QGrundmann_Moller

Section: C Library Functions (3) Updated: Thu Apr 7 2011 Local index Up

NAME

QGrundmann_Moller -

SYNOPSIS

Inherits QBase.

Public Member Functions

QGrundmann_Moller (const unsigned int _dim, const Order _order=INVALID_ORDER)

~QGrundmann_Moller ()

QuadratureType type () const

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

void init (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)

Order get_order () const

void print_info (std::ostream &os=std::cout) const

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

Static Public Member Functions

static AutoPtr< QBase > build (const std::string &name, const unsigned int _dim, const Order _order=INVALID_ORDER)

static AutoPtr< QBase > build (const QuadratureType _qt, const unsigned int _dim, const Order _order=INVALID_ORDER)

static void print_info ()

static std::string get_info ()

static unsigned int n_objects ()

Public Attributes

bool allow_rules_with_negative_weights

Protected Types

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

Protected Member Functions

virtual void init_0D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)

virtual void init_2D (const ElemType, unsigned int=0)

void increment_constructor_count (const std::string &name)

void increment_destructor_count (const std::string &name)

Protected Attributes

std::cerr<< 'ERROR: Seems as if this quadrature rule'<< std::endl<< ' is not implemented for 2D.'<< std::endl;libmesh_error();}#endif virtual void init_3D(const ElemType, unsigned int=0)#ifndef DEBUG{}#else{std::cerr<< 'ERROR: Seems as if this quadrature rule'<< std::endl<< ' is not implemented for 3D.'<< std::endl;libmesh_error();}#endif void tensor_product_quad(const QBase &q1D);void tensor_product_hex(const QBase &q1D);void tensor_product_prism(const QBase &q1D, const QBase &q2D);const unsigned int _dim;const Order _order;ElemType _type;unsigned int _p_level;std::vector< Point > _points

std::vector< Real > _weights

Static Protected Attributes

static Counts _counts

static Threads::atomic< unsigned int > _n_objects

static Threads::spin_mutex _mutex

Private Member Functions

void init_1D (const ElemType, unsigned int=0)

void init_3D (const ElemType _type=INVALID_ELEM, unsigned int p_level=0)

void gm_rule (unsigned int s)

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

Friends

std::ostream & operator<< (std::ostream &os, const QBase &q)

Detailed Description

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

The GM rules are interesting in 3D because they overlap with the conical product rules at higher order while having significantly fewer evaluation points, making them potentially much more efficient. The table below gives a comparison between the number of points in a conical product (CP) rule and the GM rule of equivalent order. The GM rules are defined to be exact for polynomials of degree d=2*s+1, s=0,1,2,3,... The table also gives the percentage of each GM rule's weights which are negative. Although the percentage of negative weights does not grow particularly quickly, the amplification factor (a measure of the effect of round-off) defined as

amp. factor = (1/V) * |w_i|,

where V is the volume of the reference element, does grow quickly. (A rule with all positive has has an amplification factor of 1.0 by definition.)

s | d | N. CP | N. GM | % neg wts | amp. factor ----------------------------------------------------------------- 0 | 1 | | 1 | | 1 | 2-3 | | 5 | | 2 | 4-5 | | 15 | | 3 | 6-7 | | 35 | 31.43 | 11.94 4 | 8-9 | 5^3=125 | 70 | 34.29 | 25.35 5 | 10-11 | 6^3=216 | 126 | 36.51 | 54.14 6 | 12-13 | 7^3=343 | 210 | 38.10 | 116.30 7 | 14-15 | 8^3=512 | 330 | 39.39 | 251.10 8 | 16-17 | 9^3=729 | 495 | 40.40 | 544.68 9 | 18-19 | 10^3=1,000 | 715 | 41.26 | 1186.16 10 | 20-21 | 11^3=1,331 | 1,001 | 41.96 | 2591.97 11 | 22-23 | 12^3=1,728 | 1,365 | 42.56 | 5680.75 ... 16 | 32-33 | 17^3=4,913 | 4,845 | 17 | 34-35 | 18^3=5,832 | 5,985 | <= Cross-over point, CP has fewer points for d >= 34 18 | 36-37 | 19^3=6,859 | 7,315 | ... 21 | 42-43 | 22^3=10,648 | 12,650 |

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

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

Author:

: John W. Peterson, 2008

Definition at line 96 of file quadrature_gm.h.

