General integrator class on tensorial hypergraphs. More...

#include <tensorial.hxx>

Public Types
typedef shape_t	shape_fun_t
	Make type of shape functions publicly available. More...

Static Public Member Functions
static constexpr unsigned int	dim ()
	The dimension of the Lebesque measure with respect to which we integrate. More...

static constexpr unsigned int	n_quad_points ()
	Calculate the amount of quadrature points. More...

static constexpr return_t	integrate_1D_phiphi (const unsigned int i, const unsigned int j)
	Integrate product of one-dimensional shape functions. More...

static constexpr return_t	integrate_1D_phiDphi (const unsigned int i, const unsigned int j)
	Integrate product of one-dimensional shape function and one derivative. More...

static constexpr return_t	integrate_1D_Dphiphi (const unsigned int i, const unsigned int j)
	Integrate product of one-dimensional shape function and one derivative. More...

static constexpr return_t	integrate_1D_DphiDphi (const unsigned int i, const unsigned int j)
	Integrate product of two one-dimensional shape functions' derivatives. More...

static constexpr return_t	integrate_vol_phiphi (const unsigned int i, const unsigned int j)
	Integrate product of shape functions over dimT-dimensional unit volume. More...

static constexpr return_t	integrate_vol_phiDphi (const unsigned int i, const unsigned int j, const unsigned int dim_der)
	Integrate product of shape function amd derivative over dimT-dimensional unit volume. More...

static constexpr return_t	integrate_vol_Dphiphi (const unsigned int i, const unsigned int j, const unsigned int dim_der)
	Integrate product of shape function and derivative over dimT-dimensional unit volume. More...

static constexpr return_t	integrate_bdr_phiphi (const unsigned int i, const unsigned int j, const unsigned int bdr)
	Integrate product of shape functions over dimT-dimensional volume's boundary. More...

static constexpr return_t	integrate_bdr_phipsi (const unsigned int i, const unsigned int j, const unsigned int bdr)
	Integrate product of shape function of volume times shape function of volume's face over dimT-dimensional volume's boundary. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_phiphifunc (const unsigned int i, const unsigned int j, geom_t &geom, const return_t f_param=0.)
	Integrate product of shape functions times some function over some geometry. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_phiphivecfunc (const unsigned int i, const unsigned int j, const unsigned int dimension, geom_t &geom, const return_t f_param=0.)
	Integrate product of shape functions times some function over some geometry. More...

template<typename geom_t >
static return_t	integrate_vol_phiphi (const unsigned int i, const unsigned int j, geom_t &geom)
	Integrate product of shape functions over some geometry. More...

template<typename geom_t , std::size_t array_size, typename floating_t >
static return_t	integrate_vol_phiphi (const std::array< floating_t, array_size > &is, const std::array< floating_t, array_size > &js, geom_t &geom)
	Integrate product of linear combinations of shape functions over some geometry. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_phifunc (const unsigned int i, geom_t &geom, const return_t f_param=0.)
	Integrate product of shape function times some function over some geometry. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_volUni_phifunc (const unsigned int i, geom_t &geom, const return_t f_param=0.)
	Average integral of product of shape function times some function over some geometry. More...

template<typename smallVec_t , typename geom_t , unsigned int poly_deg_i = shape_t::degree(), unsigned int poly_deg_j = shape_t::degree()>
static smallVec_t	integrate_vol_nablaphiphi (const unsigned int i, const unsigned int j, geom_t &geom)
	Integrate gradient of shape function times other shape function over some geometry. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_nablaphinablaphifunc (const unsigned int i, const unsigned int j, geom_t &geom, return_t f_param=0.)
	Integrate gradient of shape functions times other function over some geometry. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_derphifunc (const unsigned int i, const unsigned int dim_der, geom_t &geom, return_t f_param=0.)
	Integrate derivative of shape function times other function over some geometry. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_vol_nablaphiphivecfunc (const unsigned int i, const unsigned int j, geom_t &geom, const return_t f_param=0.)
	Integrate gradient of shape function times other shape function times vector function. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phiphinuvecfunc_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate shape function times shape function times vector function times normal. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phiphi_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of product of shape functions. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phipsinuvecfunc_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of shape function times skeletal shape function. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phipsi_cutdownwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut downwind of shape function times skeletal shape function. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_psiphinuvecfunc_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of skeletal shape function times shape function times vector fct. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_psiphi_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of skeletal shape function times shape function. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_psipsinuvecfunc_cutwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of product of skeltal shape functions times vector function. More...

