Main data structure for the mesh. More...

#include <mesh.hpp>

Public Member Functions
size_t	n_cells (size_t d) const
	Return the number of cell of a given dimension. More...

std::vector< size_t > const &	get_map_ids (size_t d, size_t i_cell) const
	Return the map_ids of the i_cell-th d-cell. More...

std::vector< size_t > const &	get_boundary (size_t d_boundary, size_t d, size_t i_cell) const
	Return a list filled with the global index of the elements on the boundary of the given dimension. More...

std::vector< size_t > const &	get_relative_map (size_t d_boundary, size_t d, size_t i_cell) const
	The index for the mapping (of index 0) used on the element among the mappings of the boundary. More...

size_t	global_to_local (size_t d_boundary, size_t d, size_t i_b, size_t i_cell) const
	Return the local index of the i_b d_boundary-cell with respect to the icell-th d-cell. More...

int	get_boundary_orientation (size_t d, size_t i_cell, size_t j_bd) const
	Return the relative orientation of the j-th (d-1)-boundary of the i-th d-cell. More...

Eigen::Vector3d	get_3D_embedding (size_t m_id, Eigen::Vector< double, dimension > const &x) const
	Interface to the extrinsic mapping. More...

Eigen::Matrix< double, 3, dimension >	get_3D_pushforward (size_t m_id, Eigen::Vector< double, dimension > const &x) const
	Interface to the extrinsic mapping. More...

template<size_t d>
dCell_map< dimension, d > const &	get_cell_map (size_t i) const
	Return the i-th dCell_map. More...

Eigen::Matrix< double, dimension, dimension >	metric (size_t m_id, Eigen::Vector< double, dimension > const &x) const
	Evaluate the metric (of the tangent space) More...

Eigen::Matrix< double, dimension, dimension >	metric_inv (size_t m_id, Eigen::Vector< double, dimension > const &x) const
	Evaluate the metric (of the cotangent space) More...

double	volume_form (size_t m_id, Eigen::Vector< double, dimension > const &x) const
	Evaluate the scaling factor of the volume form. More...

int	orientationTopCell (size_t i_cell) const
	Return the relative orientation of a top dimensional cell with respect to the manifold. More...

template<size_t k, int d>
Eigen::Matrix< double, Dimension::ExtDim(d-k, d), Dimension::ExtDim(k, d)>	getHodge (size_t i_cell, Eigen::Vector< double, d > const &x) const
	Evaluate the hodge star operator. More...

Detailed Description

template<size_t dimension>
class Manicore::Mesh< dimension >

Main data structure for the mesh.

The class is intended to be build with Mesh_builder, there is no public constructor.

Store a collection of dCell_graph and dCell_map and keep the shared library describing the mesh.

A dcell is a sub manifold of dimension d. It is defined by its parametrization into some reference charts. Some cells appears in several charts, hence, they have several parametrizations. The map_ids property of a cell give the id of the chart corresponding to each parametrizations (e.g. map_ids[0] is the chart corresponding to the first parametrization ...).

Template Parameters

dimension Dimension of the manifold

Member Function Documentation

◆ get_3D_embedding()

template<size_t dimension>

Eigen::Vector3d Manicore::Mesh< dimension >::get_3D_embedding	(	size_t	m_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

inline

Interface to the extrinsic mapping.

Optional function to help viewing the embedding of the manifold. This is not used in any computation and can be set freely in the mesh shared library

Parameters

m_id	Id of the embedding to use
x	Location in the chart

◆ get_3D_pushforward()

template<size_t dimension>

Eigen::Matrix<double,3,dimension> Manicore::Mesh< dimension >::get_3D_pushforward	(	size_t	m_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

inline

Interface to the extrinsic mapping.

Optional function to help viewing the embedding of the manifold. This is not used in any computation and can be set freely in the mesh shared library

Using the differential of I should always map into the correct tangent space, whereas J could introduce a deviation if it is not constant along the normal component.

Parameters

m_id	Id of the embedding to use
x	Location in the chart

◆ get_boundary()

template<size_t dimension>

std::vector<size_t> const& Manicore::Mesh< dimension >::get_boundary	(	size_t	d_boundary,
		size_t	d,
		size_t	i_cell
	)		const

inline

Return a list filled with the global index of the elements on the boundary of the given dimension.

Parameters

d_boundary	Dimension of the boundary cells
d	Dimension of the cell
i_cell	Index of the cell

◆ get_boundary_orientation()

template<size_t dimension>

int Manicore::Mesh< dimension >::get_boundary_orientation	(	size_t	d,
		size_t	i_cell,
		size_t	j_bd
	)		const

Return the relative orientation of the j-th (d-1)-boundary of the i-th d-cell.