Member Typedef Documentation

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > ReferenceCounter::Counts [protected, inherited]Data structure to log the information. The log is identified by the class name.

Definition at line 105 of file reference_counter.h.

Constructor & Destructor Documentation

QGrundmann_Moller::QGrundmann_Moller (const unsigned int_dim, const Order_order = INVALID_ORDER)Constructor. Declares the order of the quadrature rule.

Definition at line 31 of file quadrature_gm.C.

                                                    : QBase(d,o)
{
}

QGrundmann_Moller::~QGrundmann_Moller ()Destructor.

Definition at line 38 of file quadrature_gm.C.

{
}

Member Function Documentation

AutoPtr< QBase > QBase::build (const std::string &name, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the name string. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule. The input parameter name must be mappable through the Utility::string_to_enum<>() function.

Definition at line 36 of file quadrature_build.C.

References Utility::string_to_enum< QuadratureType >().

Referenced by InfFE< Dim, T_radial, T_map >::attach_quadrature_rule().

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

AutoPtr< QBase > QBase::build (const QuadratureType_qt, const unsigned int_dim, const Order_order = INVALID_ORDER) [static, inherited]Builds a specific quadrature rule, identified through the QuadratureType. An AutoPtr<QBase> is returned to prevent a memory leak. This way the user need not remember to delete the object. Enables run-time decision of the quadrature rule.

Definition at line 47 of file quadrature_build.C.

References libMeshEnums::FIRST, libMeshEnums::FORTYTHIRD, libMeshEnums::QCLOUGH, libMeshEnums::QGAUSS, libMeshEnums::QJACOBI_1_0, libMeshEnums::QJACOBI_2_0, libMeshEnums::QSIMPSON, libMeshEnums::QTRAP, libMeshEnums::THIRD, and libMeshEnums::TWENTYTHIRD.

{
  switch (_qt)
    {
      
    case QCLOUGH:
      {
#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Clough quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QClough(_dim, _order));
        return ap;
      }

    case QGAUSS:
      {

#ifdef DEBUG
        if (_order > FORTYTHIRD)
          {
            std::cout << 'WARNING: Gauss quadrature implemented' << std::endl
                      << ' up to FORTYTHIRD order.' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QGauss(_dim, _order));
        return ap;
      }

    case QJACOBI_1_0:
      {

#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Jacobi(1,0) quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }

        if (_dim > 1)
          {
            std::cout << 'WARNING: Jacobi(1,0) quadrature implemented' << std::endl
                      << ' in 1D only.' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QJacobi(_dim, _order, 1, 0));
        return ap;
      }

    case QJACOBI_2_0:
      {

#ifdef DEBUG
        if (_order > TWENTYTHIRD)
          {
            std::cout << 'WARNING: Jacobi(2,0) quadrature implemented' << std::endl
                      << ' up to TWENTYTHIRD order.' << std::endl;
          }

        if (_dim > 1)
          {
            std::cout << 'WARNING: Jacobi(2,0) quadrature implemented' << std::endl
                      << ' in 1D only.' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QJacobi(_dim, _order, 2, 0));
        return ap;
      }

    case QSIMPSON:
      {

#ifdef DEBUG
        if (_order > THIRD)
          {
            std::cout << 'WARNING: Simpson rule provides only' << std::endl
                      << ' THIRD order!' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QSimpson(_dim));
        return ap;
      }

    case QTRAP:
      {

#ifdef DEBUG
        if (_order > FIRST)
          {
            std::cout << 'WARNING: Trapezoidal rule provides only' << std::endl
                      << ' FIRST order!' << std::endl;
          }
#endif

