Manage the geometry of a cell. More...

#include <dcell.hpp>

Inheritance diagram for Manicore::dCell_map< dimension, d >:

[legend]

Public Member Functions
	dCell_map (Eigen::Vector< double, dimension > const &center_mass, Eigen::Matrix< double, dimension, d > const &flat_map, double diam, std::vector< Simplex< d >> const &triangulation)
	Flat constructor. More...

	dCell_map (std::vector< std::unique_ptr< ParametrizedMap< dimension, d >>> &maps, std::vector< std::unique_ptr< ParametrizedDerivedMap< dimension, d >>> &pullback_maps, std::vector< Simplex< d >> const &triangulation)
	General constructor. More...

bool	is_flat () const
	Is the cell flat. More...

std::vector< Simplex< d > > const &	get_reference_elem () const
	Return the reference element as a collection of simplexes. More...

Eigen::Vector< double, dimension >	evaluate_I (size_t rel_map_id, Eigen::Vector< double, d > const &x) const
	Evaluate the parametrization from the reference element to a chart. More...

Eigen::Vector< double, d >	evaluate_J (size_t rel_map_id, Eigen::Vector< double, dimension > const &x) const
	Evaluate the inverse mapping from the chart to the reference element. More...

double	evaluate_poly_on_ref (Eigen::Vector< double, d > const &x, size_t i_pbasis, int r) const
	Evaluate a scalar polynomial on the reference element. More...

double	evaluate_poly_pullback (size_t rel_map_id, Eigen::Vector< double, dimension > const &x, size_t i_pbasis, int r) const
	Evaluate the pullback of a scalar polynomial on the chart. More...

Eigen::Matrix< double, dimension, d >	evaluate_DI (size_t rel_map_id, Eigen::Vector< double, d > const &x) const
	Evaluate the differential of the parametrization. More...

Eigen::Matrix< double, d, dimension >	evaluate_DJ (size_t rel_map_id, Eigen::Vector< double, dimension > const &x) const
	Evaluate the differential of the inverse mapping. More...

template<size_t l>
Eigen::Matrix< double, Dimension::ExtDim(l, d), Dimension::ExtDim(l, dimension)>	evaluate_DI_p (size_t rel_map_id, Eigen::Vector< double, d > const &x) const
	Compute the action of the pullback of l-forms by the parametrization. More...

template<size_t l>
Eigen::Matrix< double, Dimension::ExtDim(l, dimension), Dimension::ExtDim(l, d)>	evaluate_DJ_p (size_t rel_map_id, Eigen::Vector< double, dimension > const &x) const
	Compute the action of the pullback of l-forms by the inverse mapping. More...

int	get_orientation (size_t rel_map_id, Eigen::Vector< double, dimension > const &x, Eigen::Matrix< double, dimension, d-1 > const &pM) const requires(d >1)
	Return the relative orientation. More...

Static Public Attributes
static constexpr size_t	cell_dim = d
	Dimension of the cell More...

Detailed Description

template<size_t dimension, size_t d>
class Manicore::dCell_map< dimension, d >

Manage the geometry of a cell.

Template Parameters

dimension	Dimension of the manifold
d	Dimension of the cell Hold the reference element, compute the mappings and pullback between the reference element and the charts.

The class is specialize to apply some optimization when dealing with flat cells.

Constructor & Destructor Documentation

◆ dCell_map() [1/2]

template<size_t dimension, size_t d>

Manicore::dCell_map< dimension, d >::dCell_map	(	Eigen::Vector< double, dimension > const &	center_mass,
		Eigen::Matrix< double, dimension, d > const &	flat_map,
		double	diam,
		std::vector< Simplex< d >> const &	triangulation
	)

Flat constructor.

Simplify the structure when dealing with flat cells. This must be a flat surface in a chart parametrized by an affine mapping, and all its boundary element must also be flat. As an additional restriction, a flat cell can only be in a single chart

Parameters

center_mass	Centroid
flat_map	Basis of the tangent space
diam	Scaling factor to apply
triangulation	Reference element given as a collection of simplexes

◆ dCell_map() [2/2]

template<size_t dimension, size_t d>

Manicore::dCell_map< dimension, d >::dCell_map	(	std::vector< std::unique_ptr< ParametrizedMap< dimension, d >>> &	maps,
		std::vector< std::unique_ptr< ParametrizedDerivedMap< dimension, d >>> &	pullback_maps,
		std::vector< Simplex< d >> const &	triangulation
	)

General constructor.

Parameters

maps	List of the parametrization of this cell
pullback_maps	Differentials of the parametrization of this cell
triangulation	Reference element given as a collection of simplexes

Member Function Documentation

◆ evaluate_DI()

template<size_t dimension, size_t d>

Eigen::Matrix< double, dimension, d > Manicore::dCell_map< dimension, d >::evaluate_DI	(	size_t	rel_map_id,
		Eigen::Vector< double, d > const &	x
	)		const

Evaluate the differential of the parametrization.

