A section evaluator using bilinear interpolation over a square 2D domain. More...

#include <bilinear_2d.h>

Inheritance diagram for fiber_bundle::bilinear_2d:

BILINEAR_2D FACET
	bilinear_2d ()
	Default constructor. More...

	bilinear_2d (const bilinear_2d &xother)
	Copy constructor. More...

virtual	~bilinear_2d ()
	Destructor. More...

double	inverse_jacobian (const double xjacobian[2][2], double xinverse_jacobian[2][2])

LINEAR_FCN_SPACE FACET
virtual int	dl () const
	The dimension of this function space. More...

virtual void	basis_at_coord (const dof_type xlocal_coord[], size_type xlocal_coord_ub)
	Computes the value of each basis function at local coordinates xlocal_coord. More...

virtual void	basis_derivs_at_coord (const dof_type xlocal_coords[], size_type xlocal_coords_ub)
	Computes the value of the derivatives each basis function at local coordinates xlocal_coord. More...

INTEGRABLE_SECTION_EVALUATOR FACET
virtual value_type	jacobian_determinant (const dof_type xcoord_dofs[], size_type xcoord_dofs_ub, size_type xdf, const coord_type xlocal_coords[], size_type xlocal_coords_ub)
	Computes the the determinant of the jacobian matrix at local coordinates xlocal_coords with coordinate dofs xcoord_dofs. More...

virtual value_type	volume (const dof_type xcoord_dofs[], size_type xcoord_dofs_ub, size_type xdf)
	Volume for specified coordinate dofs xcoord_dofs and fiber space dimension xdf. More...

virtual void	integrate (const dof_type xcoord_dofs[], size_type xcoord_dofs_ub, size_type xdf, const dof_type xintegrands[], size_type xintegrands_ub, value_type xresult_integrals[], size_type xresult_integrals_ub)
	Computes the value of the integral of the integrand array... More...

virtual void	integrate (const dof_type xcoord_dofs[], size_type xcoord_dofs_ub, size_type xdf, const dof_type xintegrand, value_type xresult_integrals[], size_type xresult_integrals_ub)
	Computes the value of the integral of the integrand... More...

virtual void	gauss_point (pod_index_type xindex, coord_type xresult[], size_type xresult_ub)
	The local coordinates of the gauss point with index xindex. More...

DIFFERENTIABLE_SECTION_EVALUATOR FACET
void	dxi_local (size_type xlocal_coord_index, const dof_type xsource_dofs[], size_type xsource_dofs_ub, dof_type xresult_dofs[], size_type xresult_dofs_ub) const
	First partial derivative of this with respect to local coordinate xlocal_coord_index. More...

virtual void	jacobian (const dof_type xcoord_dofs[], size_type xcoord_dofs_ub, size_type xdf, const dof_type xlocal_coords[], size_type xlocal_coords_ub)
	Computes the the jacobian matrix at local coordinates xlocal_coords with coordinate dofs xcoord_dofs. More...

DOMAIN FACET
virtual int	db () const
	The base dimension; the dimension of the local coordinates (independent variable). More...

virtual void	local_coordinates (pod_index_type xindex, coord_type xresult[], size_type xresult_ub) const
	The local coordinates of the dof with local index xindex. More...

void	edge_center (pod_index_type xi, coord_type xresult[], size_type xresult_ub) const
	The local cordinates of the xi-th edge. More...

void	edge_center (pod_index_type xi, block< coord_type > &xresult) const
	The local cordinates of the xi-th edge (boundary). More...

virtual bool	in_standard_domain (const dof_type xlocal_coords[], size_type xlocal_coords_ub) const
	Return true if the specified local coordinates are in the "standard" domain; otherwise return false. More...

EVALUATION FACET
virtual void	coord_at_value (const dof_type xdofs[], size_type xdofs_ub, const dof_type xglobal_coords[], size_type xglobal_coord_ub, dof_type xlocal_coords[], size_type xlocal_coords_ub) const
	The local coordinates of a point at which the field has the value xvalue. The dofs are assumed to be interleaved (x0, y0, x1, y1, ...). More...

ANY FACET
virtual bilinear_2d *	clone () const
	Virtual constructor, creates a new instance of the same type as this. More...

virtual bilinear_2d &	operator= (const section_evaluator &xother)
	Assignment operator. More...

bilinear_2d &	operator= (const bilinear_2d &xother)
	Assignment operator. More...

virtual bool	invariant () const
	Class invariant. More...

virtual bool	is_ancestor_of (const any *xother) const
	Conformance test; true if other conforms to this. More...

