A class implementing a 2nd order symmetric tensor. More...

#include <dune/fufem/symmetrictensor.hh>

Inheritance diagram for SymmetricTensor< dim, field_type >:

Public Types
enum	{ dimension = dim }
	dimension of Tensor More...

enum	{ rows = dim }

enum	{ cols = dim }

typedef typename Base::size_type	size_type

typedef typename Base::value_type	value_type

typedef value_type &	reference

typedef const value_type &	const_reference

typedef Traits::derived_type	derived_type

typedef FieldTraits< value_type >::field_type	field_type

typedef Traits::value_type	block_type

typedef DenseIterator< DenseVector, value_type >	Iterator

typedef Iterator	iterator

typedef DenseIterator< const DenseVector, const value_type >	ConstIterator

typedef ConstIterator	const_iterator

Public Member Functions
	SymmetricTensor (bool eye=false)
	Default constructor.

	SymmetricTensor (field_type a)
	Constructor for tensor with all entries being the same.

	SymmetricTensor (const Dune::FieldVector< field_type, dim *(dim+1)/2 > fvector)
	Construct from FieldVector of correct dimension.

field_type	operator* (const SymmetricTensor< dim, field_type > &B) const
	This is the contraction product of two tensors of 2nd stage \( E*F := E:F = \sum_{ij}(E_{ij}\cdot F_{ij}) \).

void	umv (const Dune::FieldVector< field_type, dim > &x, Dune::FieldVector< field_type, dim > &y) const
	Matrix-Vector product.

void	mv (const Dune::FieldVector< field_type, dim > &x, Dune::FieldVector< field_type, dim > &y) const
	Matrix-Vector product.

field_type &	operator() (int i, int j)
	Matrix style random read/write access to components.

const field_type &	operator() (int i, int j) const
	Matrix style random read access to components.

field_type	trace () const

void	addToDiag (field_type x)
	add constant value to the diagonal, leaving off-diagonal entries unaffected.

void	setDiag (field_type diagValue)
	set diagonal to "constant" value and zero non-diagonal entries

void	setDiag (const Dune::FieldVector< field_type, dim > &diagVector)
	set diagonal according to vector entries and zero non-diagonal entries

Dune::FieldMatrix< field_type, dim, dim >	matrix () const
	Return the FieldMatrix representation of the symmetric tensor.

	explicit (SIZE !=1) const expr FieldVector(const value_type &value) noexcept

	explicit (SIZE !=1) const expr FieldVector(const S &scalar) noexcept(std::is_nothrow_constructible_v< K, S >)

constexpr value_type &	front ()

constexpr const value_type &	front () const

constexpr value_type &	back ()

constexpr const value_type &	back () const

constexpr bool	empty () const

constexpr size_type	size () const

constexpr Iterator	begin ()

constexpr ConstIterator	begin () const

constexpr Iterator	end ()

constexpr ConstIterator	end () const

constexpr Iterator	beforeEnd ()

constexpr ConstIterator	beforeEnd () const

constexpr Iterator	beforeBegin ()

constexpr ConstIterator	beforeBegin () const

constexpr Iterator	find (size_type i)

constexpr ConstIterator	find (size_type i) const

constexpr Iterator	find (size_type i)

constexpr ConstIterator	find (size_type i) const

constexpr derived_type &	operator+= (const DenseVector< Other > &x)

constexpr std::enable_if< std::is_convertible< ValueType, value_type >::value, derived_type >::type &	operator+= (const ValueType &kk)

constexpr derived_type &	operator-= (const DenseVector< Other > &x)

constexpr std::enable_if< std::is_convertible< ValueType, value_type >::value, derived_type >::type &	operator-= (const ValueType &kk)

constexpr derived_type	operator+ (const DenseVector< Other > &b) const

constexpr derived_type	operator- (const DenseVector< Other > &b) const

constexpr derived_type	operator- () const

constexpr std::enable_if< std::is_convertible< FieldType, field_type >::value, derived_type >::type &	operator*= (const FieldType &kk)

constexpr std::enable_if< std::is_convertible< FieldType, field_type >::value, derived_type >::type &	operator/= (const FieldType &kk)

constexpr bool	operator== (const DenseVector< Other > &x) const

constexpr bool	operator!= (const DenseVector< Other > &x) const

constexpr derived_type &	axpy (const field_type &a, const DenseVector< Other > &x)

constexpr PromotionTraits< field_type, typenameDenseVector< Other >::field_type >::PromotedType	operator* (const DenseVector< Other > &x) const

constexpr PromotionTraits< field_type, typenameDenseVector< Other >::field_type >::PromotedType	dot (const DenseVector< Other > &x) const

constexpr FieldTraits< value_type >::real_type	one_norm () const

constexpr FieldTraits< value_type >::real_type	one_norm_real () const

constexpr FieldTraits< value_type >::real_type	two_norm () const

constexpr FieldTraits< value_type >::real_type	two_norm2 () const

constexpr FieldTraits< vt >::real_type	infinity_norm () const

constexpr FieldTraits< vt >::real_type	infinity_norm () const

constexpr FieldTraits< vt >::real_type	infinity_norm_real () const

constexpr FieldTraits< vt >::real_type	infinity_norm_real () const

constexpr size_type	N () const

constexpr size_type	dim () const

constexpr reference	operator[] (size_type i)

constexpr const_reference	operator[] (size_type i) const

constexpr reference	operator[] (size_type i)

constexpr const_reference	operator[] (size_type i) const

constexpr value_type &	operator[] (size_type i)

constexpr const value_type &	operator[] (size_type i) const

constexpr K *	data () noexcept

constexpr const K *	data () const noexcept

constexpr K *	data () noexcept

constexpr const K *	data () const noexcept

constexpr	operator const_reference () const noexcept

constexpr	operator const_reference () const noexcept

constexpr	operator reference () noexcept

constexpr	operator reference () noexcept

std::istream &	operator>> (std::istream &in, FieldVector< K, SIZE > &v)

std::ostream &	operator<< (std::ostream &s, const DenseVector< FieldVector< K, SIZE > > &v)

std::ostream &	operator<< (std::ostream &s, const DenseVector< V > &v)

Static Public Member Functions
static constexpr size_type	size () noexcept

static constexpr size_type	size () noexcept

Static Public Attributes
static constexpr int	blocklevel

Detailed Description

template<int dim, class field_type = double>
class SymmetricTensor< dim, field_type >

A class implementing a 2nd order symmetric tensor.

