562987838903880788e-01L);
1243  _points[ 5](0)=Real(2.2075922519215138391363787768336e-01L);
1244  _points[ 6](0)=Real(2.9498586629802348865100598497056e-01L);
1245  _points[ 7](0)=Real(3.7515254164081788200834771392226e-01L);
1246  _points[ 8](0)=Real(4.5895305335301908085933451474375e-01L);
1247  _points[ 9](0)=Real(5.4397667809047570974515217435547e-01L);
1248  _points[10](0)=Real(6.2777753854681427256560538094776e-01L);
1249  _points[11](0)=Real(7.0794500138508556794362242607309e-01L);
1250  _points[12](0)=Real(7.8217310308122112810113854015572e-01L);
1251  _points[13](0)=Real(8.4832708570995060757906353137179e-01L);
1252  _points[14](0)=Real(9.0450542331432870037906100932836e-01L);
1253  _points[15](0)=Real(9.4909701659654457024654762835657e-01L);
1254  _points[16](0)=Real(9.8084389384741256367666372092760e-01L);
1255 
1256  _weights[ 0]=Real(1.0748151030768621662834062204936e-02L);
1257  _weights[ 1]=Real(2.3837762018703244620506074665265e-02L);
1258  _weights[ 2]=Real(3.4307889795671880028436869439002e-02L);
1259  _weights[ 3]=Real(4.1143975847068207121110777965721e-02L);
1260  _weights[ 4]=Real(4.3922618772592577808611328095136e-02L);
1261  _weights[ 5]=Real(4.2825403927934553301439133345126e-02L);
1262  _weights[ 6]=Real(3.8555241947102353628223582107170e-02L);
1263  _weights[ 7]=Real(3.2163570112378639217164962127759e-02L);
1264  _weights[ 8]=Real(2.4829256111976082802381065145755e-02L);
1265  _weights[ 9]=Real(1.7638789331050110518481458865839e-02L);
1266  _weights[10]=Real(1.1413642238636687747573403275566e-02L);
1267  _weights[11]=Real(6.6164197603617147286557116199452e-03L);
1268  _weights[12]=Real(3.3465172918198153715474254116460e-03L);
1269  _weights[13]=Real(1.4138837589561322316624033902623e-03L);
1270  _weights[14]=Real(4.6167405877711308077043506706165e-04L);
1271  _weights[15]=Real(9.9356525335473959962406835119113e-05L);
1272  _weights[16]=Real(9.1808042001255039722337720228143e-06L);
1273 
1274  return;
1275  }
1276 
1277  case THIRTYFOURTH:
1278  case THIRTYFIFTH:
1279  {
1280  _points.resize (18);
1281  _weights.resize(18);
1282 
1283  _points[ 0](0)=Real(3.8065822475018763836485343548908e-03L);
1284  _points[ 1](0)=Real(1.9948351047343018666301273550578e-02L);
1285  _points[ 2](0)=Real(4.8549645304224630965525818224597e-02L);
1286  _points[ 3](0)=Real(8.8876259116497388048181392194957e-02L);
1287  _points[ 4](0)=Real(1.3988457083516926493003835526765e-01L);
1288  _points[ 5](0)=Real(2.0025369592363033820671255853211e-01L);
1289  _points[ 6](0)=Real(2.6842018278660208442014712803618e-01L);
1290  _points[ 7](0)=Real(3.4261859780200830045140484446480e-01L);
1291  _points[ 8](0)=Real(4.2092727587031795580391095608392e-01L);
1292  _points[ 9](0)=Real(5.0131810275027358836467598537906e-01L);
1293  _points[10](0)=Real(5.8170905267091792822883758529331e-01L);
1294  _points[11](0)=Real(6.6001812722531554655212340270381e-01L);
1295  _points[12](0)=Real(7.3421730813501325031921736140253e-01L);
1296  _points[13](0)=Real(8.0238514983641747020667379058517e-01L);
1297  _points[14](0)=Real(8.6275672070005501336081662021610e-01L);
1298  _points[15](0)=Real(9.1376986411079293616612318979159e-01L);
1299  _points[16](0)=Real(9.5410789551731665881890309384613e-01L);
1300  _points[17](0)=Real(9.8274840759428696063307389954630e-01L);
1301 
1302  _weights[ 0]=Real(9.6823988037660231774964807691529e-03L);
1303  _weights[ 1]=Real(2.1578772679193827027157750409882e-02L);
1304  _weights[ 2]=Real(3.1333907671729513327950397913143e-02L);
1305  _weights[ 3]=Real(3.8075134253447687665457823100366e-02L);
1306  _weights[ 4]=Real(4.1377182287519565332651504100178e-02L);
1307  _weights[ 5]=Real(4.1283665809957749414286828772884e-02L);
1308  _weights[ 6]=Real(3.8262794672349299757849656256339e-02L);
1309  _weights[ 7]=Real(3.3095976202072497795672769135623e-02L);
1310  _weights[ 8]=Real(2.6723424368960119486097972811646e-02L);
1311  _weights[ 9]=Real(2.0078641696369720179443819032712e-02L);
1312  _weights[10]=Real(1.3943897653647906425703531920973e-02L);
1313  _weights[11]=Real(8.8522782250949774435502470347624e-03L);