Additional Inherited Members
Public Types inherited from fiber_bundle::section_evaluator
typedef chart_point_coord_type	coord_type
	The type of local coordinate; the scalar type for the local coordinate vector space. More...

typedef vd_value_type	value_type
	The type of component in the value; the scalar type in the range vector space. More...

typedef sec_vd_dof_type	dof_type
	The type of degree of freedom. More...

Public Member Functions inherited from fiber_bundle::linear_fcn_space
	linear_fcn_space (const linear_fcn_space &xother)
	Copy constructor. More...

virtual	~linear_fcn_space ()
	Destructor. More...

const value_type *	basis_values () const
	The result of the preceding call to basis_at_coord. More...

const value_type *	basis_deriv_values () const
	The result of the preceding call to basis_derivs_at_coord. More...

virtual size_type	dof_ct () const
	The number of dofs required for each component of the dependent variable. More...

virtual void	value_at_coord (const dof_type xdofs[], size_type xdofs_ub, const dof_type xlocal_coords[], size_type xlocal_coords_ub, dof_type xresult[], size_type xresult_ub) const
	Computes the value of the function at local coordinates xlocal_coords using the degrees of freedom xdofs. More...

linear_fcn_space &	operator= (const linear_fcn_space &xother)
	Assignment operator. More...

Public Member Functions inherited from fiber_bundle::integrable_section_evaluator
	integrable_section_evaluator (const integrable_section_evaluator &xother)
	Copy constructor. More...

virtual	~integrable_section_evaluator ()
	Destructor. More...

virtual integrable_section_evaluator &	operator= (const integrable_section_evaluator &xother)
	Assignment operator. More...

Public Member Functions inherited from fiber_bundle::differentiable_section_evaluator
	differentiable_section_evaluator (const differentiable_section_evaluator &xother)
	Copy constructor. More...

virtual	~differentiable_section_evaluator ()
	Destructor. More...

void	dxi_local (size_type xlocal_coord_index, const block< dof_type > &xsource_dofs, block< dof_type > &xresult_dofs) const
	First partial derivative of this with respect to local coordinate xlocal_coord_index. More...

const value_type *	jacobian_values () const
	The result of the preceding call to jacobian. More...

virtual differentiable_section_evaluator &	operator= (const differentiable_section_evaluator &xother)
	Assignment operator. More...

Public Member Functions inherited from fiber_bundle::section_evaluator
	section_evaluator (const section_evaluator &xother)
	Copy constructor. More...

virtual	~section_evaluator ()
	Destructor. More...

void	local_coordinates (pod_index_type xindex, block< coord_type > &xresult) const
	The local coordinates of the dof with local index xindex. More...

virtual void	center (coord_type xresult[], size_type xresult_ub) const
	The local coordinates at the center of the evaluator. More...

void	center (block< coord_type > &xresult) const
	The local coordinates at the center of the evaluator. More...

bool	in_standard_domain (const block< dof_type > &xlocal_coords) const
	True if the specified local coordinates are in the "standard" domain. More...

bool	df_is_variable () const
	True if and only if the fiber dimension (number of components of the dependent variable) is variable. More...

virtual int	df () const
	The fiber dimension (number of components of dependent variable). More...

virtual dof_type	value_at_coord (const dof_type xdofs[], size_type xdofs_ub, const dof_type xlocal_coords[], size_type xlocal_coords_ub) const
	Value at a specified local_coordinate. Single component version. More...

dof_type	value_at_coord (const block< dof_type > &xdofs, const block< dof_type > &xlocal_coords) const
	Value at a specified local_coordinate. Single component version. More...

void	value_at_coord (const block< dof_type > &xdofs, const block< dof_type > &xlocal_coords, block< dof_type > &xresult) const
	Values at a specified local_coordinate. Multiple component version. More...

void	coord_at_value (const block< dof_type > &xdofs, const block< dof_type > &xvalue, block< dof_type > &xlocal_coords) const
	The local coordinates of a point at which the field has the value xvalue. The dofs are assumed to be interleaved. More...

