2D Gaussian integration class. 4x4 integration points. This integration scheme can integrate up to seventh-order polynomials exactly and is therefore a suitable "full" integration scheme for cubic (sixteen-node) elements in which the highest-order polynomial is sixth order. More...

#include <integral.h>

Inheritance diagram for oomph::Gauss< 2, 4 >:

Public Member Functions
	Gauss ()
	Default constructor (empty) More...

	Gauss (const Gauss &dummy)=delete
	Broken copy constructor. More...

void	operator= (const Gauss &)=delete
	Broken assignment operator. More...

unsigned	nweight () const
	Number of integration points of the scheme. More...

double	knot (const unsigned &i, const unsigned &j) const
	Return coordinate s[j] of integration point i. More...

double	weight (const unsigned &i) const
	Return weight of integration point i. More...

Public Member Functions inherited from oomph::Integral
	Integral ()
	Default constructor (empty) More...

	Integral (const Integral &dummy)=delete
	Broken copy constructor. More...

void	operator= (const Integral &)=delete
	Broken assignment operator. More...

virtual	~Integral ()
	Virtual destructor (empty) More...

virtual Vector< double >	knot (const unsigned &i) const
	Return local coordinates of i-th intergration point. Broken virtual. More...

Static Private Attributes
static const unsigned	Npts = 16
	Number of integration points in the scheme. More...

static const double	Knot [16][2]
	Array to hold the weights and knots (defined in cc file) More...

static const double	Weight [16]

Detailed Description

2D Gaussian integration class. 4x4 integration points. This integration scheme can integrate up to seventh-order polynomials exactly and is therefore a suitable "full" integration scheme for cubic (sixteen-node) elements in which the highest-order polynomial is sixth order.

Definition at line 388 of file integral.h.

Constructor & Destructor Documentation

◆ Gauss() [1/2]

oomph::Gauss< 2, 4 >::Gauss ( )

inline

Default constructor (empty)

Definition at line 399 of file integral.h.

◆ Gauss() [2/2]

oomph::Gauss< 2, 4 >::Gauss ( const Gauss< 2, 4 > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ knot()

double oomph::Gauss< 2, 4 >::knot	(	const unsigned &	i,
		const unsigned &	j
	)		const

inlinevirtual

Return coordinate s[j] of integration point i.

Implements oomph::Integral.

Definition at line 414 of file integral.h.

References i.

◆ nweight()

unsigned oomph::Gauss< 2, 4 >::nweight ( ) const

inlinevirtual

Number of integration points of the scheme.

Implements oomph::Integral.

Definition at line 408 of file integral.h.

◆ operator=()

void oomph::Gauss< 2, 4 >::operator= ( const Gauss< 2, 4 > & )

delete

Broken assignment operator.

◆ weight()

double oomph::Gauss< 2, 4 >::weight ( const unsigned & i ) const

inlinevirtual

Return weight of integration point i.

Implements oomph::Integral.

Definition at line 420 of file integral.h.

References i.

Member Data Documentation

◆ Knot

const double oomph::Gauss< 2, 4 >::Knot

staticprivate

Initial value:

= {
    {-0.861136311594053, -0.861136311594053},
    {-0.339981043584856, -0.861136311594053},
    {0.339981043584856, -0.861136311594053},
    {0.861136311594053, -0.861136311594053},
 
    {-0.861136311594053, -0.339981043584856},
    {-0.339981043584856, -0.339981043584856},
    {0.339981043584856, -0.339981043584856},
    {0.861136311594053, -0.339981043584856},
 
    {-0.861136311594053, 0.339981043584856},
    {-0.339981043584856, 0.339981043584856},
    {0.339981043584856, 0.339981043584856},
    {0.861136311594053, 0.339981043584856},
 
    {-0.861136311594053, 0.861136311594053},
    {-0.339981043584856, 0.861136311594053},
    {0.339981043584856, 0.861136311594053},
    {0.861136311594053, 0.861136311594053}}

Array to hold the weights and knots (defined in cc file)

Definition at line 394 of file integral.h.

◆ Npts

const unsigned oomph::Gauss< 2, 4 >::Npts = 16

staticprivate

Number of integration points in the scheme.

Definition at line 392 of file integral.h.

◆ Weight

const double oomph::Gauss< 2, 4 >::Weight

staticprivate

Initial value:

= {0.1210029932855979,
                                          0.2268518518518480,
                                          0.2268518518518480,
                                          0.1210029932855979,
                                          0.2268518518518480,
                                          0.4252933030106941,
                                          0.4252933030106941,
                                          0.2268518518518480,
                                          0.2268518518518480,
                                          0.4252933030106941,
                                          0.4252933030106941,
                                          0.2268518518518480,
                                          0.1210029932855979,
                                          0.2268518518518480,
                                          0.2268518518518480,
                                          0.1210029932855979}

Definition at line 394 of file integral.h.

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

Public Member Functions

Static Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Gauss() [1/2]

◆ Gauss() [2/2]

Member Function Documentation

◆ knot()

◆ nweight()

◆ operator=()

◆ weight()

Member Data Documentation

◆ Knot

◆ Npts

◆ Weight