1314  _weights[12]=Real(5.0502487883546813166841235600508e-03L);
1315  _weights[13]=Real(2.5207216384362558022745702364513e-03L);
1316  _weights[14]=Real(1.0535502839571923712409403476880e-03L);
1317  _weights[15]=Real(3.4109120368765498289598525047321e-04L);
1318  _weights[16]=Real(7.2937008664118705328162954331465e-05L);
1319  _weights[17]=Real(6.7100861245431215907697266774769e-06L);
1320 
1321  return;
1322  }
1323 
1324  case THIRTYSIXTH:
1325  case THIRTYSEVENTH:
1326  {
1327  _points.resize (19);
1328  _weights.resize(19);
1329 
1330  _points[ 0](0)=Real(3.4438904038624902806940509331722e-03L);
1331  _points[ 1](0)=Real(1.8056978337900562863030093954343e-02L);
1332  _points[ 2](0)=Real(4.3987395090842734455198832773659e-02L);
1333  _points[ 3](0)=Real(8.0633276366661415469721776663016e-02L);
1334  _points[ 4](0)=Real(1.2713640986156026953002535083969e-01L);
1335  _points[ 5](0)=Real(1.8240698366909185313069695387128e-01L);
1336  _points[ 6](0)=Real(2.4514956909516857055249217701821e-01L);
1337  _points[ 7](0)=Real(3.1389356741821822415240859865307e-01L);
1338  _points[ 8](0)=Real(3.8702770276933220341545290751683e-01L);
1339  _points[ 9](0)=Real(4.6283779855202027820220487054694e-01L);
1340  _points[10](0)=Real(5.3954696279208808766943066332998e-01L);
1341  _points[11](0)=Real(6.1535724480454716546694016358337e-01L);
1342  _points[12](0)=Real(6.8849179091409498918986551203802e-01L);
1343  _points[13](0)=Real(7.5723651917329793549736932794667e-01L);
1344  _points[14](0)=Real(8.1998035706323733537954006841029e-01L);
1345  _points[15](0)=Real(8.7525316298382668006594890887609e-01L);
1346  _points[16](0)=Real(9.2176068172914004889937421632274e-01L);
1347  _points[17](0)=Real(9.5841690242340714510347790926694e-01L);
1348  _points[18](0)=Real(9.8438280655170201067612761745569e-01L);
1349 
1350  _weights[ 0]=Real(8.7672970568792323661393261305840e-03L);
1351  _weights[ 1]=Real(1.9620856340232434512901283777202e-02L);
1352  _weights[ 2]=Real(2.8708149778704086122791006941433e-02L);
1353  _weights[ 3]=Real(3.5278117199476000434599584597235e-02L);
1354  _weights[ 4]=Real(3.8922386222261737550985848811514e-02L);
1355  _weights[ 5]=Real(3.9598248214880677015066061570123e-02L);
1356  _weights[ 6]=Real(3.7607500520347543950912173611332e-02L);
1357  _weights[ 7]=Real(3.3525068070610283960905700567460e-02L);
1358  _weights[ 8]=Real(2.8091607936102907649141378579235e-02L);
1359  _weights[ 9]=Real(2.2090563149823990465333672755377e-02L);
1360  _weights[10]=Real(1.6231815321996325630177612472423e-02L);
1361  _weights[11]=Real(1.1061440629037007897211784796273e-02L);
1362  _weights[12]=Real(6.9108110779321981973514541466546e-03L);
1363  _weights[13]=Real(3.8897848125530902102984958782958e-03L);
1364  _weights[14]=Real(1.9197884726923132048372710905667e-03L);
1365  _weights[15]=Real(7.9504432544855937325482850317179e-04L);
1366  _weights[16]=Real(2.5553085889097125647555166013802e-04L);
1367  _weights[17]=Real(5.4342643132004416773622274012570e-05L);
1368  _weights[18]=Real(4.9807023319691181766751703037610e-06L);
1369 
1370  return;
1371  }
1372 
1373  case THIRTYEIGHTH:
1374  case THIRTYNINTH:
1375  {
1376  _points.resize (20);
1377  _weights.resize(20);
1378 
1379  _points[ 0](0)=Real(3.1306837407435895621501417495463e-03L);
1380  _points[ 1](0)=Real(1.6422088133987832902541614256258e-02L);
1381  _points[ 2](0)=Real(4.0036900461906780996320149828793e-02L);
1382  _points[ 3](0)=Real(7.3477191785285283057566545285874e-02L);
1383  _points[ 4](0)=Real(1.1603090765548680494669743156748e-01L);
1384  _points[ 5](0)=Real(1.6679125348100943001298070145849e-01L);
1385  _points[ 6](0)=Real(2.2467641938430503840938196483210e-01L);
1386  _points[ 7](0)=Real(2.8845271218127238477194070665240e-01L);
1387  _points[ 8](0)=Real(3.5676087010245310564705506663326e-01L);
1388  _points[ 9](0)=Real(4.2814504093325668461542503477245e-01L);
1389  _points[10](0)=Real(5.0108381548284855137062465413693e-01L);
1390  _points[11](0)=Real(5.7402265818282687172751219665371e-01L);
1391  _points[12](0)=Real(6.4540704577736756661732083476397e-01L);
