Base class for finite element description. More...

#include <getfem_fem.h>

Inherits dal::static_stored_object, and enable_shared_from_this< const virtual_fem >.

Inherited by getfem::fem< base_poly >, getfem::fem< bgeot::polynomial_composite >, getfem::fem< FUNC >, getfem::fem_global_function, getfem::fem_level_set, getfem::fem_product, getfem::fem_sum, getfem::interpolated_fem, getfem::projected_fem, and getfem::torus_fem.

Public Member Functions
virtual size_type	nb_dof (size_type) const
	Number of degrees of freedom. More...

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

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

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

dim_type	dim () const
	dimension of the reference element.

dim_type	target_dim () const
	dimension of the target space.

vec_type	vectorial_type () const
	Type of vectorial element.

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

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

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

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

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

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

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

template<typename CVEC , typename VVEC >
void	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	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	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	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	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	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	grad_base_value (const base_node &x, base_tensor &t) const =0
	Give the value of all gradients (on ref. More...

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

virtual void	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	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	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	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...

Detailed Description

Base class for finite element description.

Definition at line 250 of file getfem_fem.h.

Member Function Documentation

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 291 of file getfem_fem.h.

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 340 of file getfem_fem.h.

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

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

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

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.

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.

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

Definition at line 317 of file getfem_fem.cc.

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 627 of file getfem_fem.cc.

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

src/getfem/getfem_fem.h
src/getfem_fem.cc

Public Member Functions

Detailed Description

Member Function Documentation