Classes
class	getfem::virtual_fem
	Base class for finite element description. More...

class	getfem::fem< FUNC >
	virtual_fem implementation as a vector of generic functions. More...

class	getfem::fem_precomp_
	Pre-computations on a fem (given a fixed set of points on the reference convex, this object computes the value/gradient/hessian of all base functions on this set of points and stores them. More...

class	getfem::fem_precomp_pool
	handle a pool (i.e. More...

class	getfem::fem_interpolation_context
	structure passed as the argument of fem interpolation functions. More...

Typedefs
typedef std::shared_ptr< const getfem::virtual_fem >	getfem::pfem
	type of pointer on a fem description More...

Functions
virtual size_type	getfem::virtual_fem::nb_dof (size_type) const
	Number of degrees of freedom. More...

virtual size_type	getfem::virtual_fem::nb_base (size_type cv) const
	Number of basis functions.

size_type	getfem::virtual_fem::nb_base_components (size_type cv) const
	Number of components (nb_dof() * dimension of the target space).

const std::vector< pdof_description > &	getfem::virtual_fem::dof_types () const
	Get the array of pointer on dof description.

dim_type	getfem::virtual_fem::dim () const
	dimension of the reference element.

dim_type	getfem::virtual_fem::target_dim () const
	dimension of the target space.

vec_type	getfem::virtual_fem::vectorial_type () const
	Type of vectorial element.

virtual bgeot::pconvex_ref	getfem::virtual_fem::ref_convex (size_type) const
	Return the convex of the reference element.

bgeot::pconvex_structure	getfem::virtual_fem::basic_structure (size_type cv) const
	Gives the convex of the reference element.

virtual const bgeot::convex< base_node > &	getfem::virtual_fem::node_convex (size_type) const
	Gives the convex representing the nodes on the reference element.

bgeot::pconvex_structure	getfem::virtual_fem::structure (size_type cv) const
	Gives the convex structure of the reference element nodes.

const base_node &	getfem::virtual_fem::node_of_dof (size_type cv, size_type i) const
	Gives the node corresponding to the dof i. More...

bool	getfem::virtual_fem::is_lagrange () const
	true if the base functions are such that $\varphi_i(\textrm{node\_of\_dof(j)}) = \delta_{ij}$

bool	getfem::virtual_fem::is_polynomial () const
	true if the base functions are polynomials

template<typename CVEC , typename VVEC >
void	getfem::virtual_fem::interpolation (const fem_interpolation_context &c, const CVEC &coeff, VVEC &val, dim_type Qdim) const
	Interpolate at an arbitrary point x given on the reference element. More...

template<typename MAT >
void	getfem::virtual_fem::interpolation (const fem_interpolation_context &c, MAT &M, dim_type Qdim) const
	Build the interpolation matrix for the interpolation at a fixed point x, given on the reference element. More...

template<typename CVEC , typename VMAT >
void	getfem::virtual_fem::interpolation_grad (const fem_interpolation_context &c, const CVEC &coeff, VMAT &val, dim_type Qdim=1) const
	Interpolation of the gradient. More...

template<typename CVEC , typename VMAT >
void	getfem::virtual_fem::interpolation_hess (const fem_interpolation_context &c, const CVEC &coeff, VMAT &val, dim_type Qdim) const
	Interpolation of the hessian. More...

template<typename CVEC >
void	getfem::virtual_fem::interpolation_diverg (const fem_interpolation_context &c, const CVEC &coeff, typename gmm::linalg_traits< CVEC >::value_type &val) const
	Interpolation of the divergence. More...

virtual void	getfem::virtual_fem::base_value (const base_node &x, base_tensor &t) const =0
	Give the value of all components of the base functions at the point x of the reference element. More...

virtual void	getfem::virtual_fem::grad_base_value (const base_node &x, base_tensor &t) const =0
	Give the value of all gradients (on ref. More...

virtual void	getfem::virtual_fem::hess_base_value (const base_node &x, base_tensor &t) const =0
	Give the value of all hessians (on ref. More...

virtual void	getfem::virtual_fem::real_base_value (const fem_interpolation_context &c, base_tensor &t, bool withM=true) const
	Give the value of all components of the base functions at the current point of the fem_interpolation_context. More...