1392  _points[13](0)=Real(7.1371561101528768074208343535393e-01L);
1393  _points[14](0)=Real(7.7749259203548675355112594583658e-01L);
1394  _points[15](0)=Real(8.3537891463156172517151839471341e-01L);
1395  _points[16](0)=Real(8.8614130291454714368728293036495e-01L);
1396  _points[17](0)=Real(9.2869901491875054534509783716727e-01L);
1397  _points[18](0)=Real(9.6214871215049818970916080642292e-01L);
1398  _points[19](0)=Real(9.8579578884064184668002313135922e-01L);
1399 
1400  _weights[ 0]=Real(7.9757927362766516852273101574255e-03L);
1401  _weights[ 1]=Real(1.7913752325738559101773958866323e-02L);
1402  _weights[ 2]=Real(2.6382564429125584794513408474046e-02L);
1403  _weights[ 3]=Real(3.2734644317573148047479656498988e-02L);
1404  _weights[ 4]=Real(3.6587916553227064986609295576925e-02L);
1405  _weights[ 5]=Real(3.7847390376922340715354694449373e-02L);
1406  _weights[ 6]=Real(3.6697420472018132713254249570653e-02L);
1407  _weights[ 7]=Real(3.3556431453475493479002714822739e-02L);
1408  _weights[ 8]=Real(2.9002404745589285169916357261403e-02L);
1409  _weights[ 9]=Real(2.3682290414246053980866450266495e-02L);
1410  _weights[10]=Real(1.8220503418268691551843315309759e-02L);
1411  _weights[11]=Real(1.3140919256661651742108133720781e-02L);
1412  _weights[12]=Real(8.8135560782433553289252731679767e-03L);
1413  _weights[13]=Real(5.4320908061230274500120111426487e-03L);
1414  _weights[14]=Real(3.0224891709073793749184859780611e-03L);
1415  _weights[15]=Real(1.4774444419714858062838576456553e-03L);
1416  _weights[16]=Real(6.0704570426725825415272373108771e-04L);
1417  _weights[17]=Real(1.9388830961751181076983851525948e-04L);
1418  _weights[18]=Real(4.1039102087320205549074040898061e-05L);
1419  _weights[19]=Real(3.7492209933371347725241368372638e-06L);
1420 
1421  return;
1422  }
1423 
1424 
1425  case FORTIETH:
1426  case FORTYFIRST:
1427  {
1428  _points.resize (21);
1429  _weights.resize(21);
1430 
1431  _points[ 0](0)=Real(2.8583506000918943222556277168267e-03L);
1432  _points[ 1](0)=Real(1.4999364972075522340357135916023e-02L);
1433  _points[ 2](0)=Real(3.6593863281140122626545055282186e-02L);
1434  _points[ 3](0)=Real(6.7226441667938638526563947674675e-02L);
1435  _points[ 4](0)=Real(1.0630147973769311755044868847393e-01L);
1436  _points[ 5](0)=Real(1.5305857495571921224970195300963e-01L);
1437  _points[ 6](0)=Real(2.0658770608253356867698033417515e-01L);
1438  _points[ 7](0)=Real(2.6584701401081590981089215154372e-01L);
1439  _points[ 8](0)=Real(3.2968309899010272373734914205452e-01L);
1440  _points[ 9](0)=Real(3.9685347698561900950394342909483e-01L);
1441  _points[10](0)=Real(4.6605076663517464847296649003812e-01L);
1442  _points[11](0)=Real(5.3592813869303216093268951839176e-01L);
1443  _points[12](0)=Real(6.0512553397610192844810985230774e-01L);
1444  _points[13](0)=Real(6.7229614098692961628997049948121e-01L);
1445  _points[14](0)=Real(7.3613262059728734846410297670221e-01L);
1446  _points[15](0)=Real(7.9539257374613146232498650332774e-01L);
1447  _points[16](0)=Real(8.4892277353768883984401746895126e-01L);
1448  _points[17](0)=Real(8.9568174292546676052820257429765e-01L);
1449  _points[18](0)=Real(9.3476043640122994798279429359660e-01L);
1450  _points[19](0)=Real(9.6540160736574245809294907904429e-01L);
1451  _points[20](0)=Real(9.8702556657875783654690055164718e-01L);
1452 
1453  _weights[ 0]=Real(7.2866317313744308995629793584932e-03L);
1454  _weights[ 1]=Real(1.6417061144242818824757454238052e-02L);
1455  _weights[ 2]=Real(2.4316074956305588348553255406534e-02L);
1456  _weights[ 3]=Real(3.0423854654878694196479542521305e-02L);
1457  _weights[ 4]=Real(3.4388553550627421941340376509459e-02L);
1458  _weights[ 5]=Real(3.6085277384893044986268336555960e-02L);
1459  _weights[ 6]=Real(3.5615944774693119613624648820995e-02L);
1460  _weights[ 7]=Real(3.3281046762833346236473134492600e-02L);
1461  _weights[ 8]=Real(2.9528072702082493907799384765866e-02L);
1462  _weights[ 9]=Real(2.4885083875255978309567929915161e-02L);
1463  _weights[10]=Real(1.9889780066352815019424534213776e-02L);
1464  _weights[11]=Real(1.5024528041917190276613254752701e-02L);