A \( dim\times dim \) tensor is stored internally as a Dune::FieldVector<field_type, dim*(dim+1)/2> For a symmetric 3x3-Tensor \( E \) the components are assumed to be stored in the order \( [ E(1,1),\ E(2,2),\ E(3,3),\ E(1,2),\ E(1,3),\ E(2,3) ]\) and analogous for other dimensions

Template Parameters

dim	number of lines/columns of tensor

Member Enumeration Documentation

◆ anonymous enum

template<int dim, class field_type = double>

anonymous enum

dimension of Tensor

Enumerator
dimension

◆ anonymous enum

template<int dim, class field_type = double>

anonymous enum

Enumerator
rows

◆ anonymous enum

template<int dim, class field_type = double>

anonymous enum

Enumerator
cols

Constructor & Destructor Documentation

◆ SymmetricTensor() [1/3]

template<int dim, class field_type = double>

SymmetricTensor< dim, field_type >::SymmetricTensor ( bool eye = false )

inline

Default constructor.

Tensor is initialized containing zeros if no argument is given.

Parameters

eye	if true tensor is initialized as identity

◆ SymmetricTensor() [2/3]

template<int dim, class field_type = double>

SymmetricTensor< dim, field_type >::SymmetricTensor ( field_type a )

inline

Constructor for tensor with all entries being the same.

Parameters

a	the value of all entries

◆ SymmetricTensor() [3/3]

template<int dim, class field_type = double>

SymmetricTensor< dim, field_type >::SymmetricTensor ( const Dune::FieldVector< field_type, dim *(dim+1)/2 > fvector )

inline

Construct from FieldVector of correct dimension.

Parameters

fvector the FieldVector of the internal representation of the symmetric tensor, For 3x3 the order in the vector is expected to be \([ E(1,1) E(2,2) E(3,3) E(1,2) E(1,3) E(2,3) ]\).

Member Function Documentation

◆ addToDiag()

template<int dim, class field_type = double>

void SymmetricTensor< dim, field_type >::addToDiag ( field_type x )

inline

add constant value to the diagonal, leaving off-diagonal entries unaffected.

◆ matrix()

template<int dim, class field_type = double>

Dune::FieldMatrix< field_type, dim, dim > SymmetricTensor< dim, field_type >::matrix ( ) const

inline

Return the FieldMatrix representation of the symmetric tensor.

◆ mv()

template<int dim, class field_type = double>

void SymmetricTensor< dim, field_type >::mv	(	const Dune::FieldVector< field_type, dim > &	x,
		Dune::FieldVector< field_type, dim > &	y
	)		const

inline

Matrix-Vector product.

This computes \( y=Ax \).

Parameters

x	the vector to multiply with
y	the result vector

◆ operator()() [1/2]

template<int dim, class field_type = double>

field_type & SymmetricTensor< dim, field_type >::operator()	(	int	i,
		int	j
	)

inline

Matrix style random read/write access to components.

Parameters

i	line index
j	column index

◆ operator()() [2/2]

template<int dim, class field_type = double>

const field_type & SymmetricTensor< dim, field_type >::operator()	(	int	i,
		int	j
	)		const

inline

Matrix style random read access to components.

Parameters

i	line index
j	column index

◆ operator*()

template<int dim, class field_type = double>

field_type SymmetricTensor< dim, field_type >::operator* ( const SymmetricTensor< dim, field_type > & B ) const

inline

This is the contraction product of two tensors of 2nd stage \( E*F := E:F = \sum_{ij}(E_{ij}\cdot F_{ij}) \).

Parameters

B	the `SymmetricTensor<dim>` to contract with

◆ setDiag() [1/2]

template<int dim, class field_type = double>

void SymmetricTensor< dim, field_type >::setDiag ( const Dune::FieldVector< field_type, dim > & diagVector )

inline

set diagonal according to vector entries and zero non-diagonal entries

Parameters

diagVector the vector storing the diagonal entries

◆ setDiag() [2/2]

template<int dim, class field_type = double>

void SymmetricTensor< dim, field_type >::setDiag ( field_type diagValue )

inline

set diagonal to "constant" value and zero non-diagonal entries

Parameters

diagValue the value the diagonal entries are to be

◆ trace()

template<int dim, class field_type = double>

field_type SymmetricTensor< dim, field_type >::trace ( ) const

inline

◆ umv()

template<int dim, class field_type = double>

void SymmetricTensor< dim, field_type >::umv	(	const Dune::FieldVector< field_type, dim > &	x,
		Dune::FieldVector< field_type, dim > &	y
	)		const

inline

Matrix-Vector product.

This computes \( y+=Ax \).

Parameters

x	the vector to multiply with
y	the vector \( Ax \) is added to

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

symmetrictensor.hh

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ SymmetricTensor() [1/3]

◆ SymmetricTensor() [2/3]

◆ SymmetricTensor() [3/3]

Member Function Documentation

◆ addToDiag()

◆ matrix()

◆ mv()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*()

◆ setDiag() [1/2]

◆ setDiag() [2/2]

◆ trace()

◆ umv()