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_psipsi_cutdownwind (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut downwind product of skeletal shape functions. More...

template<typename point_t , typename geom_t , return_t func, point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phifuncnuvecfunc_cutwind (const unsigned int i, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of shape function times function times vector function. More...

template<typename point_t , typename geom_t , return_t func, point_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_psifuncnuvecfunc_cutwind (const unsigned int i, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate cut upwind of skeletal shape function times function times vector function. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_nablaphiphinufunc (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate gradient of shape function times shape function times other function times normal over some geometry's boundary. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_nablaphipsinufunc (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom, return_t f_param=0.)
	Integrate gradient of shape function times shape function times other function times normal over some geometry's boundary. More...

template<typename geom_t >
static return_t	integrate_bdr_phiphi (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom)
	Integrate product of shape functions over boundary face. More...

template<typename geom_t >
static return_t	integrate_bdr_phipsi (const unsigned int i, const unsigned int j, const unsigned int bdr, geom_t &geom)
	Integrate product of shape functions of volumen and skeletal over boundary face. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdr_phifunc (const unsigned int i, const unsigned int bdr, geom_t &geom, const return_t f_param=0.)
	Integrate product of shape functions times some function over boundary face. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>
static return_t	integrate_bdrUni_psifunc (const unsigned int i, const unsigned int bdr, geom_t &geom, const return_t f_param=0.)
	Average integral of product of skeletal shape functions times some function. More...

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t, std::size_t n_coeff>
static return_t	integrate_vol_diffsquare_discana (const std::array< return_t, n_coeff > coeffs, geom_t &geom, const return_t f_param=0.)
	Squared L2 distance of some function and an discrete function on volume. More...

Static Public Attributes
static constexpr std::array< return_t, quadrature_t::n_points()>	quad_points
	Quadrature points on one-dimensional unit interval. More...

static constexpr std::array< return_t, quadrature_t::n_points()>	quad_weights
	Quadrature weights on one-dimensional unit interval. More...

static constexpr std::array< std::array< return_t, quadrature_t::n_points()>, n_fun_1D >	shape_fcts_at_quad = shape_fcts_at_quad_points()
	Shape functions evaluated at quadrature points of unit interval. More...

static constexpr std::array< std::array< return_t, quadrature_t::n_points()>, n_fun_1D >	shape_ders_at_quad = shape_ders_at_quad_points()
	Derivatives of shape functions evaluated at quadrature points of unit interval. More...

static constexpr std::array< std::array< return_t, 2 >, n_fun_1D >	shape_fcts_at_bdr
	Shape functions evaluated at boundaries of unit interval. More...

static constexpr std::array< std::array< return_t, 2 >, n_fun_1D >	shape_ders_at_bdr
	Derivatives of shape functions evaluated at boundaries of unit interval. More...

Static Private Member Functions
static constexpr std::array< std::array< return_t, quadrature_t::n_points()>, n_fun_1D >	shape_fcts_at_quad_points ()
	Shape functions evaluated at quadrature points of unit interval. More...

static constexpr std::array< std::array< return_t, quadrature_t::n_points()>, n_fun_1D >	shape_ders_at_quad_points ()
	Derivatives of shape functions evaluated at quadrature points of unit interval. More...

static constexpr std::array< std::array< return_t, 2 >, n_fun_1D >	shape_fcts_at_bdrs ()
	Shape functions evaluated at boundaries of unit interval. More...

static constexpr std::array< std::array< return_t, 2 >, n_fun_1D >	shape_ders_at_bdrs ()
	Derivatives of shape functions evaluated at boundaries of unit interval. More...

Static Private Attributes
static constexpr unsigned int	n_fun_1D = shape_t::shape_fun_t::shape_fun_1d::n_fun()
	Amount of shape functions with respect to a single spatial dimension. More...

Detailed Description

template<typename quadrature_t, typename shape_t, typename return_t = double>
class TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >

General integrator class on tensorial hypergraphs.

