Reference documentation for deal.II version Git f09805cc1d 2021-10-18 06:49:49 +0200
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Public Types | Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | Protected Attributes | Private Member Functions | Private Attributes | Static Private Attributes | List of all members
Functions::StokesLSingularity Class Referenceabstract

#include <deal.II/base/flow_function.h>

Inheritance diagram for Functions::StokesLSingularity:
[legend]

Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type
 

Public Member Functions

 StokesLSingularity ()
 Constructor setting up some data. More...
 
virtual void vector_values (const std::vector< Point< 2 >> &points, std::vector< std::vector< double >> &values) const override
 
virtual void vector_gradients (const std::vector< Point< 2 >> &points, std::vector< std::vector< Tensor< 1, 2 >>> &gradients) const override
 
virtual void vector_laplacians (const std::vector< Point< 2 >> &points, std::vector< std::vector< double >> &values) const override
 
void pressure_adjustment (double p)
 
virtual void vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const override=0
 
virtual void vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim >>> &gradients) const override=0
 
virtual void vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const
 
virtual void vector_laplacians (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const=0
 
virtual void vector_value (const Point< dim > &points, Vector< double > &value) const override
 
virtual double value (const Point< dim > &points, const unsigned int component) const override
 
virtual void vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const override
 
virtual void vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim >>> &gradients) const override
 
virtual void vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const
 
virtual void vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const override
 
virtual std::size_t memory_consumption () const override
 
virtual void value_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const
 
virtual Tensor< 1, dim, doublegradient (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double >> &gradients) const
 
virtual void gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, double >> &gradients, const unsigned int component=0) const
 
virtual double laplacian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_laplacian (const Point< dim > &p, Vector< double > &values) const
 
virtual void laplacian_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const
 
virtual SymmetricTensor< 2, dim, doublehessian (const Point< dim > &p, const unsigned int component=0) const
 
virtual void vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, double >> &values) const
 
virtual void hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, double >> &values, const unsigned int component=0) const
 
virtual void vector_hessian_list (const std::vector< Point< dim >> &points, std::vector< std::vector< SymmetricTensor< 2, dim, double >>> &values) const
 
Number get_time () const
 
virtual void set_time (const Number new_time)
 
virtual void advance_time (const Number delta_t)
 
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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Public Attributes

const unsigned int n_components
 

Static Public Attributes

static const unsigned int dimension
 

Protected Attributes

double mean_pressure
 

Private Member Functions

double Psi (double phi) const
 The auxiliary function Psi. More...
 
double Psi_1 (double phi) const
 The derivative of Psi() More...
 
double Psi_2 (double phi) const
 The 2nd derivative of Psi() More...
 
double Psi_3 (double phi) const
 The 3rd derivative of Psi() More...
 
double Psi_4 (double phi) const
 The 4th derivative of Psi() More...
 

Private Attributes

const double omega
 The angle of the reentrant corner, set to 3*pi/2. More...
 
const double coslo
 Cosine of lambda times omega. More...
 
const double lp
 Auxiliary variable 1+lambda. More...
 
const double lm
 Auxiliary variable 1-lambda. More...
 

Static Private Attributes

static const double lambda = 0.54448373678246
 

Detailed Description

A singular solution to Stokes' equations on a 2d L-shaped domain.

This function satisfies \(-\triangle \mathbf{u} + \nabla p = 0\) and represents a typical singular solution around a reentrant corner of an L-shaped domain that can be created using GridGenerator::hyper_L(). The velocity vanishes on the two faces of the re-entrant corner and \(\nabla\mathbf{u}\) and \(p\) are singular at the origin while they are smooth in the rest of the domain because they can be written as a product of a smooth function and the term \(r^{\lambda-1}\) where \(r\) is the radius and \(\lambda \approx 0.54448\) is a fixed parameter.

Taken from Houston, Schötzau, Wihler, proceeding ENUMATH 2003.

Definition at line 246 of file flow_function.h.

Member Typedef Documentation

◆ time_type

using Function< dim, double >::time_type = typename FunctionTime< typename numbers::NumberTraits<double >::real_type>::time_type
inherited

The scalar-valued real type used for representing time.

Definition at line 170 of file function.h.

Constructor & Destructor Documentation

◆ StokesLSingularity()

Functions::StokesLSingularity::StokesLSingularity ( )

Constructor setting up some data.

Definition at line 496 of file flow_function.cc.

Member Function Documentation

◆ vector_values() [1/2]

void Functions::StokesLSingularity::vector_values ( const std::vector< Point< 2 >> &  points,
std::vector< std::vector< double >> &  values 
) const
overridevirtual

Definition at line 549 of file flow_function.cc.

◆ vector_gradients() [1/3]

void Functions::StokesLSingularity::vector_gradients ( const std::vector< Point< 2 >> &  points,
std::vector< std::vector< Tensor< 1, 2 >>> &  gradients 
) const
overridevirtual

Definition at line 589 of file flow_function.cc.

