The superspace manages local polynomial bases on each element of the mesh and provides an interface to evaluate them. More...

#include <SuperSpace.hpp>

Detailed Description

template<typename Derived>
struct Bembel::SuperSpace< Derived >

The superspace manages local polynomial bases on each element of the mesh and provides an interface to evaluate them.

Definition at line 22 of file SuperSpace.hpp.

Public Member Functions
	SuperSpace ()
	Default constructor for the SuperSpace class.

	SuperSpace (Geometry &geom, int M, int P)
	Parameterized constructor for the SuperSpace class.

	SuperSpace (const SuperSpace &other)
	Copy constructor for the SuperSpace class.

	SuperSpace (SuperSpace &&other)
	Move constructor for the SuperSpace class.

SuperSpace &	operator= (SuperSpace other)
	Assignment operator for the SuperSpace class.

int	get_polynomial_degree () const

int	get_polynomial_degree_plus_one_squared () const

int	get_refinement_level () const

int	get_number_of_elements () const

int	get_number_of_patches () const

const PatchVector &	get_geometry () const

const ClusterTree &	get_mesh () const

void	init_SuperSpace (const Geometry &geom, int M, int P)

void	map2surface (const ElementTreeNode &e, const Eigen::Vector2d &xi, double w, SurfacePoint *surf_pt) const
	Evaluation of a point in the element and its Jacobian matrix.

void	addScaledBasisInteraction (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *intval, typename LinearOperatorTraits< Derived >::Scalar w, const Eigen::Vector2d &s, const Eigen::Vector2d &t) const
	Compute all products of local shape functions on the unit square at coordinates s,t, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	basisInteraction (const Eigen::Vector2d &s, const Eigen::Vector2d &t) const
	Compute all products of local shape functions on the unit square at coordinates s,t.

void	addScaledSurfaceCurlInteraction (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *intval, Scalar w, const SurfacePoint &p1, const SurfacePoint &p2) const
	Compute all products of surface curls of local shape functions on the unit square at coordinates s,t.

void	addScaledSurfaceGradientInteraction (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *intval, Scalar w, const SurfacePoint &p1, const SurfacePoint &p2) const
	Compute all products of surface gradients of local shape functions on the unit square at coordinates s,t.

void	addScaledVectorBasisInteraction (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *intval, Scalar w, const Eigen::Vector2d &s, const Eigen::Vector2d &t, const Eigen::Vector3d x_f_dx, const Eigen::Vector3d x_f_dy, const Eigen::Vector3d y_f_dx, const Eigen::Vector3d y_f_dy) const
	Compute all scalar products of vector valued local shape functions on the surface points with reference coordinates s,t, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	vectorBasisInteraction (const Eigen::Vector2d &s, const Eigen::Vector2d &t, const Eigen::Vector3d x_f_dx, const Eigen::Vector3d x_f_dy, const Eigen::Vector3d y_f_dx, const Eigen::Vector3d y_f_dy) const
	Compute all scalar products of vector valued local shape functions on the surface points with reference coordinates s,t.

void	addScaledVectorBasisDivergenceInteraction (Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *intval, Scalar w, const Eigen::Vector2d &s, const Eigen::Vector2d &t) const
	Compute all products of divergences of local shape functions on the unit square at coordinates s,t, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic >	vectorBasisDivergenceInteraction (const Eigen::Vector2d &s, const Eigen::Vector2d &t) const
	Compute all products of divergences of local shape functions on the unit square at coordinates s,t.

void	addScaledBasis (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *intval, Scalar w, const Eigen::Vector2d &s) const
	Evaluate local shape functions on the unit square at coordinate s, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	basis (const Eigen::Vector2d &s) const
	Evaluate local shape functions on the unit square at coordinate s.

void	addScaledBasisDx (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *intval, typename LinearOperatorTraits< Derived >::Scalar w, const Eigen::Vector2d &s) const
	Evaluate derivatives in x direction of local shape functions on the unit square at coordinate s, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	basisDx (const Eigen::Vector2d &s) const
	Evaluate derivatives in x direction of local shape functions on the unit square at coordinate s.

