FESeries::Fourier< dim, spacedim > Class Template Reference

#include <deal.II/fe/fe_series.h>

Inheritance diagram for FESeries::Fourier< dim, spacedim >:

Public Types
using	CoefficientType = typename std::complex<double>

Public Member Functions
	Fourier (const std::vector< unsigned int > &n_coefficients_per_direction, const hp::FECollection< dim, spacedim > &fe_collection, const hp::QCollection< dim > &q_collection, const unsigned int component=numbers::invalid_unsigned_int)
template<typename Number >
void	calculate (const ::Vector< Number > &local_dof_values, const unsigned int cell_active_fe_index, Table< dim, CoefficientType > &fourier_coefficients)
unsigned int	get_n_coefficients_per_direction (const unsigned int index) const
void	precalculate_all_transformation_matrices ()
template<class Archive >
void	save_transformation_matrices (Archive &ar, const unsigned int version)
template<class Archive >
void	load_transformation_matrices (Archive &ar, const unsigned int version)
bool	operator== (const Fourier< dim, spacedim > &fourier) const
template<typename Number >
void	calculate (const Vector< Number > &local_dof_values, const unsigned int cell_active_fe_index, Table< dim, CoefficientType > &fourier_coefficients)
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const

Static Public Member Functions
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Private Types
using	map_value_type = decltype(counter_map)::value_type
using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

Private Attributes
const std::vector< unsigned int >	n_coefficients_per_direction
SmartPointer< const hp::FECollection< dim, spacedim > >	fe_collection
const hp::QCollection< dim >	q_collection
Table< dim, Tensor< 1, dim > >	k_vectors
std::vector< FullMatrix< CoefficientType > >	fourier_transform_matrices
std::vector< CoefficientType >	unrolled_coefficients
const unsigned int	component
std::atomic< unsigned int >	counter
std::map< std::string, unsigned int >	counter_map
std::vector< std::atomic< bool > * >	validity_pointers
const std::type_info *	object_info

Static Private Attributes
static std::mutex	mutex

Detailed Description

template<int dim, int spacedim = dim>
class FESeries::Fourier< dim, spacedim >

A class to calculate expansion of a scalar FE (or a single component of vector-valued FE) field into Fourier series on a reference element. The exponential form of the Fourier series is based on completeness and Hermitian orthogonality of the set of exponential functions \( \phi_{\bf k}({\bf x}) = \exp(2 \pi i\, {\bf k} \cdot {\bf x})\). For example in 1d the L2-orthogonality condition reads

\[ \int_0^1 \phi_k(x) \phi_l^\ast(x) dx=\delta_{kl}. \]

Note that \( \phi_{\bf k} = \phi_{-\bf k}^\ast \).

The arbitrary scalar FE field on the reference element can be expanded in the complete orthogonal exponential basis as

\[ u({\bf x}) = \sum_{\bf k} c_{\bf k} \phi_{\bf k}({\bf x}). \]

From the orthogonality property of the basis, it follows that

\[ c_{\bf k} = \int_{[0,1]^d} u({\bf x}) \phi_{\bf k}^\ast ({\bf x}) d{\bf x}\,. \]

It is this complex-valued expansion coefficients, that are calculated by this class. Note that \( u({\bf x}) = \sum_i u_i N_i({\bf x})\), where \( N_i({\bf x}) \) are real-valued FiniteElement shape functions. Consequently \( c_{\bf k} \equiv c_{-\bf k}^\ast \) and we only need to compute \( c_{\bf k} \) for positive indices \( \bf k \) .

Definition at line 89 of file fe_series.h.

Member Typedef Documentation

CoefficientType

template<int dim, int spacedim = dim>

using FESeries::Fourier< dim, spacedim >::CoefficientType = typename std::complex<double>

Definition at line 92 of file fe_series.h.

map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.h.

Constructor & Destructor Documentation

Fourier()

template<int dim, int spacedim>

FESeries::Fourier< dim, spacedim >::Fourier	(	const std::vector< unsigned int > &	n_coefficients_per_direction,
		const hp::FECollection< dim, spacedim > &	fe_collection,
		const hp::QCollection< dim > &	q_collection,
		const unsigned int	component = numbers::invalid_unsigned_int )

Constructor that initializes all required data structures.

The n_coefficients_per_direction defines the number of coefficients in each direction, fe_collection is the hp::FECollection for which expansion will be used and q_collection is the hp::QCollection used to integrate the expansion for each FiniteElement in fe_collection.

As the Fourier expansion can only be performed on scalar fields, this class does not operate on vector-valued finite elements and will therefore throw an assertion. However, each component of a finite element field can be treated as a scalar field, respectively, on which Fourier expansions are again possible. For this purpose, the optional parameter component defines which component of each FiniteElement will be used. The default value of component only applies to scalar FEs, in which case it indicates that the sole component is to be decomposed. For vector-valued FEs, a non-default value must be explicitly provided.

Definition at line 191 of file fe_series_fourier.cc.