Template Parameters

quadrature_t The one-dimensional quadrature rule applied.

Parameters

shape_t Type of shape functions.

Template Parameters

return_t Floating type specification. Default is double.

Authors: Andreas Rupp, Heidelberg University, 2021.

Member Typedef Documentation

◆ shape_fun_t

template<typename quadrature_t , typename shape_t , typename return_t = double>

typedef shape_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_fun_t

Make type of shape functions publicly available.

Member Function Documentation

◆ dim()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr unsigned int TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::dim ( )

inlinestaticconstexpr

The dimension of the Lebesque measure with respect to which we integrate.

◆ integrate_1D_DphiDphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_1D_DphiDphi	(	const unsigned int	i,
		const unsigned int	j
	)

inlinestaticconstexpr

Integrate product of two one-dimensional shape functions' derivatives.

Parameters

i	Local index of local one-dimensional shape function (with derivative).
j	Local index of local one-dimensional shape function (with derivative).

Return values

integral Integral of product of both shape functions.

◆ integrate_1D_Dphiphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_1D_Dphiphi	(	const unsigned int	i,
		const unsigned int	j
	)

inlinestaticconstexpr

Integrate product of one-dimensional shape function and one derivative.

Parameters

i	Local index of local one-dimensional shape function (with derivative).
j	Local index of local one-dimensional shape function.

Return values

integral Integral of product of both shape functions.

◆ integrate_1D_phiDphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_1D_phiDphi	(	const unsigned int	i,
		const unsigned int	j
	)

inlinestaticconstexpr

Integrate product of one-dimensional shape function and one derivative.

Parameters

i	Local index of local one-dimensional shape function.
j	Local index of local one-dimensional shape function (with derivative).

Return values

integral Integral of product of both shape functions.

◆ integrate_1D_phiphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_1D_phiphi	(	const unsigned int	i,
		const unsigned int	j
	)

inlinestaticconstexpr

Integrate product of one-dimensional shape functions.

Parameters

i	Local index of local one-dimensional shape function.
j	Local index of local one-dimensional shape function.

Return values

integral Integral of product of both shape functions.

◆ integrate_bdr_nablaphiphinufunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_nablaphiphinufunc	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate gradient of shape function times shape function times other function times normal over some geometry's boundary.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_nablaphipsinufunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_nablaphipsinufunc	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate gradient of shape function times shape function times other function times normal over some geometry's boundary.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_phifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phifunc	(	const unsigned int	i,
		const unsigned int	bdr,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Integrate product of shape functions times some function over boundary face.

Template Parameters

geom_t	Geometry which is the integration domain.
fun	Function that is multiplied by shape function.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
bdr	Boundary face index.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_bdr_phifuncnuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t func, point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phifuncnuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of shape function times function times vector function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_phiphi() [1/2]

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phiphi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr
	)

inlinestaticconstexpr

Integrate product of shape functions over dimT-dimensional volume's boundary.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
bdr	Boundary face index.

Return values

integral Integral of product of both shape functions.

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◆ integrate_bdr_phiphi() [2/2]

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename geom_t >

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phiphi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom
	)

inlinestatic

Integrate product of shape functions over boundary face.

Template Parameters

geom_t Geometry which is the integration domain.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
bdr	Boundary face index.
geom	Geometrical information.

Return values

integral Integral of product of both shape functions.

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◆ integrate_bdr_phiphi_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phiphi_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of product of shape functions.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_phiphinuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phiphinuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate shape function times shape function times vector function times normal.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_phipsi() [1/2]

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phipsi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr
	)

inlinestaticconstexpr

Integrate product of shape function of volume times shape function of volume's face over dimT-dimensional volume's boundary.

Parameters

i	Local index of local volume shape function.
j	Local index of local boundary shape function.
bdr	Boundary face index.

Return values

integral Integral of product of both shape functions.

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◆ integrate_bdr_phipsi() [2/2]

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename geom_t >

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phipsi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom
	)

inlinestatic

Integrate product of shape functions of volumen and skeletal over boundary face.

Template Parameters

geom_t Geometry which is the integration domain.

Parameters

i	Local index of local volumne shape function.
j	Local index of local skeletal shape function.
bdr	Boundary face index.
geom	Geometrical information.