virtual void	getfem::virtual_fem::real_grad_base_value (const fem_interpolation_context &c, base_tensor &t, bool withM=true) const
	Give the gradient of all components of the base functions at the current point of the fem_interpolation_context. More...

virtual void	getfem::virtual_fem::real_hess_base_value (const fem_interpolation_context &c, base_tensor &t, bool withM=true) const
	Give the hessian of all components of the base functions at the current point of the fem_interpolation_context. More...

void	getfem::virtual_fem::add_node (const pdof_description &d, const base_node &pt, const dal::bit_vector &faces)
	internal function adding a node to an element for the creation of a finite element method. More...

const std::vector< FUNC > &	getfem::fem< FUNC >::base () const
	Gives the array of basic functions (components).

void	getfem::fem< FUNC >::base_value (const base_node &x, base_tensor &t) const
	Evaluates at point x, all base functions and returns the result in t(nb_base,target_dim)

void	getfem::fem< FUNC >::grad_base_value (const base_node &x, base_tensor &t) const
	Evaluates at point x, the gradient of all base functions w.r.t. More...

void	getfem::fem< FUNC >::hess_base_value (const base_node &x, base_tensor &t) const
	Evaluates at point x, the hessian of all base functions w.r.t. More...

pfem	getfem::classical_fem (bgeot::pgeometric_trans pgt, short_type k, bool complete=false)
	Give a pointer on the structures describing the classical polynomial fem of degree k on a given convex type. More...

pfem	getfem::classical_discontinuous_fem (bgeot::pgeometric_trans pg, short_type k, scalar_type alpha=0, bool complete=false)
	Give a pointer on the structures describing the classical polynomial discontinuous fem of degree k on a given convex type. More...

pfem	getfem::fem_descriptor (const std::string &name)
	get a fem descriptor from its string name.

std::string	getfem::name_of_fem (pfem p)
	get the string name of a fem descriptor.

const base_tensor &	getfem::fem_precomp_::val (size_type i) const
	returns values of the base functions

const base_tensor &	getfem::fem_precomp_::grad (size_type i) const
	returns gradients of the base functions

const base_tensor &	getfem::fem_precomp_::hess (size_type i) const
	returns hessians of the base functions

pfem_precomp	getfem::fem_precomp (pfem pf, bgeot::pstored_point_tab pspt, dal::pstatic_stored_object dep)
	Handles precomputations for FEM. More...

void	getfem::delete_fem_precomp (pfem_precomp pfp)
	Request for the removal of a pfem_precomp.

pfem_precomp	getfem::fem_precomp_pool::operator() (pfem pf, bgeot::pstored_point_tab pspt)
	Request a pfem_precomp. More...

bool	getfem::fem_interpolation_context::have_pfp () const
	true if a fem_precomp_ has been supplied.

bool	getfem::fem_interpolation_context::have_pf () const
	true if the pfem is available.

const base_matrix &	getfem::fem_interpolation_context::M () const
	non tau-equivalent transformation matrix.

void	getfem::fem_interpolation_context::base_value (base_tensor &t, bool withM=true) const
	fill the tensor with the values of the base functions (taken at point `this->xref()`)

void	getfem::fem_interpolation_context::grad_base_value (base_tensor &t, bool withM=true) const
	fill the tensor with the gradient of the base functions (taken at point `this->xref()`)

void	getfem::fem_interpolation_context::hess_base_value (base_tensor &t, bool withM=true) const
	fill the tensor with the hessian of the base functions (taken at point `this->xref()`)

const pfem	getfem::fem_interpolation_context::pf () const
	get the current FEM descriptor

size_type	getfem::fem_interpolation_context::convex_num () const
	get the current convex number

void	getfem::fem_interpolation_context::set_face_num (short_type f)
	set the current face number

short_type	getfem::fem_interpolation_context::face_num () const
	get the current face number

bool	getfem::fem_interpolation_context::is_on_face () const
	On a face ?

pfem_precomp	getfem::fem_interpolation_context::pfp () const
	get the current fem_precomp_

pfem	getfem::interior_fem_of_hho_method (pfem hho_method)
	Specific function for a HHO method to obtain the method in the interior. More...

