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 26 of file IntegrationGaussLegendreTri.h.

#include <IntegrationGaussLegendreTri.h>

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

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

Private Attributes
unsigned	_order
unsigned	_n_sampl_pt {0}

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 34 of file IntegrationGaussLegendreTri.h.

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

References _order, and setIntegrationOrder().

Member Function Documentation

getIntegrationOrder()

unsigned NumLib::IntegrationGaussLegendreTri::getIntegrationOrder ( ) const

inline

return current integration order.

Definition at line 47 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 50 of file IntegrationGaussLegendreTri.h.

{ return _n_sampl_pt; }

References _n_sampl_pt.

Referenced by setIntegrationOrder().

getNumberOfPoints() [2/2]

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 99 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;
        }
        OGS_FATAL("Integration order {:d} not implemented for triangles.",
                  order);
    }

References MathLib::GaussLegendreTri< ORDER >::NPoints, and OGS_FATAL.

getWeightedPoint() [1/3]

template<typename Method>

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

inlinestatic

Definition at line 88 of file IntegrationGaussLegendreTri.h.

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

getWeightedPoint() [2/3]

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

inline

get coordinates of a integration point

Parameters

igp	The integration point index

Returns

a weighted point

Definition at line 58 of file IntegrationGaussLegendreTri.h.

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

References getIntegrationOrder(), and getWeightedPoint().

Referenced by getWeightedPoint(), and getWeightedPoint().

getWeightedPoint() [3/3]

MathLib::WeightedPoint NumLib::IntegrationGaussLegendreTri::getWeightedPoint ( unsigned const order, unsigned const 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 70 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);
        }
        OGS_FATAL("Integration order {:d} not implemented for triangles.",
                  order);
    }

References getWeightedPoint(), and OGS_FATAL.

setIntegrationOrder()

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

inline

Change the integration order.

Definition at line 40 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 118 of file IntegrationGaussLegendreTri.h.

{0};

Referenced by getNumberOfPoints(), and setIntegrationOrder().

_order

unsigned NumLib::IntegrationGaussLegendreTri::_order

private

Definition at line 117 of file IntegrationGaussLegendreTri.h.

Referenced by IntegrationGaussLegendreTri(), getIntegrationOrder(), and setIntegrationOrder().

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

• IntegrationGaussLegendreTri.h