1465  _weights[12]=Real(1.0666270365508680718786852036243e-02L);
1466  _weights[13]=Real(7.0573209743621604363614669672455e-03L);
1467  _weights[14]=Real(4.2993100642134152210363702100934e-03L);
1468  _weights[15]=Real(2.3686215346115318974092271035074e-03L);
1469  _weights[16]=Real(1.1482414207164748272703814817286e-03L);
1470  _weights[17]=Real(4.6857361253397420043294612589344e-04L);
1471  _weights[18]=Real(1.4884999898655056859287865070751e-04L);
1472  _weights[19]=Real(3.1377233396792732027953172274463e-05L);
1473  _weights[20]=Real(2.8584835468101709504260347382715e-06L);
1474 
1475  return;
1476  }
1477 
1478  case FORTYSECOND:
1479  case FORTYTHIRD:
1480  {
1481  _points.resize (22);
1482  _weights.resize(22);
1483 
1484  _points[ 0](0)=Real(2.6200747203711594248593674552649e-03L);
1485  _points[ 1](0)=Real(1.3753657987385804025756750709059e-02L);
1486  _points[ 2](0)=Real(3.3575226848026692714308191640158e-02L);
1487  _points[ 3](0)=Real(6.1735561623069601690826574395308e-02L);
1488  _points[ 4](0)=Real(9.7732696675368642458479884996723e-02L);
1489  _points[ 5](0)=Real(1.4092439775695158519450619775816e-01L);
1490  _points[ 6](0)=Real(1.9053995518421662849913969152881e-01L);
1491  _points[ 7](0)=Real(2.4569399962450332222446519900435e-01L);
1492  _points[ 8](0)=Real(3.0540231844259902315260853518244e-01L);
1493  _points[ 9](0)=Real(3.6859942495594128250321664201293e-01L);
1494  _points[10](0)=Real(4.3415757484015513750820121247106e-01L);
1495  _points[11](0)=Real(5.0090689264793505011775015892772e-01L);
1496  _points[12](0)=Real(5.6765625027260978702177266771788e-01L);
1497  _points[13](0)=Real(6.3321452557266284279166256182373e-01L);
1498  _points[14](0)=Real(6.9641186298595172661126707689713e-01L);
1499  _points[15](0)=Real(7.5612055917893487122928793527786e-01L);
1500  _points[16](0)=Real(8.1127520683922050787811864631196e-01L);
1501  _points[17](0)=Real(8.6089175276286621730656128908876e-01L);
1502  _points[18](0)=Real(9.0408517849775272066170136431884e-01L);
1503  _points[19](0)=Real(9.4008566921081846961603077466108e-01L);
1504  _points[20](0)=Real(9.6825388381656365288164210087944e-01L);
1505  _points[21](0)=Real(9.8810245999087788318348935085438e-01L);
1506 
1507  _weights[ 0]=Real(6.6829315239216368796332393406135e-03L);
1508  _weights[ 1]=Real(1.5098062421623821319493004238262e-02L);
1509  _weights[ 2]=Real(2.2473713734526648003280648297671e-02L);
1510  _weights[ 3]=Real(2.8324458025288763364233486167273e-02L);
1511  _weights[ 4]=Real(3.2329473952869436965326587507885e-02L);
1512  _weights[ 5]=Real(3.4348599664417779736425965942178e-02L);
1513  _weights[ 6]=Real(3.4426309828130701949676126316990e-02L);
1514  _weights[ 7]=Real(3.2774586900497126738748991342107e-02L);
1515  _weights[ 8]=Real(2.9737336628427308246400548097974e-02L);
1516  _weights[ 9]=Real(2.5741821234796918381507016798653e-02L);
1517  _weights[10]=Real(2.1244167813524304464862872202199e-02L);
1518  _weights[11]=Real(1.6676482379699419616981906191727e-02L);
1519  _weights[12]=Real(1.2402453510959574984251948178874e-02L);
1520  _weights[13]=Real(8.6866984738749141556196547655377e-03L);
1521  _weights[14]=Real(5.6807683849250404394970034550940e-03L);
1522  _weights[15]=Real(3.4260685209698087638377353482425e-03L);
1523  _weights[16]=Real(1.8713879532585689543042377871244e-03L);
1524  _weights[17]=Real(9.0066625279251987400261357834378e-04L);
1525  _weights[18]=Real(3.6536328467284676654467859219800e-04L);
1526  _weights[19]=Real(1.1551470917602499323205530447797e-04L);
1527  _weights[20]=Real(2.4263177919766775694554800111547e-05L);
1528  _weights[21]=Real(2.2049570604019597784590797971169e-06L);
1529 
1530  return;
1531  }
1532 
1533 
1534  default:
1535  libmesh_error_msg("Quadrature rule " << _order << " not supported!");
1536  } // end switch(_order + 2*p)
1537  } // end else if ((_alpha == 2) && (_beta == 0))
1538 
1539  else
1540  {
1541  libMesh::err << "Unsupported combination of (alpha,beta) = ("
1542  << _alpha
1543  << ","
1544  << _beta
1545  << ") requested in Jacobi-Gauss quadrature rule."
1546  << std::endl;
1547  }
1548 }