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the reference element

◆ evaluate_DI_p()

template<size_t dimension, size_t d>

template<size_t l>

Eigen::Matrix< double, Dimension::ExtDim(l, d), Dimension::ExtDim(l, dimension)> Manicore::dCell_map< dimension, d >::evaluate_DI_p	(	size_t	rel_map_id,
		Eigen::Vector< double, d > const &	x
	)		const

Compute the action of the pullback of l-forms by the parametrization.

Template Parameters

l	Form degree

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the reference element

◆ evaluate_DJ()

template<size_t dimension, size_t d>

Eigen::Matrix< double, d, dimension > Manicore::dCell_map< dimension, d >::evaluate_DJ	(	size_t	rel_map_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

Evaluate the differential of the inverse mapping.

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the chart

◆ evaluate_DJ_p()

template<size_t dimension, size_t d>

template<size_t l>

Eigen::Matrix< double, Dimension::ExtDim(l, dimension), Dimension::ExtDim(l, d)> Manicore::dCell_map< dimension, d >::evaluate_DJ_p	(	size_t	rel_map_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

Compute the action of the pullback of l-forms by the inverse mapping.

Template Parameters

l	Form degree

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the chart

◆ evaluate_I()

template<size_t dimension, size_t d>

Eigen::Vector< double, dimension > Manicore::dCell_map< dimension, d >::evaluate_I	(	size_t	rel_map_id,
		Eigen::Vector< double, d > const &	x
	)		const

Evaluate the parametrization from the reference element to a chart.

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the reference element

◆ evaluate_J()

template<size_t dimension, size_t d>

Eigen::Vector< double, d > Manicore::dCell_map< dimension, d >::evaluate_J	(	size_t	rel_map_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

Evaluate the inverse mapping from the chart to the reference element.

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the chart

◆ evaluate_poly_on_ref()

template<size_t dimension, size_t d>

double Manicore::dCell_map< dimension, d >::evaluate_poly_on_ref	(	Eigen::Vector< double, d > const &	x,
		size_t	i_pbasis,
		int	r
	)		const

Evaluate a scalar polynomial on the reference element.

Parameters

x	Location on the reference element
i_pbasis	Index of the polynomial to evaluate
r	Polynomial basis

◆ evaluate_poly_pullback()

template<size_t dimension, size_t d>

double Manicore::dCell_map< dimension, d >::evaluate_poly_pullback	(	size_t	rel_map_id,
		Eigen::Vector< double, dimension > const &	x,
		size_t	i_pbasis,
		int	r
	)		const

Evaluate the pullback of a scalar polynomial on the chart.

Parameters

rel_map_id	Relative id of the chart to use
x	Location on the chart
i_pbasis	Index of the polynomial to evaluate
r	Polynomial basis

◆ get_orientation()

template<size_t dimension, size_t d>

int Manicore::dCell_map< dimension, d >::get_orientation	(	size_t	rel_map_id,
		Eigen::Vector< double, dimension > const &	x,
		Eigen::Matrix< double, dimension, d-1 > const &	pM
	)		const

Return the relative orientation.

Given a point on the boundary x, it attempt to find which simplex of the reference element S contains x, then compute a outward normal vector subtracting the center of S to x. The outward normal is then compared with a basis of the tangent space of the boundary to get the orientation of the boundary.

Warning: This can fail in some corner case, for example when taking x to be a vertices, or if the internal tolerance differs too much from the scaling of the element.

Parameters

rel_map_id	Relative id of the chart to use
x	Any point on the boundary in the chart (avoid vertices)
pM	Matrix of a vector basis of the tangent space of the boundary

◆ get_reference_elem()

template<size_t dimension, size_t d>

std::vector<Simplex<d> > const& Manicore::dCell_map< dimension, d >::get_reference_elem ( ) const

inline

Return the reference element as a collection of simplexes.

◆ is_flat()

template<size_t dimension, size_t d>

bool Manicore::dCell_map< dimension, d >::is_flat ( ) const

inline

Is the cell flat.

Only check that the cell was constructed with the flat constructor, does not check if the parametrization is flat

Member Data Documentation

◆ cell_dim

template<size_t dimension, size_t d>

constexpr size_t Manicore::dCell_map< dimension, d >::cell_dim = d

staticconstexpr

Dimension of the cell

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

src/Mesh/dcell.hpp

Public Member Functions

Static Public Attributes

Detailed Description

template<size_t dimension, size_t d> class Manicore::dCell_map< dimension, d >

Constructor & Destructor Documentation

◆ dCell_map() [1/2]

◆ dCell_map() [2/2]

Member Function Documentation

◆ evaluate_DI()

◆ evaluate_DI_p()

◆ evaluate_DJ()

◆ evaluate_DJ_p()

◆ evaluate_I()

◆ evaluate_J()

◆ evaluate_poly_on_ref()

◆ evaluate_poly_pullback()

◆ get_orientation()

◆ get_reference_elem()

◆ is_flat()

Member Data Documentation

◆ cell_dim

template<size_t dimension, size_t d>
class Manicore::dCell_map< dimension, d >