        AutoPtr<QBase> ap(new QTrap(_dim));
        return ap;
      }


    default:
      { 
        std::cerr << 'ERROR: Bad qt=' << _qt << std::endl;
        libmesh_error();
      }
    }


  libmesh_error();
  AutoPtr<QBase> ap(NULL);
  return ap;
}

void QGrundmann_Moller::compose_all (unsigned ints, unsigned intp, std::vector< std::vector< unsigned int > > &result) [private]Routine which generates p-compositions of a given order, s, as well as permutations thereof. This routine is called internally by the gm_rule() routine, you should not call this yourself!

Definition at line 143 of file quadrature_gm.C.

Referenced by gm_rule().

{
  // Clear out results remaining from previous calls
  result.clear();

  // Allocate storage for a workspace.  The workspace will periodically
  // be copied into the result container.
  std::vector<unsigned int> workspace(p);
  
  // The first result is always (s,0,...,0)
  workspace[0] = s;
  result.push_back(workspace);

  // the value of the first non-zero entry
  unsigned int head_value=s; 

  // When head_index=-1, it refers to 'off the front' of the array.  Therefore,
  // this needs to be a regular int rather than unsigned.  I initially tried to
  // do this with head_index unsigned and an else statement below, but then there
  // is the special case: (1,0,...,0) which does not work correctly.
  int head_index = -1;
  
  // At the end, all the entries will be in the final slot of workspace
  while (workspace.back() != s)
    {
      // Uncomment for debugging
      //std::cout << 'previous head_value=' << head_value << ' -> ';
      
      // If the previous head value is still larger than 1, reset the index
      // to 'off the front' of the array
      if (head_value > 1)
        head_index = -1;

      // Either move the index onto the front of the array or on to
      // the next value.
      head_index++;   

      // Get current value of the head entry
      head_value = workspace[head_index];

      // Uncomment for debugging
      //std::copy(workspace.begin(), workspace.end(), std::ostream_iterator<int>(std::cout, ' '));
      //std::cout << ', head_index=' << head_index;
      //std::cout << ', head_value=' << head_value << ' -> ';
      
      // Put a zero into the head_index of the array.  If head_index==0,
      // this will be overwritten in the next line with head_value-1.
      workspace[head_index] = 0;

      // The initial entry gets the current head value, minus 1.
      // If head_value > 1, the next loop iteration will start back
      // at workspace[0] again.
      libmesh_assert (head_value > 0);
      workspace[0] = head_value - 1;

      // Increment the head+1 value 
      workspace[head_index+1] += 1;

      // Save this composition in the results
      result.push_back(workspace);

      // Uncomment for debugging
      //std::copy(workspace.begin(), workspace.end(), std::ostream_iterator<int>(std::cout, ' '));
      //std::cout<<';
    }
}

unsigned int QBase::get_dim () const [inline, inherited]Returns:

: the dimension of the quadrature rule.

Definition at line 121 of file quadrature.h.

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

{ return _dim;  }

ElemType QBase::get_elem_type () const [inline, inherited]Returns:

: the current element type we're set up for

Definition at line 103 of file quadrature.h.

    { return _type; }

std::string ReferenceCounter::get_info () [static, inherited]Gets a string containing the reference information.

Definition at line 45 of file reference_counter.C.

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

Referenced by ReferenceCounter::print_info().