References _alpha, _beta, libMesh::QBase::_order, libMesh::QBase::_points, libMesh::QBase::_weights, libMesh::CONSTANT, libMesh::EIGHTH, libMesh::EIGHTTEENTH, libMesh::ELEVENTH, libMesh::err, libMesh::FIFTEENTH, libMesh::FIFTH, libMesh::FIRST, libMesh::FORTIETH, libMesh::FORTYFIRST, libMesh::FORTYSECOND, libMesh::FORTYTHIRD, libMesh::FOURTEENTH, libMesh::FOURTH, libMesh::QBase::get_order(), libMesh::NINETEENTH, libMesh::NINTH, libMesh::Real, libMesh::SECOND, libMesh::SEVENTEENTH, libMesh::SEVENTH, libMesh::SIXTEENTH, libMesh::SIXTH, libMesh::TENTH, libMesh::THIRD, libMesh::THIRTEENTH, libMesh::THIRTIETH, libMesh::THIRTYEIGHTH, libMesh::THIRTYFIFTH, libMesh::THIRTYFIRST, libMesh::THIRTYFOURTH, libMesh::THIRTYNINTH, libMesh::THIRTYSECOND, libMesh::THIRTYSEVENTH, libMesh::THIRTYSIXTH, libMesh::THIRTYTHIRD, libMesh::TWELFTH, libMesh::TWENTIETH, libMesh::TWENTYEIGHTH, libMesh::TWENTYFIFTH, libMesh::TWENTYFIRST, libMesh::TWENTYFOURTH, libMesh::TWENTYNINTH, libMesh::TWENTYSECOND, libMesh::TWENTYSEVENTH, libMesh::TWENTYSIXTH, and libMesh::TWENTYTHIRD.

