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Reference documentation for deal.II version 9.4.1
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#include <deal.II/base/function_spherical.h>
Public Types | |
using | time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type |
Public Member Functions | |
Spherical (const Point< dim > ¢er=Point< dim >(), const unsigned int n_components=1) | |
virtual double | value (const Point< dim > &point, const unsigned int component=0) const override |
virtual Tensor< 1, dim > | gradient (const Point< dim > &p, const unsigned int component=0) const override |
virtual SymmetricTensor< 2, dim > | hessian (const Point< dim > &p, const unsigned int component=0) const override |
virtual std::size_t | memory_consumption () const override |
Tensor< 1, 3 > | gradient (const Point< 3 > &p_, const unsigned int component) const |
SymmetricTensor< 2, 3 > | hessian (const Point< 3 > &p_, const unsigned int component) const |
virtual void | vector_value (const Point< dim > &p, Vector< RangeNumberType > &values) const |
virtual void | value_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const |
virtual void | vector_value_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const |
virtual void | vector_values (const std::vector< Point< dim > > &points, std::vector< std::vector< RangeNumberType > > &values) const |
virtual void | vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients) const |
virtual void | gradient_list (const std::vector< Point< dim > > &points, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients, const unsigned int component=0) const |
virtual void | vector_gradients (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const |
virtual void | vector_gradient_list (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const |
virtual RangeNumberType | laplacian (const Point< dim > &p, const unsigned int component=0) const |
virtual void | vector_laplacian (const Point< dim > &p, Vector< RangeNumberType > &values) const |
virtual void | laplacian_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const |
virtual void | vector_laplacian_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const |
virtual void | vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &values) const |
virtual void | hessian_list (const std::vector< Point< dim > > &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &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, RangeNumberType > > > &values) const |
Number | get_time () const |
virtual void | set_time (const Number new_time) |
virtual void | advance_time (const Number delta_t) |
Public Attributes | |
const unsigned int | n_components |
Static Public Attributes | |
static constexpr unsigned int | dimension = dim |
Private Member Functions | |
virtual double | svalue (const std::array< double, dim > &sp, const unsigned int component) const |
virtual std::array< double, dim > | sgradient (const std::array< double, dim > &sp, const unsigned int component) const |
virtual std::array< double, 6 > | shessian (const std::array< double, dim > &sp, const unsigned int component) const |
Private Attributes | |
const Tensor< 1, dim > | coordinate_system_offset |
Number | time |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
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 |
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 |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
void | check_no_subscribers () const noexcept |
using | map_value_type = decltype(counter_map)::value_type |
using | map_iterator = decltype(counter_map)::iterator |
static std::mutex | mutex |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
An abstract base class for a scalar-valued function f=f(r,\theta,\phi) defined in spherical coordinates. This class wraps transformation of values, gradients and hessians from spherical coordinates to the Cartesian coordinate system used by the Function base class. Therefore derived classes only need to implement those functions in spherical coordinates (specifically svalue(), sgradient() and shessian() ). The convention for angles is the same as in GeometricUtilities::Coordinates.
Definition at line 44 of file function_spherical.h.
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inherited |
The scalar-valued real type used for representing time.
Definition at line 169 of file function.h.
Functions::Spherical< dim >::Spherical | ( | const Point< dim > & | center = Point<dim>() , |
const unsigned int | n_components = 1 |
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Constructor which should be provided with center
defining the origin of the coordinate system.
Note that components of this function are treated as entirely separate quantities – not as the components of a vector that will be re-interpreted in a different coordinate system.
Definition at line 158 of file function_spherical.cc.
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overridevirtual |
Return the value of the function at the given point.
This function converts the given point to spherical coordinates, calls svalue() with it, and returns the result.
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 170 of file function_spherical.cc.
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overridevirtual |
Return the gradient with respect to the Cartesian coordinates at point p
.
This function converts the given point to spherical coordinates, calls sgradient() with it, and converts the result into Cartesian coordinates.
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 183 of file function_spherical.cc.
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overridevirtual |
Return the Hessian with respect to the Cartesian coordinates at point p
.
This function converts the given point to spherical coordinates, calls sgradient and shessian() with it, and converts the result into Cartesian coordinates.
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 239 of file function_spherical.cc.
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overridevirtual |
Return an estimate for the memory consumption, in bytes, of this object.
Reimplemented from Function< dim, RangeNumberType >.
Definition at line 310 of file function_spherical.cc.
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privatevirtual |
Return the value at point sp
. Here, sp
is provided in spherical coordinates.
Definition at line 319 of file function_spherical.cc.
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privatevirtual |
Return the gradient in spherical coordinates.
The returned object should contain derivatives in the following order: \{ f_{,r},\, f_{,\theta},\, f_{,\phi}\}.
Definition at line 330 of file function_spherical.cc.
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privatevirtual |
Return the Hessian in spherical coordinates.
The returned object should contain derivatives in the following order: \{ f_{,rr},\, f_{,\theta\theta},\, f_{,\phi\phi},\, f_{,r\theta},\, f_{,r\phi},\, f_{,\theta\phi}\}.
Definition at line 341 of file function_spherical.cc.
Tensor< 1, 3 > Functions::Spherical< 3 >::gradient | ( | const Point< 3 > & | p_, |
const unsigned int | component | ||
) | const |
Definition at line 195 of file function_spherical.cc.
SymmetricTensor< 2, 3 > Functions::Spherical< 3 >::hessian | ( | const Point< 3 > & | p_, |
const unsigned int | component | ||
) | const |
Definition at line 250 of file function_spherical.cc.
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virtualinherited |
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 in Functions::ConstantFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, VectorFunctionFromScalarFunctionObject< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, Functions::IncrementalFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.
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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::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.
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virtualinherited |
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 in Functions::ConstantFunction< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.
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virtualinherited |
For each component of the function, fill a vector of 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.
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virtualinherited |
Return the gradient of all components of the function at the given point.
Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.
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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.
Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.
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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.
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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.
Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.
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virtualinherited |
Compute the Laplacian of a given component at point p
.
Reimplemented in Functions::CosineGradFunction< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::ConstantFunction< dim, RangeNumberType >, and Functions::ConstantFunction< dim, double >.
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virtualinherited |
Compute the Laplacian of all components at point p
and store them in values
.
Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.
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virtualinherited |
Compute the Laplacian of one component at a set of points.
Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.
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virtualinherited |
Compute the Laplacians of all components at a set of points.
Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.
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virtualinherited |
Compute the Hessian of all components at point p
and store them in values
.
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virtualinherited |
Compute the Hessian of one component at a set of points.
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virtualinherited |
Compute the Hessians of all components at a set of points.
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inherited |
Return the value of the time variable.
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virtualinherited |
Set the time to new_time
, overwriting the old value.
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virtualinherited |
Advance the time by the given time step delta_t
.
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private |
A vector from the origin to the center of spherical coordinate system.
Definition at line 129 of file function_spherical.h.
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staticconstexprinherited |
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.
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inherited |
Number of vector components.
Definition at line 164 of file function.h.
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privateinherited |
Store the present time.
Definition at line 113 of file function_time.h.