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)

  std::ostringstream out;
  
  out << '
      << ' ---------------------------------------------------------------------------- 
      << '| Reference count information                                                |
      << ' ---------------------------------------------------------------------------- ;
  
  for (Counts::iterator it = _counts.begin();
       it != _counts.end(); ++it)
    {
      const std::string name(it->first);
      const unsigned int creations    = it->second.first;
      const unsigned int destructions = it->second.second;

      out << '| ' << name << ' reference count information:
          << '|  Creations:    ' << creations    << '
          << '|  Destructions: ' << destructions << ';
    }
  
  out << ' ---------------------------------------------------------------------------- ;

  return out.str();

#else

  return '';
  
#endif
}

Order QBase::get_order () const [inline, inherited]Returns:

: the order of the quadrature rule.

Definition at line 167 of file quadrature.h.

Referenced by InfFE< Dim, T_radial, T_map >::attach_quadrature_rule().

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

unsigned int QBase::get_p_level () const [inline, inherited]Returns:

: the current p refinement level we're initialized with

Definition at line 109 of file quadrature.h.

    { return _p_level; }

const std::vector<Point>& QBase::get_points () const [inline, inherited]Returns:

: a std::vector containing the quadrature point locations on a reference object.

Definition at line 127 of file quadrature.h.

References QBase::_points.

Referenced by FE< Dim, T >::edge_reinit(), QClough::init_1D(), QMonomial::init_2D(), QGauss::init_2D(), QClough::init_2D(), QMonomial::init_3D(), QGauss::init_3D(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), InfFE< Dim, T_radial, T_map >::reinit(), and REINIT_ERROR().

{ return _points;  }

std::vector<Point>& QBase::get_points () [inline, inherited]Returns:

: a std::vector containing the quadrature point locations on a reference object as a writeable reference.

Definition at line 133 of file quadrature.h.

References QBase::_points.

{ return _points;  }

const std::vector<Real>& QBase::get_weights () const [inline, inherited]Returns:

: a std::vector containing the quadrature weights.

Definition at line 138 of file quadrature.h.

References QBase::_weights.

{ return _weights; }

std::vector<Real>& QBase::get_weights () [inline, inherited]Returns:

: a std::vector containing the quadrature weights.

Definition at line 143 of file quadrature.h.

References QBase::_weights.

{ return _weights; }

void QGrundmann_Moller::gm_rule (unsigned ints) [private]This routine is called from the different cases of init_3D(). It actually fills the _points and _weights vectors for a given rule index, s.

Definition at line 46 of file quadrature_gm.C.

References QBase::_points, QBase::_weights, compose_all(), std::max(), and MeshTools::weight().

Referenced by init_3D().

{
  // A GM rule of index s can integrate polynomials of degree 2*s+1 exactly
  const unsigned int degree = 2*s+1;

  // Here we are considering only tetrahedra rules, so dim==3
  const unsigned int dim = 3;
  
  // The number of points for rule of index s is
  // (dim+1+s)! / (dim+1)! / s!
  // In 3D, this is = 1/24 * P_{i=1}^4 (s+i)
  const unsigned int n_pts = (s+4)*(s+3)*(s+2)*(s+1) / 24;
  //std::cout << 'n_pts=' << n_pts << std::endl;

  // Allocate space for points and weights
  _points.resize(n_pts);
  _weights.resize(n_pts);

  // (-1)^i -> This one flips sign at each iteration of the i-loop below.
  int one_pm=1;

  // Where we store all the integer point compositions/permutations
  std::vector<std::vector<unsigned int> > permutations;

  // Index into the vector where we should start adding the next round of points/weights
  unsigned int offset=0;

  // Implement the GM formula 4.1 on page 286 of the paper
  for (unsigned int i=0; i<=s; ++i)
    {
      // Get all the ordered compositions (and their permutations)
      // of |beta| = s-i into dim+1=4 parts
      compose_all(s-i, dim+1, permutations);
      //std::cout << 'n. permutations=' << permutations.size() << std::endl;

      for (unsigned int p=0; p<permutations.size(); ++p)
        {
          // We use the first dim=3 entries of each permutation to
          // construct an integration point.
          for (unsigned int j=0; j<3; ++j)
            _points[offset+p](j) =
              static_cast<Real>(2.*permutations[p][j] + 1.) /
              static_cast<Real>(  degree + dim - 2.*i     );
        }
      