◆ init_2D()

void libMesh::QBase::init_2D ( const ElemType  type = INVALID_ELEM,
unsigned int  p_level = 0 
)
protectedvirtualinherited

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 in libMesh::QGrundmann_Moller, libMesh::QMonomial, libMesh::QNodal, libMesh::QGauss, libMesh::QSimpson, libMesh::QConical, libMesh::QGrid, libMesh::QTrap, libMesh::QGaussLobatto, and libMesh::QClough.

Definition at line 123 of file quadrature.C.

124 {
125  libmesh_not_implemented();
126 }

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

◆ init_3D()

void libMesh::QBase::init_3D ( const ElemType  type = INVALID_ELEM,
unsigned int  p_level = 0 
)
protectedvirtualinherited

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 in libMesh::QGrundmann_Moller, libMesh::QMonomial, libMesh::QNodal, libMesh::QGauss, libMesh::QSimpson, libMesh::QConical, libMesh::QGrid, libMesh::QTrap, libMesh::QGaussLobatto, and libMesh::QClough.

Definition at line 130 of file quadrature.C.

131 {
132  libmesh_not_implemented();
133 }

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

◆ 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.

84  { 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.

127  {
128  libmesh_assert (!_points.empty());
129  return cast_int<unsigned int>(_points.size());
130  }

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]

QJacobi& libMesh::QJacobi::operator= ( const QJacobi &  )
default

◆ operator=() [2/2]

QJacobi& libMesh::QJacobi::operator= ( QJacobi &&  )
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.

38 {
39  libmesh_assert(!_points.empty());
40  libmesh_assert(!_weights.empty());
41 
42  Real summed_weights=0;
43  os << "N_Q_Points=" << this->n_points() << std::endl << std::endl;
44  for (auto qpoint: index_range(_points))
45  {
46  os << " Point " << qpoint << ":\n"
47  << " "
48  << _points[qpoint]
49  << "\n Weight:\n "
50  << " w=" << _weights[qpoint] << "\n" << std::endl;
51 
52  summed_weights += _weights[qpoint];
53  }
54  os << "Summed Weights: " << summed_weights << std::endl;
55 }

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.

88 {
89  if (_enable_print_counter)
90  out_stream << ReferenceCounter::get_info();
91 }

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.

165  {
166  libmesh_assert_less (i, _points.size());
167  return _points[i];
168  }

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.

139 {
140  // Make sure we are in 1D
141  libmesh_assert_equal_to (_dim, 1);
142 
143  Real
144  h_new = new_range.second - new_range.first,
145  h_old = old_range.second - old_range.first;
146 
147  // Make sure that we have sane ranges
148  libmesh_assert_greater (h_new, 0.);
149  libmesh_assert_greater (h_old, 0.);
150 
151  // Make sure there are some points
152  libmesh_assert_greater (_points.size(), 0);
153 
154  // Compute the scale factor
155  Real scfact = h_new/h_old;
156 
157  // We're mapping from old_range -> new_range
158  for (auto i : index_range(_points))
159  {
160  _points[i](0) = new_range.first +
161  (_points[i](0) - old_range.first) * scfact;
162 
163  // Scale the weights
164  _weights[i] *= scfact;
165  }
166 }

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.

239 { 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.

199 {
200  const unsigned int np = q1D.n_points();
201 
202  _points.resize(np * np * np);
203 
204  _weights.resize(np * np * np);
205 
206  unsigned int q=0;
207 
208  for (unsigned int k=0; k<np; k++)
209  for (unsigned int j=0; j<np; j++)
210  for (unsigned int i=0; i<np; i++)
211  {
212  _points[q](0) = q1D.qp(i)(0);
213  _points[q](1) = q1D.qp(j)(0);
214  _points[q](2) = q1D.qp(k)(0);
215 
216  _weights[q] = q1D.w(i) * q1D.w(j) * q1D.w(k);
217 
218  q++;
219  }
220 }

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.

226 {
227  const unsigned int n_points1D = q1D.n_points();
228  const unsigned int n_points2D = q2D.n_points();
229 
230  _points.resize (n_points1D * n_points2D);
231  _weights.resize (n_points1D * n_points2D);
232 
233  unsigned int q=0;
234 
235  for (unsigned int j=0; j<n_points1D; j++)
236  for (unsigned int i=0; i<n_points2D; i++)
237  {
238  _points[q](0) = q2D.qp(i)(0);
239  _points[q](1) = q2D.qp(i)(1);
240  _points[q](2) = q1D.qp(j)(0);
241 
242  _weights[q] = q2D.w(i) * q1D.w(j);
243 
244  q++;
245  }
246 
247 }

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.

172 {
173 
174  const unsigned int np = q1D.n_points();
175 
176  _points.resize(np * np);
177 
178  _weights.resize(np * np);
179 
180  unsigned int q=0;
181 
182  for (unsigned int j=0; j<np; j++)
183  for (unsigned int i=0; i<np; i++)
184  {
185  _points[q](0) = q1D.qp(i)(0);
186  _points[q](1) = q1D.qp(j)(0);
187 
188  _weights[q] = q1D.w(i)*q1D.w(j);
189 
190  q++;
191  }
192 }

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::QJacobi::type ( ) const
overridevirtual
Returns
The QuadratureType, either QJACOBI_1_0 or QJACOBI_2_0.