virtual dof_type	min (const dof_type xdofs[], size_type xdofs_ub) const
	The minimum value of the scalar or component section defined by xdofs. More...

dof_type	min (const block< dof_type > &xdofs) const
	The minimum value of the scalar or component section defined by xdofs. More...

virtual void	min (const dof_type xdofs[], size_type xdofs_ub, dof_type xresult[], size_type xresult_ub) const
	The minimum value of the vector section defined by xdofs. More...

void	min (const block< dof_type > &xdofs, block< dof_type > &xresult) const
	The minimum value of the vector section defined by xdofs. More...

virtual dof_type	max (const dof_type xdofs[], size_type xdofs_ub) const
	The maximum value of the scalar or component section defined by xdofs. More...

dof_type	max (const block< dof_type > &xdofs) const
	The maximum value of the scalar or component section defined by xdofs. More...

virtual void	max (const dof_type xdofs[], size_type xdofs_ub, dof_type xresult[], size_type xresult_ub) const
	The maximum value of the vector section defined by xdofs. More...

void	max (const block< dof_type > &xdofs, block< dof_type > &xresult) const
	The maximum value of the vector section defined by xdofs. More...

Public Member Functions inherited from sheaf::any
bool	is_same_type (const any *other) const
	True if other is the same type as this. More...

virtual	~any ()
	Destructor. More...

bool	invariant_check () const
	True if invariant checking is enabled. More...

void	enable_invariant_check () const
	Enable invariant checking. More...

void	disable_invariant_check () const
	Disable invariant check. Intended for preventing recursive calls to invariant and for suppressing invariant checking during multi-phase initialization. More...

int	disable_invariance_check_request_depth () const
	Number of times disable_invariant_check has been called without matching call to enable_invariant_check. More...

Protected Member Functions inherited from fiber_bundle::linear_fcn_space
	linear_fcn_space ()
	Default constructor. More...

Protected Member Functions inherited from fiber_bundle::integrable_section_evaluator
	integrable_section_evaluator ()
	Default constructor. More...

Protected Member Functions inherited from fiber_bundle::differentiable_section_evaluator
	differentiable_section_evaluator ()
	Default constructor. More...

Protected Member Functions inherited from fiber_bundle::section_evaluator
	section_evaluator ()
	Default constructor. More...

Protected Member Functions inherited from sheaf::any
	any ()
	default constructor More...

Protected Attributes inherited from fiber_bundle::linear_fcn_space
value_type *	_basis_values
	The result of the preceding call to basis_at_coord. More...

value_type *	_basis_deriv_values
	The result of the preceding call to basis_derivs_at_coord. More...

Protected Attributes inherited from fiber_bundle::differentiable_section_evaluator
value_type *	_jacobian_values
	The result of the preceding call to "jacobian". More...

Detailed Description

A section evaluator using bilinear interpolation over a square 2D domain.

Definition at line 42 of file bilinear_2d.h.

Constructor & Destructor Documentation

◆ bilinear_2d() [1/2]

fiber_bundle::bilinear_2d::bilinear_2d ( )

Default constructor.

Postcondition

invariant()

Definition at line 35 of file bilinear_2d.cc.

◆ bilinear_2d() [2/2]

fiber_bundle::bilinear_2d::bilinear_2d ( const bilinear_2d & xother )

Copy constructor.

Postcondition

invariant()

Definition at line 55 of file bilinear_2d.cc.

References ~bilinear_2d().

◆ ~bilinear_2d()

fiber_bundle::bilinear_2d::~bilinear_2d ( )

virtual

Destructor.

Postcondition

invariant()

Definition at line 74 of file bilinear_2d.cc.

References fiber_bundle::st2_algebra::determinant(), dl(), fiber_bundle::sec_at0_algebra::fabs(), and fiber_bundle::sec_at0_algebra::sqrt().

Referenced by bilinear_2d().

Member Function Documentation

◆ basis_at_coord()

void fiber_bundle::bilinear_2d::basis_at_coord	(	const dof_type	xlocal_coord[],
		size_type	xlocal_coord_ub
	)

virtual

Computes the value of each basis function at local coordinates xlocal_coord.

Precondition

xlocal_coord != 0

xlocal_coord_ub >= db()

Postcondition

invariant()

Implements fiber_bundle::linear_fcn_space.

Definition at line 242 of file bilinear_2d.cc.

References basis_derivs_at_coord().