      // Compute the weight for this i, being careful to avoid overflow.
      // This technique is borrowed from Burkardt's code as well.
      // Use once for each of the points obtained from the permutations array.
      Real weight = one_pm;

      // This for loop needs to run for dim, degree, or dim+degree-i iterations,
      // whichever is largest.
      const unsigned int weight_loop_index =
        std::max(dim, std::max(degree, degree+dim-i));
      
      for (unsigned int j=1; j<=weight_loop_index; ++j)
        {
          if (j <= degree) // Accumulate (d+n-2i)^d term
            weight *= static_cast<Real>(degree+dim-2*i);

          if (j <= 2*s) // Accumulate 2^{-2s}
            weight *= 0.5;

          if (j <= i) // Accumulate (i!)^{-1}
            weight /= static_cast<Real>(j);

          if (j <= degree+dim-i) // Accumulate ( (d+n-i)! )^{-1}
            weight /= static_cast<Real>(j);
        }

      // This is the weight for each of the points computed previously
      for (unsigned int j=0; j<permutations.size(); ++j)
        _weights[offset+j] = weight;
      
      // Change sign for next iteration
      one_pm = -one_pm;

      // Update offset for the next set of points
      offset += permutations.size();
    }
}

void ReferenceCounter::increment_constructor_count (const std::string &name) [inline, protected, inherited]Increments the construction counter. Should be called in the constructor of any derived class that will be reference counted.

Definition at line 149 of file reference_counter.h.

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

Referenced by ReferenceCountedObject< Value >::ReferenceCountedObject().

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

  p.first++;
}

void ReferenceCounter::increment_destructor_count (const std::string &name) [inline, protected, inherited]Increments the destruction counter. Should be called in the destructor of any derived class that will be reference counted.

Definition at line 167 of file reference_counter.h.

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

Referenced by ReferenceCountedObject< Value >::~ReferenceCountedObject().

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

  p.second++;
}

void QBase::init (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [inherited]Initializes the data structures to contain a quadrature rule for an object of type type.

Definition at line 26 of file quadrature.C.

References QBase::init_0D(), QBase::init_1D(), and QBase::init_2D().

Referenced by FE< Dim, T >::edge_reinit(), QClough::init_1D(), QTrap::init_2D(), QSimpson::init_2D(), QMonomial::init_2D(), QGrid::init_2D(), QGauss::init_2D(), QClough::init_2D(), QTrap::init_3D(), QSimpson::init_3D(), QMonomial::init_3D(), QGrid::init_3D(), QGauss::init_3D(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), QGauss::QGauss(), QJacobi::QJacobi(), QSimpson::QSimpson(), QTrap::QTrap(), InfFE< Dim, T_radial, T_map >::reinit(), and REINIT_ERROR().

{
  // check to see if we have already
  // done the work for this quadrature rule
  if (t == _type && p == _p_level)
    return;
  else
    {
      _type = t;
      _p_level = p;
    }
    
  
  
  switch(_dim)
    {
    case 0:
      this->init_0D(_type,_p_level);

      return;
      
    case 1:
      this->init_1D(_type,_p_level);

      return;
      
    case 2:
      this->init_2D(_type,_p_level);

      return;

    case 3:
      this->init_3D(_type,_p_level);

      return;

    default:
      libmesh_error();
    }
}

void QBase::init_0D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [protected, virtual, inherited]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.

Definition at line 70 of file quadrature.C.

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

Referenced by QBase::init().

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

void QGrundmann_Moller::init_1D (const ElemType_type, unsignedp_level = 0) [inline, private, virtual]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.

Implements QBase.

Definition at line 119 of file quadrature_gm.h.