Variables
const typedef fem< bgeot::base_poly > *	getfem::ppolyfem
	Classical polynomial FEM.

const typedef fem< bgeot::polynomial_composite > *	getfem::ppolycompfem
	Polynomial composite FEM.

const typedef fem< bgeot::base_rational_fraction > *	getfem::prationalfracfem
	Rational fration FEM.

Detailed Description

Typedef Documentation

◆ pfem

typedef std::shared_ptr<const getfem::virtual_fem> getfem::pfem

type of pointer on a fem description

See also: getfem::virtual_fem

Definition at line 244 of file getfem_fem.h.

Function Documentation

◆ nb_dof()

virtual size_type getfem::virtual_fem::nb_dof ( size_type ) const

inlinevirtual

Number of degrees of freedom.

Parameters

cv	the convex number for this FEM. This information is rarely used, but is needed by some "special" FEMs, such as getfem::interpolated_fem.

Reimplemented in getfem::interpolated_fem, getfem::projected_fem, and getfem::fem_global_function.

Definition at line 296 of file getfem_fem.h.

◆ node_of_dof()

const base_node& getfem::virtual_fem::node_of_dof	(	size_type	cv,
		size_type	i
	)		const

inline

Gives the node corresponding to the dof i.

Parameters

cv	the convex number for this FEM. This information is rarely used, by is needed by some "special" FEMs, such as getfem::interpolated_fem.
i	the local dof number (`i < nb_dof(cv)`)

Definition at line 345 of file getfem_fem.h.

◆ interpolation() [1/2]

template<typename CVEC , typename VVEC >

void getfem::virtual_fem::interpolation	(	const fem_interpolation_context &	c,
		const CVEC &	coeff,
		VVEC &	val,
		dim_type	Qdim
	)		const

Interpolate at an arbitrary point x given on the reference element.

Parameters

c	the fem_interpolation_context, should have been suitably initialized for the point of evaluation.
coeff	is the vector of coefficient relatively to the base functions, its length should be `Qdim*this->nb_dof()`.
val	contains the interpolated value, on output (its size should be `Qdim*this->target_dim()`).
Qdim	is the optional Q dimension, if the FEM is considered as a "vectorized" one.

Definition at line 858 of file getfem_fem.h.

◆ interpolation() [2/2]

template<typename MAT >

void getfem::virtual_fem::interpolation	(	const fem_interpolation_context &	c,
		MAT &	M,
		dim_type	Qdim
	)		const

Build the interpolation matrix for the interpolation at a fixed point x, given on the reference element.

The matrix M is filled, such that for a given coeff vector, the interpolation is given by M*coeff.

Definition at line 880 of file getfem_fem.h.

◆ interpolation_grad()

template<typename CVEC , typename VMAT >

void getfem::virtual_fem::interpolation_grad	(	const fem_interpolation_context &	c,
		const CVEC &	coeff,
		VMAT &	val,
		dim_type	Qdim = `1`
	)		const

Interpolation of the gradient.

The output is stored in the $Q\times N$ matrix val.

Definition at line 902 of file getfem_fem.h.

◆ interpolation_hess()

template<typename CVEC , typename VMAT >

void getfem::virtual_fem::interpolation_hess	(	const fem_interpolation_context &	c,
		const CVEC &	coeff,
		VMAT &	val,
		dim_type	Qdim
	)		const

Interpolation of the hessian.

The output is stored in the $Q\times (N^2)$ matrix val.

Definition at line 929 of file getfem_fem.h.

◆ interpolation_diverg()

template<typename CVEC >

void getfem::virtual_fem::interpolation_diverg	(	const fem_interpolation_context &	c,
		const CVEC &	coeff,
		typename gmm::linalg_traits< CVEC >::value_type &	val
	)		const

Interpolation of the divergence.

The output is stored in the scalar val.

Definition at line 957 of file getfem_fem.h.

◆ base_value()

virtual void getfem::virtual_fem::base_value	(	const base_node &	x,
		base_tensor &	t
	)		const

pure virtual

Give the value of all components of the base functions at the point x of the reference element.

Basic function used essentially by fem_precomp.