Implements libMesh::QBase.

Definition at line 30 of file quadrature_jacobi.C.

31 {
32  if ((_alpha == 1) && (_beta == 0))
33  return QJACOBI_1_0;
34 
35  else if ((_alpha == 2) && (_beta == 0))
36  return QJACOBI_2_0;
37 
38  else
39  libmesh_error_msg("Invalid Jacobi quadrature rule: alpha = " << _alpha << ", beta = " << _beta);
40 }

References _alpha, _beta, libMesh::QJACOBI_1_0, and libMesh::QJACOBI_2_0.

◆ 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.

174  {
175  libmesh_assert_less (i, _weights.size());
176  return _weights[i];
177  }

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

◆ _alpha

unsigned int libMesh::QJacobi::_alpha
private

Definition at line 85 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().

◆ _beta

unsigned int libMesh::QJacobi::_beta
private

Definition at line 86 of file quadrature_jacobi.h.

Referenced by init_1D(), and type().

◆ _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(), 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(), 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(), 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(), libMesh::QNodal::init_1D(), 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(), 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(), 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(), 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(), libMesh::QGrundmann_Moller::init_2D(), libMesh::QClough::init_3D(), libMesh::QGaussLobatto::init_3D(), libMesh::QConical::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(), 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(), libMesh::QNodal::init_1D(), 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(), 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(), 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().

