dolfinx::fem::CoordinateElement Class Reference

This class manages coordinate mappings for isoparametric cells. More...

#include <CoordinateElement.h>

Public Member Functions
	CoordinateElement (std::shared_ptr< basix::FiniteElement > element)
	Create a coordinate element from a Basix element. More...
	CoordinateElement (mesh::CellType celltype, int degree)
	Create a Lagrage coordinate element. More...
virtual	~CoordinateElement ()=default
	Destructor.
mesh::CellType	cell_shape () const
	Cell shape. More...
int	topological_dimension () const
	Return the topological dimension of the cell shape.
xt::xtensor< double, 4 >	tabulate (int n, const xt::xtensor< double, 2 > &X) const
	Compute basis values and derivatives at set of points. More...
void	compute_jacobian (const xt::xtensor< double, 4 > &dphi, const xt::xtensor< double, 2 > &cell_geometry, xt::xtensor< double, 3 > &J) const
	Compute Jacobian for a cell with given geometry using the basis functions and first order derivatives. More...
void	compute_jacobian_inverse (const xt::xtensor< double, 3 > &J, xt::xtensor< double, 3 > &K) const
	Compute the inverse of the Jacobian. If the coordinate element is affine, it computes the inverse at only one point. More...
void	compute_jacobian_determinant (const xt::xtensor< double, 3 > &J, xt::xtensor< double, 1 > &detJ) const
	Compute the determinant of the Jacobian. If the coordinate element is affine, it computes the determinant at only one point. More...
ElementDofLayout	dof_layout () const
	Return the dof layout.
void	pull_back (xt::xtensor< double, 2 > &X, xt::xtensor< double, 3 > &J, xt::xtensor< double, 1 > &detJ, xt::xtensor< double, 3 > &K, const xt::xtensor< double, 2 > &x, const xt::xtensor< double, 2 > &cell_geometry) const
	Compute reference coordinates X, and J, detJ and K for physical coordinates x.
void	permute_dofs (xtl::span< std::int32_t > dofs, const std::uint32_t cell_perm) const
	Permutes a list of DOF numbers on a cell.
void	unpermute_dofs (xtl::span< std::int32_t > dofs, const std::uint32_t cell_perm) const
	Reverses a DOF permutation.
bool	needs_permutation_data () const
	Indicates whether the coordinate map needs permutation data passing in (for higher order geometries)

Static Public Member Functions
static void	push_forward (xt::xtensor< double, 2 > &x, const xt::xtensor< double, 2 > &cell_geometry, const xt::xtensor< double, 2 > &phi)
	Compute physical coordinates x for points X in the reference configuration. More...

Public Attributes
double	non_affine_atol = 1.0e-8
	Absolute increment stopping criterium for non-affine Newton solver.
int	non_affine_max_its = 10
	Maximum number of iterations for non-affine Newton solver.

Detailed Description

This class manages coordinate mappings for isoparametric cells.

Constructor & Destructor Documentation

CoordinateElement() [1/2]

CoordinateElement::CoordinateElement ( std::shared_ptr< basix::FiniteElement >  element )

explicit

Create a coordinate element from a Basix element.

Parameters

[in]

element

Element from Basix

CoordinateElement() [2/2]

CoordinateElement::CoordinateElement	(	mesh::CellType	celltype,
		int	degree
	)

Create a Lagrage coordinate element.

Parameters

[in]	celltype	The cell shape
[in]	degree	Polynomial degree of the map

Member Function Documentation

cell_shape()

mesh::CellType CoordinateElement::cell_shape

(

)

const

Cell shape.

Returns

The cell shape

compute_jacobian()

void CoordinateElement::compute_jacobian	(	const xt::xtensor< double, 4 > &	dphi,
		const xt::xtensor< double, 2 > &	cell_geometry,
		xt::xtensor< double, 3 > &	J
	)		const

Compute Jacobian for a cell with given geometry using the basis functions and first order derivatives.

Parameters

[in]	dphi	Pre-computed first order derivatives of basis functions at set of points. The shape of dphi is (tdim, number of points, number of basis fn, 1).
[in]	cell_geometry	Coordinates/geometry
[in,out]	J	The Jacobian The shape of J is (number of points, geometric dimension, topological dimenson).

compute_jacobian_determinant()

void CoordinateElement::compute_jacobian_determinant	(	const xt::xtensor< double, 3 > &	J,
		xt::xtensor< double, 1 > &	detJ
	)		const

Compute the determinant of the Jacobian. If the coordinate element is affine, it computes the determinant at only one point.

Parameters

[in]	J	Polynomial degree of the map The shape of J is (number of points, geometric dimension, topological dimenson).
[in,out]	detJ	Jacobian The shape of detJ is (number of points)

compute_jacobian_inverse()

void CoordinateElement::compute_jacobian_inverse	(	const xt::xtensor< double, 3 > &	J,
		xt::xtensor< double, 3 > &	K
	)		const

Compute the inverse of the Jacobian. If the coordinate element is affine, it computes the inverse at only one point.

Parameters

[in]	J	The Jacobian The shape of J is (number of points, geometric dimension, topological dimenson).
[in,out]	K	The inverse of the Jacobian The shape of J is (number of points, tpological dimension, geometrical dimenson).

push_forward()

void CoordinateElement::push_forward ( xt::xtensor< double, 2 > &  x, const xt::xtensor< double, 2 > &  cell_geometry, const xt::xtensor< double, 2 > &  phi  )

static

Compute physical coordinates x for points X in the reference configuration.

Parameters

[in,out]	x	The physical coordinates of the reference points X
[in]	cell_geometry	The cell node coordinates (physical)
[in]	phi	Tabulated basis functions at reference points X

tabulate()

xt::xtensor< double, 4 > CoordinateElement::tabulate	(	int	n,
		const xt::xtensor< double, 2 > &	X
	)		const

Compute basis values and derivatives at set of points.

Parameters

[in]	n	The order of derivatives, up to and including, to compute. Use 0 for the basis functions only.
[in]	X	The points at which to compute the basis functions. The shape of x is (number of points, geometric dimension).

Returns

The basis functions (and derivatives). The shape is (derivative, number point, number of basis fn, value size).

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

• /__w/dolfinx/dolfinx/cpp/dolfinx/fem/CoordinateElement.h
• /__w/dolfinx/dolfinx/cpp/dolfinx/fem/CoordinateElement.cpp