Referenced by dl().

◆ basis_derivs_at_coord()

void fiber_bundle::bilinear_2d::basis_derivs_at_coord	(	const dof_type	xlocal_coords[],
		size_type	xlocal_coords_ub
	)

virtual

Computes the value of the derivatives each basis function at local coordinates xlocal_coord.

Precondition

xlocal_coords != 0

xlocal_coords_ub >= db()

Postcondition

invariant()

Implements fiber_bundle::linear_fcn_space.

Definition at line 275 of file bilinear_2d.cc.

References jacobian_determinant().

Referenced by basis_at_coord().

◆ clone()

fiber_bundle::bilinear_2d * fiber_bundle::bilinear_2d::clone ( ) const

virtual

Virtual constructor, creates a new instance of the same type as this.

Postcondition

result != 0

is_same_type(result)

result->invariant()

Implements fiber_bundle::linear_fcn_space.

Definition at line 1124 of file bilinear_2d.cc.

References invariant(), and operator=().

Referenced by coord_at_value().

◆ coord_at_value()

void fiber_bundle::bilinear_2d::coord_at_value	(	const dof_type	xdofs[],
		size_type	xdofs_ub,
		const dof_type	xglobal_coords[],
		size_type	xglobal_coord_ub,
		dof_type	xlocal_coords[],
		size_type	xlocal_coords_ub
	)		const

virtual

The local coordinates of a point at which the field has the value xvalue. The dofs are assumed to be interleaved (x0, y0, x1, y1, ...).

Precondition

xdofs != 0

xdofs_ub >= 8

xglobal_coords != 0

xglobal_coord_ub >= 2

xlocal_coords != 0

xlocal_coords_ub >= 2

-unexecutable( xdofs must be interleaved )

Postcondition

invariant()

Implements fiber_bundle::section_evaluator.

Definition at line 1044 of file bilinear_2d.cc.

References clone().

Referenced by in_standard_domain().

◆ db()

int fiber_bundle::bilinear_2d::db ( ) const

virtual

The base dimension; the dimension of the local coordinates (independent variable).

Todo:: xlocal_coords_ub, etc.

Postcondition

result == 2

Implements fiber_bundle::section_evaluator.

Definition at line 881 of file bilinear_2d.cc.

References local_coordinates().

Referenced by jacobian().

◆ dl()

int fiber_bundle::bilinear_2d::dl ( ) const

virtual

The dimension of this function space.

Postcondition

result == 4

Implements fiber_bundle::linear_fcn_space.

Definition at line 219 of file bilinear_2d.cc.

References basis_at_coord().

Referenced by ~bilinear_2d().

◆ dxi_local()

void fiber_bundle::bilinear_2d::dxi_local	(	size_type	xlocal_coord_index,
		const dof_type	xsource_dofs[],
		size_type	xsource_dofs_ub,
		dof_type	xresult_dofs[],
		size_type	xresult_dofs_ub
	)		const

virtual

First partial derivative of this with respect to local coordinate xlocal_coord_index.

Precondition

xlocal_coord_index < db()

xsource_dofs != 0

xresult_dofs != 0

Implements fiber_bundle::differentiable_section_evaluator.

Definition at line 608 of file bilinear_2d.cc.

References jacobian().

Referenced by gauss_point().

◆ edge_center() [1/2]

void fiber_bundle::bilinear_2d::edge_center	(	pod_index_type	xi,
		coord_type	xresult[],
		size_type	xresult_ub
	)		const

The local cordinates of the xi-th edge.

Precondition

xresult != 0

xresult_ub >= db()

Definition at line 939 of file bilinear_2d.cc.

Referenced by local_coordinates(), and fields::edge_centered_polygon_refiner::refine_coordinates().

◆ edge_center() [2/2]

void fiber_bundle::bilinear_2d::edge_center	(	pod_index_type	xi,
		block< coord_type > &	xresult
	)		const

The local cordinates of the xi-th edge (boundary).

Precondition

precondition_of(center(xresult.base(), xresult.ub()))

Postcondition

postcondition_of(edge_center(xresult.base(), xresult.ub()))

xresult.ct() == db()

Definition at line 985 of file bilinear_2d.cc.