◆ vector_laplacians() [1/2]

void Functions::StokesLSingularity::vector_laplacians ( const std::vector< Point< 2 >> &  points,
std::vector< std::vector< double >> &  values 
) const
overridevirtual

Definition at line 649 of file flow_function.cc.

◆ Psi()

double Functions::StokesLSingularity::Psi ( double  phi) const
inlineprivate

The auxiliary function Psi.

Definition at line 505 of file flow_function.cc.

◆ Psi_1()

double Functions::StokesLSingularity::Psi_1 ( double  phi) const
inlineprivate

The derivative of Psi()

Definition at line 513 of file flow_function.cc.

◆ Psi_2()

double Functions::StokesLSingularity::Psi_2 ( double  phi) const
inlineprivate

The 2nd derivative of Psi()

Definition at line 521 of file flow_function.cc.

◆ Psi_3()

double Functions::StokesLSingularity::Psi_3 ( double  phi) const
inlineprivate

The 3rd derivative of Psi()

Definition at line 529 of file flow_function.cc.

◆ Psi_4()

double Functions::StokesLSingularity::Psi_4 ( double  phi) const
inlineprivate

The 4th derivative of Psi()

Definition at line 539 of file flow_function.cc.

◆ pressure_adjustment()

void Functions::FlowFunction< dim >::pressure_adjustment ( double  p)
inherited

Store an adjustment for the pressure function, such that its mean value is p.

Definition at line 42 of file flow_function.cc.

◆ vector_values() [2/2]

virtual void Functions::FlowFunction< dim >::vector_values ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< double >> &  values 
) const
overridepure virtualinherited

Values in a structure more suitable for vector valued functions. The outer vector is indexed by solution component, the inner by quadrature point.

Reimplemented from Function< dim >.

◆ vector_gradients() [2/3]

virtual void Functions::FlowFunction< dim >::vector_gradients ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim >>> &  gradients 
) const
overridepure virtualinherited

Gradients in a structure more suitable for vector valued functions. The outer vector is indexed by solution component, the inner by quadrature point.

◆ vector_gradients() [3/3]

virtual void Function< dim, double >::vector_gradients ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim, double >>> &  gradients 
) const
virtualinherited

For each component of the function, fill a vector of gradient values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

◆ vector_laplacians() [2/2]

virtual void Functions::FlowFunction< dim >::vector_laplacians ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< double >> &  values 
) const
pure virtualinherited

Force terms in a structure more suitable for vector valued functions. The outer vector is indexed by solution component, the inner by quadrature point.

Warning
This is not the true Laplacian, but the force term to be used as right hand side in Stokes' equations

◆ vector_value()

void Functions::FlowFunction< dim >::vector_value ( const Point< dim > &  points,
Vector< double > &  value 
) const
overridevirtualinherited

Return all components of a vector-valued function at a given point.

values shall have the right size beforehand, i.e. n_components.

The default implementation will call value() for each component.

Reimplemented from Function< dim >.

Definition at line 78 of file flow_function.cc.

◆ value()

double Functions::FlowFunction< dim >::value ( const Point< dim > &  points,
const unsigned int  component 
) const
overridevirtualinherited

Return the value of the function at the given point. Unless there is only one component (i.e. the function is scalar), you should state the component you want to have evaluated; it defaults to zero, i.e. the first component.

Reimplemented from Function< dim >.

Definition at line 103 of file flow_function.cc.

◆ vector_value_list()

void Functions::FlowFunction< dim >::vector_value_list ( const std::vector< Point< dim >> &  points,
std::vector< Vector< double >> &  values 
) const
overridevirtualinherited

Set values to the point values of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array, and that all elements be vectors with the same number of components as this function has.

By default, this function repeatedly calls vector_value() for each point separately, to fill the output array.

Reimplemented from Function< dim >.

Definition at line 50 of file flow_function.cc.

◆ vector_gradient_list() [1/2]

void Functions::FlowFunction< dim >::vector_gradient_list ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim >>> &  gradients 
) const
overridevirtualinherited

Definition at line 125 of file flow_function.cc.

◆ vector_gradient_list() [2/2]

virtual void Function< dim, double >::vector_gradient_list ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< Tensor< 1, dim, double >>> &  gradients 
) const
virtualinherited

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

◆ vector_laplacian_list()

void Functions::FlowFunction< dim >::vector_laplacian_list ( const std::vector< Point< dim >> &  points,
std::vector< Vector< double >> &  values 
) const
overridevirtualinherited

The force term in the momentum equation.

Reimplemented from Function< dim >.

Definition at line 153 of file flow_function.cc.

◆ memory_consumption()

std::size_t Functions::FlowFunction< dim >::memory_consumption ( ) const
overridevirtualinherited

Return an estimate for the memory consumption, in bytes, of this object.

Reimplemented from Function< dim >.

Definition at line 181 of file flow_function.cc.

◆ value_list()

virtual void Function< dim, double >::value_list ( const std::vector< Point< dim >> &  points,
std::vector< double > &  values,
const unsigned int  component = 0 
) const
virtualinherited

Set values to the point values of the specified component of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array.

