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Reference documentation for deal.II version 9.6.0
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#include <deal.II/fe/fe_series.h>
Public Types | |
using | CoefficientType = double |
Public Member Functions | |
Legendre (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 > &legendre_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 Legendre< dim, spacedim > &legendre) const |
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 |
std::vector< FullMatrix< CoefficientType > > | legendre_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 |
A class to calculate expansion of a scalar FE (or a single component of vector-valued FE) field into series of Legendre functions on a reference element.
Legendre functions are solutions to Legendre's differential equation
\[ \frac{d}{dx}\left([1-x^2] \frac{d}{dx} P_n(x)\right) + n[n+1] P_n(x) = 0 \]
and can be expressed using Rodrigues' formula
\[ P_n(x) = \frac{1}{2^n n!} \frac{d^n}{dx^n}[x^2-1]^n. \]
These polynomials are orthogonal with respect to the \( L^2 \) inner product on the interval \( [-1;1] \)
\[ \int_{-1}^1 P_m(x) P_n(x) = \frac{2}{2n + 1} \delta_{mn} \]
and are complete. A family of \( L^2 \)-orthogonal polynomials on \( [0;1] \) can be constructed via
\[ \widetilde P_m = \sqrt{2} P_m(2x-1). \]
An arbitrary scalar FE field on the reference element \( [0;1] \) can be expanded in the complete orthogonal basis as
\[ u(x) = \sum_{m} c_m \widetilde P_{m}(x). \]
From the orthogonality property of the basis, it follows that
\[ c_m = \frac{2m+1}{2} \int_0^1 u(x) \widetilde P_m(x) dx . \]
This class calculates coefficients \( c_{\bf k} \) using \( dim \)-dimensional Legendre polynomials constructed from \( \widetilde P_m(x) \) using tensor product rule.
Definition at line 259 of file fe_series.h.
using FESeries::Legendre< dim, spacedim >::CoefficientType = double |
Definition at line 262 of file fe_series.h.
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privateinherited |
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.
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privateinherited |
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
FESeries::Legendre< dim, spacedim >::Legendre | ( | 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 Legendre 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 Legendre 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 198 of file fe_series_legendre.cc.
void FESeries::Legendre< dim, spacedim >::calculate | ( | const ::Vector< Number > & | local_dof_values, |
const unsigned int | cell_active_fe_index, | ||
Table< dim, CoefficientType > & | legendre_coefficients ) |
Calculate legendre_coefficients
of the cell vector field given by local_dof_values
corresponding to FiniteElement with cell_active_fe_index
.
Definition at line 281 of file fe_series_legendre.cc.
unsigned int FESeries::Legendre< 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 270 of file fe_series_legendre.cc.
void FESeries::Legendre< 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 250 of file fe_series_legendre.cc.
void FESeries::Legendre< 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.
void FESeries::Legendre< dim, spacedim >::load_transformation_matrices | ( | Archive & | ar, |
const unsigned int | version ) |
Read all transformation matrices from a stream and recover them for this object.
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inline |
Test for equality of two series expansion objects.
Definition at line 235 of file fe_series_legendre.cc.
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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.
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inherited |
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.
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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.
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inlineinherited |
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.
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inherited |
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.
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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.
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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.
Definition at line 52 of file subscriptor.cc.
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private |
Number of coefficients in each direction for each finite element in the registered hp::FECollection.
Definition at line 350 of file fe_series.h.
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private |
hp::FECollection for which transformation matrices will be calculated.
Definition at line 355 of file fe_series.h.
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private |
hp::QCollection used in calculation of transformation matrices.
Definition at line 360 of file fe_series.h.
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private |
Transformation matrices for each FiniteElement.
Definition at line 365 of file fe_series.h.
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private |
Auxiliary vector to store unrolled coefficients.
Definition at line 370 of file fe_series.h.
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private |
Which component of FiniteElement should be used to calculate the expansion.
Definition at line 376 of file fe_series.h.
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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.
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mutableprivateinherited |
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.
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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.
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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.
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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.