References sheaf::auto_block< T, un_block_initialization_policy< T > >::base(), sheaf::auto_block< T, un_block_initialization_policy< T > >::ct(), in_standard_domain(), sheaf::auto_block< T, un_block_initialization_policy< T > >::set_ct(), and sheaf::auto_block< T, un_block_initialization_policy< T > >::ub().

◆ gauss_point()

void fiber_bundle::bilinear_2d::gauss_point	(	pod_index_type	xindex,
		coord_type	xresult[],
		size_type	xresult_ub
	)

virtual

The local coordinates of the gauss point with index xindex.

Precondition

(0 <= xindex) && (xindex < dof_ct())

xresult_ub >= db()

Postcondition

in_standard_domain(xresult, xresult_ub)

Implements fiber_bundle::integrable_section_evaluator.

Definition at line 567 of file bilinear_2d.cc.

References dxi_local(), and fiber_bundle::sec_at0_algebra::sqrt().

Referenced by integrate().

◆ in_standard_domain()

bool fiber_bundle::bilinear_2d::in_standard_domain	(	const dof_type	xlocal_coords[],
		size_type	xlocal_coords_ub
	)		const

virtual

Return true if the specified local coordinates are in the "standard" domain; otherwise return false.

Precondition

xlocal_coords != 0

xlocal_coords_ub >= 2

Implements fiber_bundle::section_evaluator.

Definition at line 1009 of file bilinear_2d.cc.

References coord_at_value().

Referenced by edge_center().

◆ integrate() [1/2]

void fiber_bundle::bilinear_2d::integrate	(	const dof_type	xcoord_dofs[],
		size_type	xcoord_dofs_ub,
		size_type	xdf,
		const dof_type	xintegrands[],
		size_type	xintegrands_ub,
		value_type	xresult_integrals[],
		size_type	xresult_integrals_ub
	)

virtual

Computes the value of the integral of the integrand array...

Todo:: Get these correct.

Precondition

xcoord_dofs != 0

xcoord_dofs_ub >= dl()*db()

xintegrands != 0

xintegrands_ub >= dl()

xresult_integrals != 0

xresult_integrals_ub > 0

Issue:: Interpreting the number of integrands per node as xintegrands_ub/xresult_integrals_ub.

Todo:: Add method number_of_gauss_points().

Postcondition

invariant()

Implements fiber_bundle::integrable_section_evaluator.

Definition at line 429 of file bilinear_2d.cc.

Referenced by volume().

◆ integrate() [2/2]

void fiber_bundle::bilinear_2d::integrate	(	const dof_type	xcoord_dofs[],
		size_type	xcoord_dofs_ub,
		size_type	xdf,
		const dof_type	xintegrand,
		value_type	xresult_integrals[],
		size_type	xresult_integrals_ub
	)

virtual

Computes the value of the integral of the integrand...

Todo:: Get these correct.

Precondition

xcoord_dofs != 0

xcoord_dofs_ub >= dl()*db()

xresult_integrals != 0

xresult_integrals_ub >= dl()

Todo:: Add method number_of_gauss_points().

Postcondition

invariant()

Reimplemented from fiber_bundle::integrable_section_evaluator.

Definition at line 506 of file bilinear_2d.cc.

References gauss_point().

◆ invariant()

bool fiber_bundle::bilinear_2d::invariant ( ) const

virtual

Class invariant.

Invariant

basis_values() != 0

Reimplemented from fiber_bundle::linear_fcn_space.

Definition at line 1193 of file bilinear_2d.cc.

References is_ancestor_of().

Referenced by clone(), and operator=().

◆ is_ancestor_of()

bool fiber_bundle::bilinear_2d::is_ancestor_of ( const any * xother ) const

virtual

Conformance test; true if other conforms to this.

Precondition

xother != 0

Reimplemented from fiber_bundle::linear_fcn_space.

Definition at line 1226 of file bilinear_2d.cc.

Referenced by invariant().

◆ jacobian()

void fiber_bundle::bilinear_2d::jacobian	(	const dof_type	xcoord_dofs[],
		size_type	xcoord_dofs_ub,
		size_type	xdf,
		const dof_type	xlocal_coords[],
		size_type	xlocal_coords_ub
	)

virtual

Computes the the jacobian matrix at local coordinates xlocal_coords with coordinate dofs xcoord_dofs.

Todo:: Fix!