By default, this function repeatedly calls value() for each point separately, to fill the output array.

Reimplemented in Functions::Polynomial< dim >, Functions::CutOffFunctionCinfty< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionW1< dim >, Functions::CutOffFunctionLinfty< dim >, Functions::JumpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::ExpFunction< dim >, Functions::CosineGradFunction< dim >, Functions::CosineFunction< dim >, Functions::PillowFunction< dim >, Functions::Q1WedgeFunction< dim >, FunctionDerivative< dim >, Functions::SquareFunction< dim >, and Functions::Bessel1< dim >.

◆ gradient()

virtual Tensor<1, dim, double > Function< dim, double >::gradient ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_gradient()

virtual void Function< dim, double >::vector_gradient ( const Point< dim > &  p,
std::vector< Tensor< 1, dim, double >> &  gradients 
) const
virtualinherited

Return the gradient of all components of the function at the given point.

◆ gradient_list()

virtual void Function< dim, double >::gradient_list ( const std::vector< Point< dim >> &  points,
std::vector< Tensor< 1, dim, double >> &  gradients,
const unsigned int  component = 0 
) const
virtualinherited

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

◆ laplacian()

virtual double Function< dim, double >::laplacian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

◆ vector_laplacian()

virtual void Function< dim, double >::vector_laplacian ( const Point< dim > &  p,
Vector< double > &  values 
) const
virtualinherited

Compute the Laplacian of all components at point p and store them in values.

◆ laplacian_list()

virtual void Function< dim, double >::laplacian_list ( const std::vector< Point< dim >> &  points,
std::vector< double > &  values,
const unsigned int  component = 0 
) const
virtualinherited

◆ hessian()

virtual SymmetricTensor<2, dim, double > Function< dim, double >::hessian ( const Point< dim > &  p,
const unsigned int  component = 0 
) const
virtualinherited

Compute the Hessian of a given component at point p, that is the gradient of the gradient of the function.

Reimplemented in Functions::CosineFunction< dim >, Functions::LevelSet::Plane< dim >, Functions::CSpline< dim >, Functions::Spherical< dim >, Functions::LevelSet::Sphere< dim >, and Functions::CoordinateRestriction< dim >.

◆ vector_hessian()

virtual void Function< dim, double >::vector_hessian ( const Point< dim > &  p,
std::vector< SymmetricTensor< 2, dim, double >> &  values 
) const
virtualinherited

Compute the Hessian of all components at point p and store them in values.

◆ hessian_list()

virtual void Function< dim, double >::hessian_list ( const std::vector< Point< dim >> &  points,
std::vector< SymmetricTensor< 2, dim, double >> &  values,
const unsigned int  component = 0 
) const
virtualinherited

Compute the Hessian of one component at a set of points.

◆ vector_hessian_list()

virtual void Function< dim, double >::vector_hessian_list ( const std::vector< Point< dim >> &  points,
std::vector< std::vector< SymmetricTensor< 2, dim, double >>> &  values 
) const
virtualinherited

Compute the Hessians of all components at a set of points.

◆ get_time()

template<typename Number = double>
Number FunctionTime< Number >::get_time ( ) const
inherited

Return the value of the time variable.

◆ set_time()

template<typename Number = double>
virtual void FunctionTime< Number >::set_time ( const Number  new_time)
virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

template<typename Number = double>
virtual void FunctionTime< Number >::advance_time ( const Number  delta_t)
virtualinherited

Advance the time by the given time step delta_t.

◆ 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 136 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 156 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 301 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 318 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const
inherited

List the subscribers to deallog.

Definition at line 204 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 310 of file subscriptor.h.

Member Data Documentation

◆ omega

const double Functions::StokesLSingularity::omega
private

The angle of the reentrant corner, set to 3*pi/2.

Definition at line 280 of file flow_function.h.

◆ lambda

const double Functions::StokesLSingularity::lambda = 0.54448373678246
staticprivate

The exponent of the radius, computed as the solution to \(\sin(\lambda\omega)+\lambda \sin(\omega)=0\)

Definition at line 283 of file flow_function.h.

◆ coslo

const double Functions::StokesLSingularity::coslo
private

Cosine of lambda times omega.

Definition at line 285 of file flow_function.h.

◆ lp

const double Functions::StokesLSingularity::lp
private

Auxiliary variable 1+lambda.

Definition at line 287 of file flow_function.h.

◆ lm

const double Functions::StokesLSingularity::lm
private

Auxiliary variable 1-lambda.

Definition at line 289 of file flow_function.h.

◆ mean_pressure

double Functions::FlowFunction< dim >::mean_pressure
protectedinherited

Mean value of the pressure to be added by derived classes.

Definition at line 127 of file flow_function.h.

◆ dimension

const unsigned int Function< dim, double >::dimension
staticinherited

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 159 of file function.h.

◆ n_components

const unsigned int Function< dim, double >::n_components
inherited

Number of vector components.

Definition at line 164 of file function.h.


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