Return values

integral Integral of product of both shape functions.

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◆ integrate_bdr_phipsi_cutdownwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phipsi_cutdownwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut downwind of shape function times skeletal shape function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_phipsinuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_phipsinuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of shape function times skeletal shape function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_psifuncnuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t func, point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_psifuncnuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of skeletal shape function times function times vector function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_psiphi_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_psiphi_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of skeletal shape function times shape function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_psiphinuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_psiphinuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of skeletal shape function times shape function times vector fct.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_psipsi_cutdownwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_psipsi_cutdownwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut downwind product of skeletal shape functions.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdr_psipsinuvecfunc_cutwind()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdr_psipsinuvecfunc_cutwind	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	bdr,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate cut upwind of product of skeltal shape functions times vector function.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
bdr	Index of the boundatry face to integrate over.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_bdrUni_psifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_bdrUni_psifunc	(	const unsigned int	i,
		const unsigned int	bdr,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Average integral of product of skeletal shape functions times some function.

Template Parameters

geom_t	Geometry which is the integration domain.
fun	Function that is multiplied by shape function.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
bdr	Boundary face index.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_derphifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_derphifunc	(	const unsigned int	i,
		const unsigned int	dim_der,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate derivative of shape function times other function over some geometry.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
dim_der	Dimension with respect to which derivative is calculated.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_vol_diffsquare_discana()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t, std::size_t n_coeff>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_diffsquare_discana	(	const std::array< return_t, n_coeff >	coeffs,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Squared L2 distance of some function and an discrete function on volume.

Template Parameters

geom_t	Geometry which is the integration domain.
fun	Function whose distance is measured.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

coeffs	Coefficients of discrete function.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Squared distance of functions.

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◆ integrate_vol_Dphiphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_Dphiphi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	dim_der
	)

inlinestaticconstexpr

Integrate product of shape function and derivative over dimT-dimensional unit volume.

Parameters

i	Local index of local shape function (with derivative).
j	Local index of local shape function.
dim_der	Dimension of the derivative.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_nablaphinablaphifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_nablaphinablaphifunc	(	const unsigned int	i,
		const unsigned int	j,
		geom_t &	geom,
		return_t	f_param = `0.`
	)

inlinestatic

Integrate gradient of shape functions times other function over some geometry.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Weight function that is additionally integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
geom	Geometrical information.
f_param	Time at which fun is evaluated.

Return values

integral Integral of product of both shape function's weighted gradients.

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◆ integrate_vol_nablaphiphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename smallVec_t , typename geom_t , unsigned int poly_deg_i = shape_t::degree(), unsigned int poly_deg_j = shape_t::degree()>

static smallVec_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_nablaphiphi	(	const unsigned int	i,
		const unsigned int	j,
		geom_t &	geom
	)

inlinestatic

Integrate gradient of shape function times other shape function over some geometry.

Note: poly_deg_i and poly_deg_j must be set to the maximum polynomial degree (which is also their default value) if the basis is not hierarchical.

Template Parameters

smallVec_t	Type of the return value.
geom_t	Geometry which is the integration domain.
poly_deg_i	Polynomial degree of shape functions associated to i.
poly_deg_j	Polynomial degree of shape functions associated to j.

Parameters

i	Local index of local shape function with gradient.
j	Local index of local shape function.
geom	Geometrical information.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_nablaphiphivecfunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_nablaphiphivecfunc	(	const unsigned int	i,
		const unsigned int	j,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Integrate gradient of shape function times other shape function times vector function.

Template Parameters

smallVec_t	Type of vector which is returned by the function.
point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Function that is also to be integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local gradient shape function.
j	Local index of local shape function.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phiDphi()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiDphi	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	dim_der
	)

inlinestaticconstexpr

Integrate product of shape function amd derivative over dimT-dimensional unit volume.

Parameters

i	Local index of local shape function.
j	Local index of local shape function (with derivative).
dim_der	Dimension of the derivative.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phifunc	(	const unsigned int	i,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Integrate product of shape function times some function over some geometry.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Function whose product with shape function is integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phiphi() [1/3]

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename geom_t , std::size_t array_size, typename floating_t >

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiphi	(	const std::array< floating_t, array_size > &	is,
		const std::array< floating_t, array_size > &	js,
		geom_t &	geom
	)

inlinestatic

Integrate product of linear combinations of shape functions over some geometry.