Precondition

xcoord_dofs != 0

xcoord_dofs_ub >= xdf*dl()

xdf == 2 || xdf == 3

xlocal_coords != 0

xlocal_coords_ub >= 2

cthis->jacobian_values() != 0

///

Issue:: This can probably be made more efficient by reordering /// the loops.

Postcondition

invariant()

Reimplemented from fiber_bundle::differentiable_section_evaluator.

Definition at line 657 of file bilinear_2d.cc.

References db(), and fiber_bundle::differentiable_section_evaluator::jacobian_values().

Referenced by dxi_local().

◆ jacobian_determinant()

fiber_bundle::section_evaluator::value_type fiber_bundle::bilinear_2d::jacobian_determinant	(	const dof_type	xcoord_dofs[],
		size_type	xcoord_dofs_ub,
		size_type	xdf,
		const coord_type	xlocal_coords[],
		size_type	xlocal_coords_ub
	)

virtual

Computes the the determinant of the jacobian matrix at local coordinates xlocal_coords with coordinate dofs xcoord_dofs.

Precondition

xcoord_dofs != 0

xcoord_dofs_ub >= dl()*db()

xdf == 2 || xdf == 3

Reimplemented from fiber_bundle::differentiable_section_evaluator.

Definition at line 329 of file bilinear_2d.cc.

References fiber_bundle::sec_at0_algebra::fabs(), fiber_bundle::sec_at0_algebra::sqrt(), and volume().

Referenced by basis_derivs_at_coord().

◆ local_coordinates()

void fiber_bundle::bilinear_2d::local_coordinates	(	pod_index_type	xindex,
		coord_type	xresult[],
		size_type	xresult_ub
	)		const

virtual

The local coordinates of the dof with local index xindex.

Precondition

(0 <= xindex) && (xindex < dof_ct())

xresult_ub >= db()

Postcondition

in_standard_domain(xresult, xresult_ub)

Implements fiber_bundle::section_evaluator.

Definition at line 905 of file bilinear_2d.cc.

References edge_center().

Referenced by db().

◆ operator=() [1/2]

fiber_bundle::bilinear_2d & fiber_bundle::bilinear_2d::operator= ( const section_evaluator & xother )

virtual

Assignment operator.

Precondition

is_ancestor_of(&xother)

Not Implemented.

Postcondition

invariant()

Reimplemented from fiber_bundle::linear_fcn_space.

Definition at line 1148 of file bilinear_2d.cc.

Referenced by clone().

◆ operator=() [2/2]

fiber_bundle::bilinear_2d & fiber_bundle::bilinear_2d::operator= ( const bilinear_2d & xother )

Assignment operator.

Precondition

is_ancestor_of(&xother)

Not Implemented.

Postcondition

invariant()

Definition at line 1168 of file bilinear_2d.cc.

References invariant().

◆ volume()

fiber_bundle::section_evaluator::value_type fiber_bundle::bilinear_2d::volume	(	const dof_type	xcoord_dofs[],
		size_type	xcoord_dofs_ub,
		size_type	xdf
	)

virtual

Volume for specified coordinate dofs xcoord_dofs and fiber space dimension xdf.

Precondition

xcoord_dofs != 0

xcoord_dofs_ub >= dl()*db()

xdf == 2 || xdf == 3

Todo:: Add method number_of_gauss_points().

Postcondition

invariant()

Implements fiber_bundle::integrable_section_evaluator.

Definition at line 387 of file bilinear_2d.cc.

References integrate().

Referenced by jacobian_determinant().

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

BILINEAR_2D FACET

LINEAR_FCN_SPACE FACET

INTEGRABLE_SECTION_EVALUATOR FACET

DIFFERENTIABLE_SECTION_EVALUATOR FACET

DOMAIN FACET

EVALUATION FACET

ANY FACET

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ bilinear_2d() [1/2]

◆ bilinear_2d() [2/2]

◆ ~bilinear_2d()

Member Function Documentation

◆ basis_at_coord()

◆ basis_derivs_at_coord()

◆ clone()

◆ coord_at_value()

◆ db()

◆ dl()

◆ dxi_local()

◆ edge_center() [1/2]

◆ edge_center() [2/2]

◆ gauss_point()

◆ in_standard_domain()

◆ integrate() [1/2]

◆ integrate() [2/2]

◆ invariant()

◆ is_ancestor_of()

◆ jacobian()

◆ jacobian_determinant()

◆ local_coordinates()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ volume()