void	addScaledBasisDy (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *intval, typename LinearOperatorTraits< Derived >::Scalar w, const Eigen::Vector2d &s) const
	Evaluate derivatives in y direction of local shape functions on the unit square at coordinate s, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	basisDy (const Eigen::Vector2d &s) const
	Evaluate derivatives in y direction of local shape functions on the unit square at coordinate s.

void	addScaledBasis1D (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *intval, Scalar w, double s) const
	Evaluate local shape functions on the unit interval at coordinate s, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	basis1D (double s) const
	Evaluate local shape functions on the unit interval at coordinate s.

void	addScaledBasis1DDx (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *intval, Scalar w, double s) const
	Evaluate derivatives of local shape functions on the unit interval at coordinate s, scale by w and add to intval.

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 >	basis1DDx (double s) const
	Evaluate derivatives of local shape functions on the unit interval at coordinate s.

Public Types
typedef LinearOperatorTraits< Derived >::Scalar	Scalar

Member Typedef Documentation

◆ Scalar

template<typename Derived >

typedef LinearOperatorTraits<Derived>::Scalar Bembel::SuperSpace< Derived >::Scalar

Definition at line 23 of file SuperSpace.hpp.

Constructor & Destructor Documentation

◆ SuperSpace() [1/4]

template<typename Derived >

Bembel::SuperSpace< Derived >::SuperSpace ( )

inline

Default constructor for the SuperSpace class.

This constructor creates a SuperSpace object with default parameters.

Definition at line 32 of file SuperSpace.hpp.

◆ SuperSpace() [2/4]

template<typename Derived >

Bembel::SuperSpace< Derived >::SuperSpace	(	Geometry &	geom,
		int	M,
		int	P
	)

inline

Parameterized constructor for the SuperSpace class.

This constructor initializes a SuperSpace object with the provided parameters.

Parameters

geom	The geometry object defining the space.
M	The refinement level of the space.
P	The degree of polynomials used in the space.

Definition at line 43 of file SuperSpace.hpp.

◆ SuperSpace() [3/4]

template<typename Derived >

Bembel::SuperSpace< Derived >::SuperSpace ( const SuperSpace< Derived > & other )

inline

Copy constructor for the SuperSpace class.

This constructor initializes a SuperSpace object by copying another SuperSpace object.

Parameters

other The SuperSpace object to copy from.

Definition at line 52 of file SuperSpace.hpp.

◆ SuperSpace() [4/4]

template<typename Derived >

Bembel::SuperSpace< Derived >::SuperSpace ( SuperSpace< Derived > && other )

inline

Move constructor for the SuperSpace class.

This constructor initializes a SuperSpace object by moving from another SuperSpace object.

Parameters

other The SuperSpace object to move from.

Definition at line 74 of file SuperSpace.hpp.

Member Function Documentation

◆ addScaledBasis()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasis	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *	intval,
		Scalar	w,
		const Eigen::Vector2d &	s
	)		const

inline

Evaluate local shape functions on the unit square at coordinate s, scale by w and add to intval.

Definition at line 302 of file SuperSpace.hpp.

◆ addScaledBasis1D()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasis1D	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *	intval,
		Scalar	w,
		double	s
	)		const

inline

Evaluate local shape functions on the unit interval at coordinate s, scale by w and add to intval.

Definition at line 363 of file SuperSpace.hpp.

◆ addScaledBasis1DDx()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasis1DDx	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *	intval,
		Scalar	w,
		double	s
	)		const

inline

Evaluate derivatives of local shape functions on the unit interval at coordinate s, scale by w and add to intval.

Definition at line 380 of file SuperSpace.hpp.

◆ addScaledBasisDx()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasisDx	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *	intval,
		typename LinearOperatorTraits< Derived >::Scalar	w,
		const Eigen::Vector2d &	s
	)		const

inline

Evaluate derivatives in x direction of local shape functions on the unit square at coordinate s, scale by w and add to intval.

Definition at line 321 of file SuperSpace.hpp.

◆ addScaledBasisDy()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasisDy	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > *	intval,
		typename LinearOperatorTraits< Derived >::Scalar	w,
		const Eigen::Vector2d &	s
	)		const

inline

Evaluate derivatives in y direction of local shape functions on the unit square at coordinate s, scale by w and add to intval.

Definition at line 342 of file SuperSpace.hpp.