Implemented in getfem::fem< FUNC >, getfem::fem< base_poly >, getfem::fem< bgeot::polynomial_composite >, getfem::fem_level_set, getfem::interpolated_fem, getfem::projected_fem, getfem::fem_global_function, and getfem::torus_fem.

◆ grad_base_value() [1/2]

virtual void getfem::virtual_fem::grad_base_value	(	const base_node &	x,
		base_tensor &	t
	)		const

pure virtual

Give the value of all gradients (on ref.

element) of the components of the base functions at the point x of the reference element. Basic function used essentially by fem_precomp.

Implemented in getfem::fem< FUNC >, getfem::fem< base_poly >, getfem::fem< bgeot::polynomial_composite >, getfem::fem_level_set, getfem::interpolated_fem, getfem::projected_fem, getfem::fem_global_function, and getfem::torus_fem.

◆ hess_base_value() [1/2]

virtual void getfem::virtual_fem::hess_base_value	(	const base_node &	x,
		base_tensor &	t
	)		const

pure virtual

Give the value of all hessians (on ref.

element) of the components of the base functions at the point x of the reference element. Basic function used essentially by fem_precomp.

Implemented in getfem::fem< FUNC >, getfem::fem< base_poly >, getfem::fem< bgeot::polynomial_composite >, getfem::fem_level_set, getfem::interpolated_fem, getfem::projected_fem, getfem::fem_global_function, and getfem::torus_fem.

◆ real_base_value()

void getfem::virtual_fem::real_base_value	(	const fem_interpolation_context &	c,
		base_tensor &	t,
		bool	withM = `true`
	)		const

virtual

Give the value of all components of the base functions at the current point of the fem_interpolation_context.

Used by elementary computations. if withM is false the matrix M for non tau-equivalent elements is not taken into account.

Reimplemented in getfem::interpolated_fem, getfem::projected_fem, getfem::fem_level_set, getfem::fem_global_function, and getfem::torus_fem.

Definition at line 309 of file getfem_fem.cc.

◆ real_grad_base_value()

void getfem::virtual_fem::real_grad_base_value	(	const fem_interpolation_context &	c,
		base_tensor &	t,
		bool	withM = `true`
	)		const

virtual

Give the gradient of all components of the base functions at the current point of the fem_interpolation_context.

Used by elementary computations. if withM is false the matrix M for non tau-equivalent elements is not taken into account.

Reimplemented in getfem::interpolated_fem, getfem::projected_fem, getfem::fem_level_set, getfem::fem_global_function, and getfem::torus_fem.

Definition at line 313 of file getfem_fem.cc.

◆ real_hess_base_value()

void getfem::virtual_fem::real_hess_base_value	(	const fem_interpolation_context &	c,
		base_tensor &	t,
		bool	withM = `true`
	)		const

virtual

Give the hessian of all components of the base functions at the current point of the fem_interpolation_context.

Used by elementary computations. if withM is false the matrix M for non tau-equivalent elements is not taken into account.

Reimplemented in getfem::fem_level_set, getfem::interpolated_fem, getfem::projected_fem, getfem::fem_global_function, and getfem::torus_fem.

Definition at line 317 of file getfem_fem.cc.

◆ add_node()

void getfem::virtual_fem::add_node	(	const pdof_description &	d,
		const base_node &	pt,
		const dal::bit_vector &	faces
	)

internal function adding a node to an element for the creation of a finite element method.

Important : the faces should be the faces on which the corresponding base function is non zero.

Definition at line 648 of file getfem_fem.cc.

◆ grad_base_value() [2/2]

template<class FUNC >

void getfem::fem< FUNC >::grad_base_value	(	const base_node &	x,
		base_tensor &	t
	)		const

inlinevirtual

Evaluates at point x, the gradient of all base functions w.r.t.

the reference element directions 0,..,dim-1 and returns the result in t(nb_base,target_dim,dim)

Implements getfem::virtual_fem.

Definition at line 566 of file getfem_fem.h.

◆ hess_base_value() [2/2]

template<class FUNC >

void getfem::fem< FUNC >::hess_base_value	(	const base_node &	x,
		base_tensor &	t
	)		const

inlinevirtual

Evaluates at point x, the hessian of all base functions w.r.t.

the reference element directions 0,..,dim-1 and returns the result in t(nb_base,target_dim,dim,dim)

Implements getfem::virtual_fem.