  {
    // See about making this non-pure virtual in the base class
    libmesh_error();
  }

virtual void QBase::init_2D (const ElemType, unsigned int = 0) [inline, protected, virtual, inherited]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 redefined, gives an error (when DEBUG defined) when called.

Reimplemented in QClough, QConical, QGauss, QGrid, QMonomial, QSimpson, and QTrap.

Definition at line 234 of file quadrature.h.

Referenced by QBase::init().

{}

void QGrundmann_Moller::init_3D (const ElemType_type = INVALID_ELEM, unsigned intp_level = 0) [private]The GM rules are only defined for 3D since better 2D rules for simplexes are available.

Definition at line 27 of file quadrature_gm_3D.C.

References QBase::allow_rules_with_negative_weights, gm_rule(), libMeshEnums::TET10, and libMeshEnums::TET4.

{
  // Nearly all GM rules contain negative weights, so if you are not
  // allowing rules with negative weights, we cannot continue!
  if (!allow_rules_with_negative_weights)
    {
      std::cerr << 'You requested a Grundmann-Moller rule but
                << 'are not allowing rules with negative weights!
                << 'Either select a different quadrature class or
                << 'set allow_rules_with_negative_weights==true.' 
                << std::endl;
      
      libmesh_error();
    }
  
  switch (_type)
    {
    case TET4:
    case TET10:
      {
        // Untested above _order=23 but should work...
        gm_rule( (_order + 2*p)/2 );
        return;
        
      } // end case TET4, TET10


      
      //---------------------------------------------
      // Unsupported element type
    default:
      {
        std::cerr << 'ERROR: Unsupported element type: ' << _type << std::endl;
        libmesh_error();
      }
    } // end switch (_type)

  // We must have returned or errored-out by this point.  If not,
  // throw an error now.
  libmesh_error();
  return;
}

static unsigned int ReferenceCounter::n_objects () [inline, static, inherited]Prints the number of outstanding (created, but not yet destroyed) objects.

Definition at line 76 of file reference_counter.h.

References ReferenceCounter::_n_objects.

Referenced by System::read_serialized_blocked_dof_objects(), and System::write_serialized_blocked_dof_objects().

  { return _n_objects; }

unsigned int QBase::n_points () const [inline, inherited]Returns:

: the number of points associated with the quadrature rule.

Definition at line 115 of file quadrature.h.

References QBase::_points.

Referenced by FEBase::coarsened_dof_values(), QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), FEMSystem::eulerian_residual(), InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), FEMSystem::mass_residual(), and QBase::print_info().

    { libmesh_assert (!_points.empty()); return _points.size(); }

void ReferenceCounter::print_info () [static, inherited]Prints the reference information to std::cout.

Definition at line 83 of file reference_counter.C.

References ReferenceCounter::get_info().

{
#if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
  
  std::cout << ReferenceCounter::get_info();
  
#endif
}

void QBase::print_info (std::ostream &os = std::cout) const [inline, inherited]Prints information relevant to the quadrature rule.

Definition at line 350 of file quadrature.h.

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

Referenced by operator<<().

{
  libmesh_assert(!_points.empty());
  libmesh_assert(!_weights.empty());

  os << 'N_Q_Points=' << this->n_points() << std::endl << std::endl;
  for (unsigned int qp=0; qp<this->n_points(); qp++)
    {
      os << ' Point ' << qp << ':
         << '  '
         << _points[qp]
         << ' Weight:'
         << '  w=' << _weights[qp] << ' << std::endl;
    }
}

Point QBase::qp (const unsigned inti) const [inline, inherited]Returns:

: the $ i^{th} $ quadrature point on the reference object.

Definition at line 148 of file quadrature.h.

References QBase::_points.

Referenced by QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), and QBase::print_info().

    { libmesh_assert (i < _points.size()); return _points[i]; }

void QBase::scale (std::pair< Real, Real >old_range, std::pair< Real, Real >new_range) [inherited]Maps the points of a 1D interval quadrature rule (typically [-1,1]) to any other 1D interval (typically [0,1]) and scales the weights accordingly. The quadrature rule will be mapped from the entries of old_range to the entries of new_range.