Member Function Documentation

calculate() [1/2]

template<int dim, int spacedim = dim>

template<typename Number >

void FESeries::Fourier< dim, spacedim >::calculate	(	const ::Vector< Number > &	local_dof_values,
		const unsigned int	cell_active_fe_index,
		Table< dim, CoefficientType > &	fourier_coefficients )

Calculate fourier_coefficients of the cell vector field given by local_dof_values corresponding to FiniteElement with cell_active_fe_index .

get_n_coefficients_per_direction()

template<int dim, int spacedim>

unsigned int FESeries::Fourier< dim, spacedim >::get_n_coefficients_per_direction

(

const unsigned int

index

)

const

Return the number of coefficients in each coordinate direction for the finite element associated with index in the provided hp::FECollection.

Definition at line 266 of file fe_series_fourier.cc.

precalculate_all_transformation_matrices()

template<int dim, int spacedim>

void FESeries::Fourier< dim, spacedim >::precalculate_all_transformation_matrices

(

)

Calculate all transformation matrices to transfer the finite element solution to the series expansion representation.

These matrices will be generated on demand by calling calculate() and stored for recurring purposes. Usually, this operation consumes a lot of workload. With this function, all matrices will be calculated in advance. This way, we can separate their costly generation from the actual application.

Definition at line 245 of file fe_series_fourier.cc.

save_transformation_matrices()

template<int dim, int spacedim = dim>

template<class Archive >

void FESeries::Fourier< dim, spacedim >::save_transformation_matrices	(	Archive &	ar,
		const unsigned int	version )

Write all transformation matrices of this object to a stream for the purpose of serialization.

Since any of its transformation matrices has to be generated only once for a given scenario, it is common practice to determine them in advance calling precalculate_all_transformation_matrices() and keep them via serialization.

load_transformation_matrices()

template<int dim, int spacedim = dim>

template<class Archive >

void FESeries::Fourier< dim, spacedim >::load_transformation_matrices	(	Archive &	ar,
		const unsigned int	version )

Read all transformation matrices from a stream and recover them for this object.

operator==()

template<int dim, int spacedim>

bool FESeries::Fourier< dim, spacedim >::operator== ( const Fourier< dim, spacedim > & fourier ) const

inline

Test for equality of two series expansion objects.

Definition at line 229 of file fe_series_fourier.cc.

calculate() [2/2]

template<int dim, int spacedim = dim>

template<typename Number >

void FESeries::Fourier< dim, spacedim >::calculate	(	const Vector< Number > &	local_dof_values,
		const unsigned int	cell_active_fe_index,
		Table< dim, CoefficientType > &	fourier_coefficients )

Definition at line 277 of file fe_series_fourier.cc.

subscribe()

void Subscriptor::subscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 135 of file subscriptor.cc.

unsubscribe()

void Subscriptor::unsubscribe ( std::atomic< bool > *const validity, const std::string & identifier = "" ) const

inherited

Unsubscribes a user from the object.

Note

The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 155 of file subscriptor.cc.

n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

serialize()

template<class Archive >

void Subscriptor::serialize ( Archive & ar, const unsigned int version )

inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note

Since this function is just a consistency check it does nothing in release mode.

If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

Member Data Documentation

n_coefficients_per_direction

template<int dim, int spacedim = dim>

const std::vector<unsigned int> FESeries::Fourier< dim, spacedim >::n_coefficients_per_direction

private

Number of coefficients in each direction for each finite element in the registered hp::FECollection.

Definition at line 180 of file fe_series.h.

fe_collection

template<int dim, int spacedim = dim>

SmartPointer<const hp::FECollection<dim, spacedim> > FESeries::Fourier< dim, spacedim >::fe_collection

private

hp::FECollection for which transformation matrices will be calculated.

Definition at line 185 of file fe_series.h.

q_collection

template<int dim, int spacedim = dim>

const hp::QCollection<dim> FESeries::Fourier< dim, spacedim >::q_collection

private

hp::QCollection used in calculation of transformation matrices.

Definition at line 190 of file fe_series.h.

k_vectors

template<int dim, int spacedim = dim>

Table<dim, Tensor<1, dim> > FESeries::Fourier< dim, spacedim >::k_vectors

private

Angular frequencies \( 2 \pi {\bf k} \) .

Definition at line 195 of file fe_series.h.

fourier_transform_matrices

template<int dim, int spacedim = dim>

std::vector<FullMatrix<CoefficientType> > FESeries::Fourier< dim, spacedim >::fourier_transform_matrices

private

Transformation matrices for each FiniteElement.

Definition at line 200 of file fe_series.h.

unrolled_coefficients

template<int dim, int spacedim = dim>

std::vector<CoefficientType> FESeries::Fourier< dim, spacedim >::unrolled_coefficients

private

Auxiliary vector to store unrolled coefficients.

Definition at line 205 of file fe_series.h.

component

template<int dim, int spacedim = dim>

const unsigned int FESeries::Fourier< dim, spacedim >::component

private

Which component of FiniteElement should be used to calculate the expansion.

Definition at line 211 of file fe_series.h.

counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

---

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

• include/deal.II/fe/fe_series.h
• source/fe/fe_series_fourier.cc