Multiply by this factor when doing an integration on the boundary

Parameters

d	Dimension of the cell
i_cell	Index of the cell
j_bd	Relative index of the boundary cell

◆ get_cell_map()

template<size_t dimension>

template<size_t d>

dCell_map<dimension,d> const& Manicore::Mesh< dimension >::get_cell_map ( size_t i ) const

Return the i-th dCell_map.

Template Parameters

d	Dimension of the cell

◆ get_map_ids()

template<size_t dimension>

std::vector<size_t> const& Manicore::Mesh< dimension >::get_map_ids	(	size_t	d,
		size_t	i_cell
	)		const

inline

Return the map_ids of the i_cell-th d-cell.

Parameters

d	Dimension of the cell
i_cell	Index of the cell

◆ get_relative_map()

template<size_t dimension>

std::vector<size_t> const& Manicore::Mesh< dimension >::get_relative_map	(	size_t	d_boundary,
		size_t	d,
		size_t	i_cell
	)		const

inline

The index for the mapping (of index 0) used on the element among the mappings of the boundary.

The first parametrization of an element correspond to a given chart U, this function return the index of the parametrization of the element on its boundary corresponding to this chart U.

Parameters

d_boundary	Dimension of the boundary cell
d	Dimension of the cell
i_cell	Index of the cell

◆ getHodge()

template<size_t dimension>

template<size_t k, int d>

Eigen::Matrix< double, Dimension::ExtDim(d-k, d), Dimension::ExtDim(k, d)> Manicore::Mesh< dimension >::getHodge	(	size_t	i_cell,
		Eigen::Vector< double, d > const &	x
	)		const

Evaluate the hodge star operator.

Template Parameters

k	Form degree
d	Dimension of the cell

Returns: Matrix from \( \Lambda^k(\mathbb{R}^d) \) to \( \Lambda^{d-k}(\mathbb{R}^d) \)

Parameters

i_cell	Index of the cell
x	Location on the reference element of the cell

◆ global_to_local()

template<size_t dimension>

size_t Manicore::Mesh< dimension >::global_to_local	(	size_t	d_boundary,
		size_t	d,
		size_t	i_b,
		size_t	i_cell
	)		const

inline

Return the local index of the i_b d_boundary-cell with respect to the icell-th d-cell.

Search among the boundary elements of the i_cell-th d-cell for a d_boundary-cell with global index i_b. Return Mesh::get_boundary (d_boundary,d,i_cell).size() on failure (and abort when debugging).

Parameters

d_boundary	Dimension of the boundary cell
d	Dimension of the cell
i_b	Global index of the boundary cell
i_cell	Index of the cell

◆ metric()

template<size_t dimension>

Eigen::Matrix<double,dimension,dimension> Manicore::Mesh< dimension >::metric	(	size_t	m_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

inline

Evaluate the metric (of the tangent space)

Parameters

m_id	Id of the chart to use
x	Location in the chart

◆ metric_inv()

template<size_t dimension>

Eigen::Matrix<double,dimension,dimension> Manicore::Mesh< dimension >::metric_inv	(	size_t	m_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

inline

Evaluate the metric (of the cotangent space)

Parameters

m_id	Id of the chart to use
x	Location in the chart

◆ n_cells()

template<size_t dimension>

size_t Manicore::Mesh< dimension >::n_cells ( size_t d ) const

inline

Return the number of cell of a given dimension.

Parameters

d	Dimension of the cell

◆ orientationTopCell()

template<size_t dimension>

int Manicore::Mesh< dimension >::orientationTopCell ( size_t i_cell ) const

inline

Return the relative orientation of a top dimensional cell with respect to the manifold.

◆ volume_form()

template<size_t dimension>

double Manicore::Mesh< dimension >::volume_form	(	size_t	m_id,
		Eigen::Vector< double, dimension > const &	x
	)		const

inline

Evaluate the scaling factor of the volume form.

Parameters

m_id	Id of the chart to use
x	Location in the chart

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

src/Mesh/mesh.hpp

Public Member Functions

Detailed Description

template<size_t dimension> class Manicore::Mesh< dimension >

Member Function Documentation

◆ get_3D_embedding()

◆ get_3D_pushforward()

◆ get_boundary()

◆ get_boundary_orientation()

◆ get_cell_map()

◆ get_map_ids()

◆ get_relative_map()

◆ getHodge()

◆ global_to_local()

◆ metric()

◆ metric_inv()

◆ n_cells()

◆ orientationTopCell()

◆ volume_form()

template<size_t dimension>
class Manicore::Mesh< dimension >