Definition at line 81 of file quadrature.C.

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

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

{
  // Make sure we are in 1D
  libmesh_assert(_dim == 1);
  
  // Make sure that we have sane ranges 
  libmesh_assert(new_range.second > new_range.first);
  libmesh_assert(old_range.second > old_range.first);

  // Make sure there are some points
  libmesh_assert(_points.size() > 0);

  // We're mapping from old_range -> new_range 
  for (unsigned int i=0; i<_points.size(); i++)
    {
      _points[i](0) =
        (_points[i](0) - old_range.first) *
        (new_range.second - new_range.first) /
        (old_range.second - old_range.first) +
        new_range.first;
    }

  // Compute the scale factor and scale the weights
  const Real scfact = (new_range.second - new_range.first) /
                      (old_range.second - old_range.first);

  for (unsigned int i=0; i<_points.size(); i++)
    _weights[i] *= scfact;
}

QuadratureType QGrundmann_Moller::type () const [inline, virtual]Returns:

: QGRUNDMANN_MOLLER

Implements QBase.

Definition at line 114 of file quadrature_gm.h.

References libMeshEnums::QGRUNDMANN_MOLLER.

{ return QGRUNDMANN_MOLLER; }

Real QBase::w (const unsigned inti) const [inline, inherited]Returns:

: the $ i^{th} $ quadrature weight.

Definition at line 154 of file quadrature.h.

References QBase::_weights.

Referenced by QConical::conical_product_pyramid(), QConical::conical_product_tet(), QConical::conical_product_tri(), QGauss::init_3D(), QGauss::keast_rule(), QMonomial::kim_rule(), and QMonomial::stroud_rule().

    { libmesh_assert (i < _weights.size()); return _weights[i]; }

Friends And Related Function Documentation

std::ostream& operator<< (std::ostream &os, const QBase &q) [friend, inherited]Same as above, but allows you to use the stream syntax.

Definition at line 196 of file quadrature.C.

{
  q.print_info(os);
  return os;
}

Member Data Documentation

ReferenceCounter::Counts ReferenceCounter::_counts [static, protected, inherited]Actually holds the data.

Definition at line 110 of file reference_counter.h.

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

Threads::spin_mutex ReferenceCounter::_mutex [static, protected, inherited]Mutual exclusion object to enable thread-safe reference counting.

Definition at line 123 of file reference_counter.h.

Threads::atomic< unsigned int > ReferenceCounter::_n_objects [static, protected, inherited]The number of objects. Print the reference count information when the number returns to 0.

Definition at line 118 of file reference_counter.h.

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

std::cerr<< 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 2D.' << std::endl; libmesh_error(); }#endif virtual void init_3D (const ElemType, unsigned int =0)#ifndef DEBUG {}#else { std::cerr << 'ERROR: Seems as if this quadrature rule' << std::endl << ' is not implemented for 3D.' << std::endl; libmesh_error(); }#endif void tensor_product_quad (const QBase& q1D); void tensor_product_hex (const QBase& q1D); void tensor_product_prism (const QBase& q1D, const QBase& q2D); const unsigned int _dim; const Order _order; ElemType _type; unsigned int _p_level; std::vector<Point> QBase::_points [protected, inherited]

Definition at line 320 of file quadrature.h.

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

std::vector<Real> QBase::_weights [protected, inherited]The value of the quadrature weights.

Definition at line 325 of file quadrature.h.

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

bool QBase::allow_rules_with_negative_weights [inherited]Flag (default true) controlling the use of quadrature rules with negative weights. Set this to false to ONLY use (potentially) safer but more expensive rules with all positive weights.

Negative weights typically appear in Gaussian quadrature rules over three-dimensional elements. 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 203 of file quadrature.h.

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