◆ addScaledBasisInteraction()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledBasisInteraction	(	Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *	intval,
		typename LinearOperatorTraits< Derived >::Scalar	w,
		const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t
	)		const

inline

Compute all products of local shape functions on the unit square at coordinates s,t, scale by w and add to intval.

Definition at line 173 of file SuperSpace.hpp.

◆ addScaledSurfaceCurlInteraction()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledSurfaceCurlInteraction	(	Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *	intval,
		Scalar	w,
		const SurfacePoint &	p1,
		const SurfacePoint &	p2
	)		const

inline

Compute all products of surface curls of local shape functions on the unit square at coordinates s,t.

Definition at line 196 of file SuperSpace.hpp.

◆ addScaledSurfaceGradientInteraction()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledSurfaceGradientInteraction	(	Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *	intval,
		Scalar	w,
		const SurfacePoint &	p1,
		const SurfacePoint &	p2
	)		const

inline

Compute all products of surface gradients of local shape functions on the unit square at coordinates s,t.

Definition at line 223 of file SuperSpace.hpp.

◆ addScaledVectorBasisDivergenceInteraction()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledVectorBasisDivergenceInteraction	(	Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *	intval,
		Scalar	w,
		const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t
	)		const

inline

Compute all products of divergences of local shape functions on the unit square at coordinates s,t, scale by w and add to intval.

Definition at line 279 of file SuperSpace.hpp.

◆ addScaledVectorBasisInteraction()

template<typename Derived >

void Bembel::SuperSpace< Derived >::addScaledVectorBasisInteraction	(	Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > *	intval,
		Scalar	w,
		const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t,
		const Eigen::Vector3d	x_f_dx,
		const Eigen::Vector3d	x_f_dy,
		const Eigen::Vector3d	y_f_dx,
		const Eigen::Vector3d	y_f_dy
	)		const

inline

Compute all scalar products of vector valued local shape functions on the surface points with reference coordinates s,t, scale by w and add to intval.

Definition at line 236 of file SuperSpace.hpp.

◆ basis()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Bembel::SuperSpace< Derived >::basis ( const Eigen::Vector2d & s ) const

inline

Evaluate local shape functions on the unit square at coordinate s.

Definition at line 309 of file SuperSpace.hpp.

◆ basis1D()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Bembel::SuperSpace< Derived >::basis1D ( double s ) const

inline

Evaluate local shape functions on the unit interval at coordinate s.

Definition at line 370 of file SuperSpace.hpp.

◆ basis1DDx()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Bembel::SuperSpace< Derived >::basis1DDx ( double s ) const

inline

Evaluate derivatives of local shape functions on the unit interval at coordinate s.

Definition at line 388 of file SuperSpace.hpp.

◆ basisDx()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Bembel::SuperSpace< Derived >::basisDx ( const Eigen::Vector2d & s ) const

inline

Evaluate derivatives in x direction of local shape functions on the unit square at coordinate s.

Definition at line 330 of file SuperSpace.hpp.

◆ basisDy()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > Bembel::SuperSpace< Derived >::basisDy ( const Eigen::Vector2d & s ) const

inline

Evaluate derivatives in y direction of local shape functions on the unit square at coordinate s.

Definition at line 351 of file SuperSpace.hpp.

◆ basisInteraction()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > Bembel::SuperSpace< Derived >::basisInteraction	(	const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t
	)		const

inline

Compute all products of local shape functions on the unit square at coordinates s,t.

Definition at line 183 of file SuperSpace.hpp.

◆ get_geometry()

template<typename Derived >

const PatchVector & Bembel::SuperSpace< Derived >::get_geometry ( ) const

inline

Definition at line 122 of file SuperSpace.hpp.

◆ get_mesh()

template<typename Derived >

const ClusterTree & Bembel::SuperSpace< Derived >::get_mesh ( ) const

inline

Definition at line 123 of file SuperSpace.hpp.

◆ get_number_of_elements()

template<typename Derived >

int Bembel::SuperSpace< Derived >::get_number_of_elements ( ) const

inline

Definition at line 120 of file SuperSpace.hpp.

◆ get_number_of_patches()

template<typename Derived >

int Bembel::SuperSpace< Derived >::get_number_of_patches ( ) const

inline

Definition at line 121 of file SuperSpace.hpp.