The documentation for this class was generated from the following files:
libMesh::QJacobi::_alpha
unsigned int _alpha
Definition: quadrature_jacobi.h:85
libMesh::THIRTYFOURTH
Definition: enum_order.h:75
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:357
libMesh::QMONOMIAL
Definition: enum_quadrature_type.h:41
libMesh::TWENTYFIFTH
Definition: enum_order.h:66
libMesh::THIRTYSECOND
Definition: enum_order.h:73
libMesh::THIRTYFIFTH
Definition: enum_order.h:76
libMesh::QCLOUGH
Definition: enum_quadrature_type.h:44
libMesh::NINETEENTH
Definition: enum_order.h:60
libMesh::SIXTH
Definition: enum_order.h:47
libMesh::QBase::n_points
unsigned int n_points() const
Definition: quadrature.h:126
libMesh::FOURTEENTH
Definition: enum_order.h:55
libMesh::FORTYSECOND
Definition: enum_order.h:83
libMesh::index_range
IntRange< std::size_t > index_range(const std::vector< T > &vec)
Helper function that returns an IntRange<std::size_t> representing all the indices of the passed-in v...
Definition: int_range.h:106
libMesh::ReferenceCounter::_counts
static Counts _counts
Actually holds the data.
Definition: reference_counter.h:122
libMesh::QBase::init_1D
virtual void init_1D(const ElemType type=INVALID_ELEM, unsigned int p_level=0)=0
Initializes the 1D quadrature rule by filling the points and weights vectors with the appropriate val...
libMesh::ReferenceCounter::_n_objects
static Threads::atomic< unsigned int > _n_objects
The number of objects.
Definition: reference_counter.h:130
libMesh::FIFTH
Definition: enum_order.h:46
libMesh::THIRTEENTH
Definition: enum_order.h:54
libMesh::THIRTYSEVENTH
Definition: enum_order.h:78
libMesh::SECOND
Definition: enum_order.h:43
libMesh::QGAUSS
Definition: enum_quadrature_type.h:34
libMesh::THIRTIETH
Definition: enum_order.h:71
libMesh::ReferenceCounter::get_info
static std::string get_info()
Gets a string containing the reference information.
Definition: reference_counter.C:47
libMesh::TWENTIETH
Definition: enum_order.h:61
libMesh::QBase::init_3D
virtual void init_3D(const ElemType type=INVALID_ELEM, unsigned int p_level=0)
Initializes the 3D quadrature rule by filling the points and weights vectors with the appropriate val...
Definition: quadrature.C:130
libMesh::QBase::init
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.
Definition: quadrature.C:59
libMesh::TWELFTH
Definition: enum_order.h:53
dim
unsigned int dim
Definition: adaptivity_ex3.C:113
libMesh::TWENTYEIGHTH
Definition: enum_order.h:69
libMesh::QBase::build
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.
Definition: quadrature_build.C:41
libMesh::FORTYTHIRD
Definition: enum_order.h:84
libMesh::QSIMPSON
Definition: enum_quadrature_type.h:37
libMesh::THIRTYEIGHTH
Definition: enum_order.h:79
libMesh::QBase::_order
Order _order
The polynomial order which the quadrature rule is capable of integrating exactly.
Definition: quadrature.h:345
libMesh::libmesh_assert
libmesh_assert(ctx)
libMesh::ELEVENTH
Definition: enum_order.h:52
libMesh::EIGHTTEENTH
Definition: enum_order.h:59
libMesh::TWENTYSECOND
Definition: enum_order.h:63
libMesh::TWENTYTHIRD
Definition: enum_order.h:64
libMesh::QTRAP
Definition: enum_quadrature_type.h:38
libMesh::QNODAL
Definition: enum_quadrature_type.h:46
libMesh::TWENTYFIRST
Definition: enum_order.h:62
libMesh::FORTYFIRST
Definition: enum_order.h:82
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
A convenient spin mutex object which can be used for obtaining locks.
Definition: threads.C:29
libMesh::TWENTYSIXTH
Definition: enum_order.h:67
libMesh::THIRTYFIRST
Definition: enum_order.h:72
libMesh::QBase::QBase
QBase(unsigned int dim, Order order=INVALID_ORDER)
Constructor.
Definition: quadrature.C:27
libMesh::QBase::_type
ElemType _type
The type of element for which the current values have been computed.
Definition: quadrature.h:351
libMesh::FORTIETH
Definition: enum_order.h:81
libMesh::QJacobi::_beta
unsigned int _beta
Definition: quadrature_jacobi.h:86
libMesh::CONSTANT
Definition: enum_order.h:41
libMesh::TWENTYSEVENTH
Definition: enum_order.h:68
libMesh::EIGHTH
Definition: enum_order.h:49
libMesh::TENTH
Definition: enum_order.h:51
libMesh::FOURTH
Definition: enum_order.h:45
libMesh::TWENTYNINTH
Definition: enum_order.h:70
libMesh::QBase::_weights
std::vector< Real > _weights
The quadrature weights.
Definition: quadrature.h:369
libMesh::QGAUSS_LOBATTO
Definition: enum_quadrature_type.h:43
libMesh::QBase::type
virtual QuadratureType type() const =0
libMesh::QJACOBI_1_0
Definition: enum_quadrature_type.h:35
libMesh::SEVENTH
Definition: enum_order.h:48
libMesh::FIFTEENTH
Definition: enum_order.h:56
libMesh::THIRTYNINTH
Definition: enum_order.h:80
libMesh::QJACOBI_2_0
Definition: enum_quadrature_type.h:36
libMesh::THIRTYTHIRD
Definition: enum_order.h:74
libMesh::SIXTEENTH
Definition: enum_order.h:57
libMesh::THIRD
Definition: enum_order.h:44
libMesh::NINTH
Definition: enum_order.h:50
libMesh::err
OStreamProxy err
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:121
libMesh::QBase::get_order
Order get_order() const
Definition: quadrature.h:211
libMesh::QCONICAL
Definition: enum_quadrature_type.h:42
libMesh::ReferenceCounter::_enable_print_counter
static bool _enable_print_counter
Flag to control whether reference count information is printed when print_info is called.
Definition: reference_counter.h:141
libMesh::TWENTYFOURTH
Definition: enum_order.h:65
libMesh::QBase::init_0D
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 val...
Definition: quadrature.C:113
libMesh::QBase::_dim
unsigned int _dim
The spatial dimension of the quadrature rule.
Definition: quadrature.h:339
libMesh::out
OStreamProxy out
libMesh::QBase::_points
std::vector< Point > _points
The locations of the quadrature points in reference element space.
Definition: quadrature.h:363
libMesh::FIRST
Definition: enum_order.h:42
libMesh::THIRTYSIXTH
Definition: enum_order.h:77
libMesh::Quality::name
std::string name(const ElemQuality q)
This function returns a string containing some name for q.
Definition: elem_quality.C:42
libMesh::EDGE2
Definition: enum_elem_type.h:35
libMesh::QGRUNDMANN_MOLLER
Definition: enum_quadrature_type.h:40
libMesh::QGRID
Definition: enum_quadrature_type.h:39
libMesh::QBase::init_2D
virtual void init_2D(const ElemType type=INVALID_ELEM, unsigned int p_level=0)
Initializes the 2D quadrature rule by filling the points and weights vectors with the appropriate val...
Definition: quadrature.C:123
libMesh::SEVENTEENTH
Definition: enum_order.h:58
Generated on Sat Jan 25 2020 12:08:41 for libMesh by   doxygen 1.8.16