domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition Class Reference

A transition function that falls off as $f(r)=ar+b$. More...

#include <SphereTransition.hpp>

Public Member Functions
	SphereTransition (double r_min, double r_max, bool reverse=false)
double	operator() (const std::array< double, 3 > &source_coords) const override
DataVector	operator() (const std::array< DataVector, 3 > &source_coords) const override
std::optional< double >	original_radius_over_radius (const std::array< double, 3 > &target_coords, double radial_distortion) const override
	The inverse of the transition function. More...
std::array< double, 3 >	gradient (const std::array< double, 3 > &source_coords) const override
std::array< DataVector, 3 >	gradient (const std::array< DataVector, 3 > &source_coords) const override
	WRAPPED_PUPable_decl_template (SphereTransition)
	SphereTransition (CkMigrateMessage *const msg)
void	pup (PUP::er &p) override
std::unique_ptr< ShapeMapTransitionFunction >	get_clone () const override
bool	operator== (const ShapeMapTransitionFunction &other) const override
bool	operator!= (const ShapeMapTransitionFunction &other) const override
Public Member Functions inherited from domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction
virtual std::optional< double >	original_radius_over_radius (const std::array< double, 3 > &target_coords, double radial_distortion) const =0
	The inverse of the transition function. More...
virtual bool	operator== (const ShapeMapTransitionFunction &other) const =0
virtual bool	operator!= (const ShapeMapTransitionFunction &other) const =0
	WRAPPED_PUPable_abstract (ShapeMapTransitionFunction)
	ShapeMapTransitionFunction (CkMigrateMessage *m)

Detailed Description

A transition function that falls off as $f(r)=ar+b$.

Details

The coefficients $a$ and $b$ are chosen so that the function $f(r)=ar+b$ falls off linearly from 1 at r_min to 0 at r_max. The coefficients are

$$\begin{array}{}\text{(1)}& a& =\frac{-1}{r_{\text{max}}-r_{\text{min}}}\text{(2)}& b& =\frac{r_{\text{max}}}{r_{\text{max}}-r_{\text{min}}}=-a{r}_{\text{max}}\end{array}$$

If reverse is set to true, then the function falls off from 0 at r_min to 1 at r_max. To do this, the coefficients are modified as $a\to -a$ and $b\to 1-b$.

The function can be called beyond r_min and r_max. Within r_min the value is 1, and outside r_max the value is 0. This is reversed if reverse is true. However, the gradient function cannot be called with a point beyond r_min and r_max.

Member Function Documentation

get_clone()

std::unique_ptr< ShapeMapTransitionFunction > domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::get_clone ( ) const

inlineoverridevirtual

Evaluate the gradient of the transition function with respect to the Cartesian coordinates x, y and z at the Cartesian coordinates source_coords.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

gradient() [1/2]

std::array< DataVector, 3 > domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::gradient ( const std::array< DataVector, 3 > &  source_coords ) const

overridevirtual

Evaluate the gradient of the transition function with respect to the Cartesian coordinates x, y and z at the Cartesian coordinates source_coords.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

gradient() [2/2]

std::array< double, 3 > domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::gradient ( const std::array< double, 3 > &  source_coords ) const

overridevirtual

Evaluate the gradient of the transition function with respect to the Cartesian coordinates x, y and z at the Cartesian coordinates source_coords.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

operator!=()

bool domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::operator!= ( const ShapeMapTransitionFunction &  other ) const

overridevirtual

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

operator()() [1/2]

DataVector domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::operator() ( const std::array< DataVector, 3 > &  source_coords ) const

overridevirtual

Evaluate the transition function $f(r,\theta ,\varphi )\in [0,1]$ at the Cartesian coordinates source_coords.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

operator()() [2/2]

double domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::operator() ( const std::array< double, 3 > &  source_coords ) const

overridevirtual

Evaluate the transition function $f(r,\theta ,\varphi )\in [0,1]$ at the Cartesian coordinates source_coords.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

operator==()

bool domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::operator== ( const ShapeMapTransitionFunction &  other ) const

overridevirtual

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

original_radius_over_radius()

std::optional< double > domain::CoordinateMaps::ShapeMapTransitionFunctions::SphereTransition::original_radius_over_radius ( const std::array< double, 3 > &  target_coords, double  radial_distortion  ) const

overridevirtual

The inverse of the transition function.

This method returns $r/\tilde{r}$ given the mapped coordinates ${\tilde{x}}^i$ (target_coords) and the spherical harmonic expansion $\mathrm{\Sigma }(t,\theta ,\varphi )=\sum _{lm}{\lambda }_{lm}(t)Y_{lm}(\theta ,\varphi )$ (radial_distortion). See domain::CoordinateMaps::TimeDependent::Shape for details on how this quantity is used to compute the inverse of the Shape map.

To derive the expression for this inverse, solve Eq. ( $\text{???}$) for $r$ after substituting $f(r,\theta ,\varphi )$.

Parameters

target_coords	The mapped Cartesian coordinates ${\tilde{x}}^i$.
radial_distortion	The spherical harmonic expansion $\mathrm{\Sigma }(t,\theta ,\varphi )$.

Returns: The quantity $r/\tilde{r}$.

Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.

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

• src/Domain/CoordinateMaps/TimeDependent/ShapeMapTransitionFunctions/SphereTransition.hpp