Template Parameters

geom_t	Geometry which is the integration domain.
array_size	Size of arrays containing coefficients of linear combinations.
floating_t	The floating point type for the calculation.

Parameters

is	Coefficients of local shape functions.
js	Coefficients of local shape functions.
geom	Geometrical information.

Return values

integral Integral of product of lineat combinations of shape functions.

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◆ integrate_vol_phiphi() [2/3]

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiphi	(	const unsigned int	i,
		const unsigned int	j
	)

inlinestaticconstexpr

Integrate product of shape functions over dimT-dimensional unit volume.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phiphi() [3/3]

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename geom_t >

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiphi	(	const unsigned int	i,
		const unsigned int	j,
		geom_t &	geom
	)

inlinestatic

Integrate product of shape functions over some geometry.

Template Parameters

geom_t Geometry which is the integration domain.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
geom	Geometrical information.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phiphifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiphifunc	(	const unsigned int	i,
		const unsigned int	j,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Integrate product of shape functions times some function over some geometry.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Function that is also to be integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_vol_phiphivecfunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , point_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_vol_phiphivecfunc	(	const unsigned int	i,
		const unsigned int	j,
		const unsigned int	dimension,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Integrate product of shape functions times some function over some geometry.

Template Parameters

smallVec_t	Type of vector which is returned by the function.
point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Function that is also to be integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
j	Local index of local shape function.
dimension	Local dimension with respect to which the vector-function is integrated.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ integrate_volUni_phifunc()

template<typename quadrature_t , typename shape_t , typename return_t = double>

template<typename point_t , typename geom_t , return_t fun, typename smallVec_t = point_t>

static return_t TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::integrate_volUni_phifunc	(	const unsigned int	i,
		geom_t &	geom,
		const return_t	f_param = `0.`
	)

inlinestatic

Average integral of product of shape function times some function over some geometry.

Template Parameters

point_t	Type of point which is the first argument of the function.
geom_t	Geometry which is the integration domain.
fun	Function whose product with shape function is integrated.
smallVec_t	Type of local point with respect to hyperedge. Defaults to point_t.

Parameters

i	Local index of local shape function.
geom	Geometrical information.
f_param	Function parameter (e.g. time) with respect to which it is evaluated.

Return values

integral Integral of product of both shape functions.

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◆ n_quad_points()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr unsigned int TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::n_quad_points ( )

inlinestaticconstexpr

Calculate the amount of quadrature points.

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◆ shape_ders_at_bdrs()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr std::array<std::array<return_t, 2>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_ders_at_bdrs ( )

inlinestaticconstexprprivate

Derivatives of shape functions evaluated at boundaries of unit interval.

◆ shape_ders_at_quad_points()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr std::array<std::array<return_t, quadrature_t::n_points()>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_ders_at_quad_points ( )

inlinestaticconstexprprivate

Derivatives of shape functions evaluated at quadrature points of unit interval.

◆ shape_fcts_at_bdrs()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr std::array<std::array<return_t, 2>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_fcts_at_bdrs ( )

inlinestaticconstexprprivate

Shape functions evaluated at boundaries of unit interval.

◆ shape_fcts_at_quad_points()

template<typename quadrature_t , typename shape_t , typename return_t = double>

static constexpr std::array<std::array<return_t, quadrature_t::n_points()>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_fcts_at_quad_points ( )

inlinestaticconstexprprivate

Shape functions evaluated at quadrature points of unit interval.

Member Data Documentation

◆ n_fun_1D

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr unsigned int TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::n_fun_1D = shape_t::shape_fun_t::shape_fun_1d::n_fun()

staticconstexprprivate

Amount of shape functions with respect to a single spatial dimension.

◆ quad_points

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<return_t, quadrature_t::n_points()> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::quad_points

staticconstexpr

Initial value:

=

quadrature_t::template points<return_t>()

Quadrature points on one-dimensional unit interval.

