NumLib::IntegrationGaussLegendreTri Class Reference

Detailed Description

Gauss-Legendre quadrature rule for triangles.

Gauss-Legendre quadrature rule for triangles is originally given as

\[ \int F(x,y) dx dy = \int F(x(r, s), y(r, s)) j(r,s) dr ds \approx \frac{1}{2} \sum_i ( F(x(r_i, s_i), y(r_i, s_i)) w_i ) \]

To make it consistent with other elements, we rewrite the above formula as

\[ \int F(x,y) dx dy \approx \sum_i ( F(x(r_i, s_i), y(r_i, s_i)) w'_i ) \]

by defining the new weight \( w'=\frac{1}{2} w \).

Definition at line 36 of file IntegrationGaussLegendreTri.h.

#include <IntegrationGaussLegendreTri.h>

Public Types
using	WeightedPoint = MathLib::TemplateWeightedPoint< double, double, 2 >

Public Member Functions
	IntegrationGaussLegendreTri (unsigned order=2)
void	setIntegrationOrder (unsigned order)
	Change the integration order. More...
unsigned	getIntegrationOrder () const
	return current integration order. More...
unsigned	getNumberOfPoints () const
	return the number of sampling points More...
WeightedPoint	getWeightedPoint (unsigned igp) const

Static Public Member Functions
static WeightedPoint	getWeightedPoint (unsigned order, unsigned igp)
template<typename Method >
static WeightedPoint	getWeightedPoint (unsigned igp)
static unsigned	getNumberOfPoints (unsigned order)

Private Attributes
unsigned	_order
unsigned	_n_sampl_pt {0}

Member Typedef Documentation

WeightedPoint

using NumLib::IntegrationGaussLegendreTri::WeightedPoint = MathLib::TemplateWeightedPoint<double, double, 2>

Definition at line 39 of file IntegrationGaussLegendreTri.h.

Constructor & Destructor Documentation

IntegrationGaussLegendreTri()

NumLib::IntegrationGaussLegendreTri::IntegrationGaussLegendreTri ( unsigned  order = 2 )

inlineexplicit

Construct this object with the given integration order

Parameters

order

integration order (default 2)

Definition at line 46 of file IntegrationGaussLegendreTri.h.

                                                             : _order(order)
    {
        this->setIntegrationOrder(order);
    }

References setIntegrationOrder().

Member Function Documentation

getIntegrationOrder()

unsigned NumLib::IntegrationGaussLegendreTri::getIntegrationOrder ( ) const

inline

return current integration order.

Definition at line 59 of file IntegrationGaussLegendreTri.h.

{ return _order; }

References _order.

Referenced by getWeightedPoint().

getNumberOfPoints() [1/2]

unsigned NumLib::IntegrationGaussLegendreTri::getNumberOfPoints ( ) const

inline

return the number of sampling points

Definition at line 62 of file IntegrationGaussLegendreTri.h.

{ return _n_sampl_pt; }

References _n_sampl_pt.

Referenced by setIntegrationOrder().

getNumberOfPoints() [2/2]

static unsigned NumLib::IntegrationGaussLegendreTri::getNumberOfPoints ( unsigned  order )

inlinestatic

get the number of integration points

Parameters

order

the number of integration points

Returns

the number of points

Definition at line 110 of file IntegrationGaussLegendreTri.h.

    {
        switch (order)
        {
            case 1:
                return MathLib::GaussLegendreTri<1>::NPoints;
            case 2:
                return MathLib::GaussLegendreTri<2>::NPoints;
            case 3:
                return MathLib::GaussLegendreTri<3>::NPoints;
            case 4:
                return MathLib::GaussLegendreTri<4>::NPoints;
        }
        return 0;
    }

getWeightedPoint() [1/3]

template<typename Method >

static WeightedPoint NumLib::IntegrationGaussLegendreTri::getWeightedPoint ( unsigned  igp )

inlinestatic

Definition at line 99 of file IntegrationGaussLegendreTri.h.

    {
        return WeightedPoint(Method::X[igp], 0.5 * Method::W[igp]);
    }

getWeightedPoint() [2/3]

WeightedPoint NumLib::IntegrationGaussLegendreTri::getWeightedPoint ( unsigned  igp ) const

inline

get coordinates of a integration point

Parameters

igp	The integration point index

Returns

a weighted point

Definition at line 70 of file IntegrationGaussLegendreTri.h.

    {
        return getWeightedPoint(getIntegrationOrder(), igp);
    }

References getIntegrationOrder().

getWeightedPoint() [3/3]

static WeightedPoint NumLib::IntegrationGaussLegendreTri::getWeightedPoint ( unsigned  order, unsigned  igp  )

inlinestatic

get coordinates of a integration point

Parameters

order	the number of integration points
igp	the sampling point id

Returns

weight

Definition at line 82 of file IntegrationGaussLegendreTri.h.

    {
        switch (order)
        {
            case 1:
                return getWeightedPoint<MathLib::GaussLegendreTri<1>>(igp);
            case 2:
                return getWeightedPoint<MathLib::GaussLegendreTri<2>>(igp);
            case 3:
                return getWeightedPoint<MathLib::GaussLegendreTri<3>>(igp);
            case 4:
                return getWeightedPoint<MathLib::GaussLegendreTri<4>>(igp);
        }
        return WeightedPoint(std::array<double, 2>(), 0);
    }

setIntegrationOrder()

void NumLib::IntegrationGaussLegendreTri::setIntegrationOrder ( unsigned  order )

inline

Change the integration order.

Definition at line 52 of file IntegrationGaussLegendreTri.h.

    {
        _order = order;
        _n_sampl_pt = getNumberOfPoints(order);
    }

References _n_sampl_pt, _order, and getNumberOfPoints().

Referenced by IntegrationGaussLegendreTri().

Member Data Documentation

_n_sampl_pt

unsigned NumLib::IntegrationGaussLegendreTri::_n_sampl_pt {0}

private

Definition at line 128 of file IntegrationGaussLegendreTri.h.

Referenced by getNumberOfPoints(), and setIntegrationOrder().

_order

unsigned NumLib::IntegrationGaussLegendreTri::_order

private

Definition at line 127 of file IntegrationGaussLegendreTri.h.

Referenced by getIntegrationOrder(), and setIntegrationOrder().

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

• NumLib/Fem/Integration/IntegrationGaussLegendreTri.h