◆ get_polynomial_degree()

template<typename Derived >

int Bembel::SuperSpace< Derived >::get_polynomial_degree ( ) const

inline

Definition at line 115 of file SuperSpace.hpp.

◆ get_polynomial_degree_plus_one_squared()

template<typename Derived >

int Bembel::SuperSpace< Derived >::get_polynomial_degree_plus_one_squared ( ) const

inline

Definition at line 116 of file SuperSpace.hpp.

◆ get_refinement_level()

template<typename Derived >

int Bembel::SuperSpace< Derived >::get_refinement_level ( ) const

inline

Definition at line 119 of file SuperSpace.hpp.

◆ init_SuperSpace()

template<typename Derived >

void Bembel::SuperSpace< Derived >::init_SuperSpace	(	const Geometry &	geom,
		int	M,
		int	P
	)

inline

Definition at line 127 of file SuperSpace.hpp.

◆ map2surface()

template<typename Derived >

void Bembel::SuperSpace< Derived >::map2surface	(	const ElementTreeNode &	e,
		const Eigen::Vector2d &	xi,
		double	w,
		SurfacePoint *	surf_pt
	)		const

inline

Evaluation of a point in the element and its Jacobian matrix.

This function performs the affine transformation of an element to the reference domain of the patch and returns the output in a surface point.

Parameters

e	: Element to be evaluated,
xi	: Point in [0, 1]^2 of the element
w	: Quadrature weight
surf_pt	: Evaluated point and its jacobian

Definition at line 160 of file SuperSpace.hpp.

◆ operator=()

template<typename Derived >

SuperSpace & Bembel::SuperSpace< Derived >::operator= ( SuperSpace< Derived > other )

inline

Assignment operator for the SuperSpace class.

This operator assigns the contents of another SuperSpace object to this one.

Parameters

other The SuperSpace object to copy from.

Returns: A reference to the updated SuperSpace object.

Definition at line 97 of file SuperSpace.hpp.

◆ vectorBasisDivergenceInteraction()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > Bembel::SuperSpace< Derived >::vectorBasisDivergenceInteraction	(	const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t
	)		const

inline

Compute all products of divergences of local shape functions on the unit square at coordinates s,t.

Definition at line 289 of file SuperSpace.hpp.

◆ vectorBasisInteraction()

template<typename Derived >

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > Bembel::SuperSpace< Derived >::vectorBasisInteraction	(	const Eigen::Vector2d &	s,
		const Eigen::Vector2d &	t,
		const Eigen::Vector3d	x_f_dx,
		const Eigen::Vector3d	x_f_dy,
		const Eigen::Vector3d	y_f_dx,
		const Eigen::Vector3d	y_f_dy
	)		const

inline

Compute all scalar products of vector valued local shape functions on the surface points with reference coordinates s,t.

Definition at line 263 of file SuperSpace.hpp.

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

Bembel/src/AnsatzSpace/SuperSpace.hpp

Detailed Description

Public Member Functions

Public Types

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ SuperSpace() [1/4]

◆ SuperSpace() [2/4]

◆ SuperSpace() [3/4]

◆ SuperSpace() [4/4]

Member Function Documentation

◆ addScaledBasis()

◆ addScaledBasis1D()

◆ addScaledBasis1DDx()

◆ addScaledBasisDx()

◆ addScaledBasisDy()

◆ addScaledBasisInteraction()

◆ addScaledSurfaceCurlInteraction()

◆ addScaledSurfaceGradientInteraction()

◆ addScaledVectorBasisDivergenceInteraction()

◆ addScaledVectorBasisInteraction()

◆ basis()

◆ basis1D()

◆ basis1DDx()

◆ basisDx()

◆ basisDy()

◆ basisInteraction()

◆ get_geometry()

◆ get_mesh()

◆ get_number_of_elements()

◆ get_number_of_patches()

◆ get_polynomial_degree()

◆ get_polynomial_degree_plus_one_squared()

◆ get_refinement_level()

◆ init_SuperSpace()

◆ map2surface()

◆ operator=()

◆ vectorBasisDivergenceInteraction()

◆ vectorBasisInteraction()