Definition at line 581 of file getfem_fem.h.

◆ classical_fem()

pfem getfem::classical_fem	(	bgeot::pgeometric_trans	pgt,
		short_type	k,
		bool	complete = `false`
	)

Give a pointer on the structures describing the classical polynomial fem of degree k on a given convex type.

Parameters

pgt	the geometric transformation (which defines the convex type).
k	the degree of the fem.
complete	a flag which requests complete Langrange polynomial elements even if the provided pgt is an incomplete one (e.g. 8-node quadrilateral or 20-node hexahedral).

Returns: a ppolyfem.

Definition at line 4141 of file getfem_fem.cc.

◆ classical_discontinuous_fem()

pfem getfem::classical_discontinuous_fem	(	bgeot::pgeometric_trans	pg,
		short_type	k,
		scalar_type	alpha = `0`,
		bool	complete = `false`
	)

Give a pointer on the structures describing the classical polynomial discontinuous fem of degree k on a given convex type.

Parameters

pgt	the geometric transformation (which defines the convex type).
k	the degree of the fem.
alpha	the "inset" factor for the dof nodes: with alpha = 0, the nodes are located as usual (i.e. with node on the convex border), and for 0 < alpha < 1, they converge to the center of gravity of the convex.
complete	a flag which requests complete Langrange polynomial elements even if the provided pgt is an incomplete one (e.g. 8-node quadrilateral or 20-node hexahedral).

Returns: a ppolyfem.

Definition at line 4146 of file getfem_fem.cc.

◆ fem_precomp()

pfem_precomp getfem::fem_precomp	(	pfem	pf,
		bgeot::pstored_point_tab	pspt,
		dal::pstatic_stored_object	dep
	)

Handles precomputations for FEM.

statically allocates a fem-precomputation object, and returns a pointer to it. The fem_precomp_ objects are "cached", i.e. they are stored in a global pool and if this function is called two times with the same arguments, a pointer to the same object will be returned.

Parameters

pf	a pointer to the fem object.
pspt	a pointer to a list of points in the reference convex.CAUTION: this array must not be destroyed as long as the fem_precomp is used!!.

Moreover pspt is supposed to identify uniquely the set of points. This means that you should NOT alter its content at any time after using this function.

If you need a set of "temporary" getfem::fem_precomp_, create them via a getfem::fem_precomp_pool structure. All memory will be freed when this structure will be destroyed.

Definition at line 4333 of file getfem_fem.cc.

◆ operator()()

pfem_precomp getfem::fem_precomp_pool::operator()	(	pfem	pf,
		bgeot::pstored_point_tab	pspt
	)

inline

Request a pfem_precomp.

If not already in the pool, the pfem_precomp is computed, and added to the pool.

Parameters

pf	a pointer to the fem object.
pspt	a pointer to a list of points in the reference convex.

CAUTION: this array must not be destroyed as long as the fem_precomp is used!!

Moreover pspt is supposed to identify uniquely the set of points. This means that you should NOT alter its content until the fem_precomp_pool is destroyed.

Definition at line 735 of file getfem_fem.h.

◆ interior_fem_of_hho_method()

pfem getfem::interior_fem_of_hho_method ( pfem hho_method )

Specific function for a HHO method to obtain the method in the interior.

If the method is not of composite type, return the argument.

Definition at line 866 of file getfem_fem_composite.cc.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ pfem

Function Documentation

◆ nb_dof()

◆ node_of_dof()

◆ interpolation() [1/2]

◆ interpolation() [2/2]

◆ interpolation_grad()

◆ interpolation_hess()

◆ interpolation_diverg()

◆ base_value()

◆ grad_base_value() [1/2]

◆ hess_base_value() [1/2]

◆ real_base_value()

◆ real_grad_base_value()

◆ real_hess_base_value()

◆ add_node()

◆ grad_base_value() [2/2]

◆ hess_base_value() [2/2]

◆ classical_fem()

◆ classical_discontinuous_fem()

◆ fem_precomp()

◆ operator()()

◆ interior_fem_of_hho_method()