◆ quad_weights

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<return_t, quadrature_t::n_points()> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::quad_weights

staticconstexpr

Initial value:

=

quadrature_t::template weights<return_t>()

Quadrature weights on one-dimensional unit interval.

◆ shape_ders_at_bdr

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<std::array<return_t, 2>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_ders_at_bdr

staticconstexpr

Initial value:

=

shape_ders_at_bdrs()

Derivatives of shape functions evaluated at boundaries of unit interval.

◆ shape_ders_at_quad

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<std::array<return_t, quadrature_t::n_points()>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_ders_at_quad = shape_ders_at_quad_points()

staticconstexpr

Derivatives of shape functions evaluated at quadrature points of unit interval.

◆ shape_fcts_at_bdr

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<std::array<return_t, 2>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_fcts_at_bdr

staticconstexpr

Initial value:

=

shape_fcts_at_bdrs()

Shape functions evaluated at boundaries of unit interval.

◆ shape_fcts_at_quad

template<typename quadrature_t , typename shape_t , typename return_t = double>

constexpr std::array<std::array<return_t, quadrature_t::n_points()>, n_fun_1D> TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >::shape_fcts_at_quad = shape_fcts_at_quad_points()

staticconstexpr

Shape functions evaluated at quadrature points of unit interval.

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

/home/runner/work/HyperHDG/HyperHDG/submodules/tensor_product_polynomials.git/include/tpp/quadrature/tensorial.hxx

Public Types

Static Public Member Functions

Static Public Attributes

Static Private Member Functions

Static Private Attributes

Detailed Description

template<typename quadrature_t, typename shape_t, typename return_t = double> class TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >

Member Typedef Documentation

◆ shape_fun_t

Member Function Documentation

◆ dim()

◆ integrate_1D_DphiDphi()

◆ integrate_1D_Dphiphi()

◆ integrate_1D_phiDphi()

◆ integrate_1D_phiphi()

◆ integrate_bdr_nablaphiphinufunc()

◆ integrate_bdr_nablaphipsinufunc()

◆ integrate_bdr_phifunc()

◆ integrate_bdr_phifuncnuvecfunc_cutwind()

◆ integrate_bdr_phiphi() [1/2]

◆ integrate_bdr_phiphi() [2/2]

◆ integrate_bdr_phiphi_cutwind()

◆ integrate_bdr_phiphinuvecfunc_cutwind()

◆ integrate_bdr_phipsi() [1/2]

◆ integrate_bdr_phipsi() [2/2]

◆ integrate_bdr_phipsi_cutdownwind()

◆ integrate_bdr_phipsinuvecfunc_cutwind()

◆ integrate_bdr_psifuncnuvecfunc_cutwind()

◆ integrate_bdr_psiphi_cutwind()

◆ integrate_bdr_psiphinuvecfunc_cutwind()

◆ integrate_bdr_psipsi_cutdownwind()

◆ integrate_bdr_psipsinuvecfunc_cutwind()

◆ integrate_bdrUni_psifunc()

◆ integrate_vol_derphifunc()

◆ integrate_vol_diffsquare_discana()

◆ integrate_vol_Dphiphi()

◆ integrate_vol_nablaphinablaphifunc()

◆ integrate_vol_nablaphiphi()

◆ integrate_vol_nablaphiphivecfunc()

◆ integrate_vol_phiDphi()

◆ integrate_vol_phifunc()

◆ integrate_vol_phiphi() [1/3]

◆ integrate_vol_phiphi() [2/3]

◆ integrate_vol_phiphi() [3/3]

◆ integrate_vol_phiphifunc()

◆ integrate_vol_phiphivecfunc()

◆ integrate_volUni_phifunc()

◆ n_quad_points()

◆ shape_ders_at_bdrs()

◆ shape_ders_at_quad_points()

◆ shape_fcts_at_bdrs()

◆ shape_fcts_at_quad_points()

Member Data Documentation

◆ n_fun_1D

◆ quad_points

◆ quad_weights

◆ shape_ders_at_bdr

◆ shape_ders_at_quad

◆ shape_fcts_at_bdr

◆ shape_fcts_at_quad

template<typename quadrature_t, typename shape_t, typename return_t = double>
class TPP::Quadrature::Tensorial< quadrature_t, shape_t, return_t >