A transition function that falls off as \(G(r,\theta,\phi) = \frac{f(r)}{r} = \frac{ar + b}{r}\). More...
#include <SphereTransition.hpp>
Public Member Functions | |
| SphereTransition (double r_min, double r_max, bool reverse=false, bool interior=false) | |
| double | operator() (const std::array< double, 3 > &source_coords, const std::optional< size_t > &one_over_radius_power) const override |
| DataVector | operator() (const std::array< DataVector, 3 > &source_coords, const std::optional< size_t > &one_over_radius_power) 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 *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 std::unique_ptr< ShapeMapTransitionFunction > | get_clone () const =0 |
| 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 \(G(r,\theta,\phi) = \frac{f(r)}{r} = \frac{ar + b}{r}\).
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{align} \label{eq:transition_func} a &= \frac{-1}{r_{\text{max}} - r_{\text{min}}} \\ b &= \frac{r_{\text{max}}}{r_{\text{max}} - r_{\text{min}}} = -a r_{\text{max}} \end{align}
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 \(a \rightarrow -a\) and \(b \rightarrow 1-b\).
The function can be called within r_min, but only if interior is true and reverse is false. Within r_min,
\begin{equation} G(r,\theta,\phi) = \frac{r^2}{r_{\text{min}}^3}. \end{equation}
which is chosen to match Eq. \(\ref{eq:transition_func}\) at \(r_{\text{min}}\) and go to 0 at \(r=0\).
This function cannot be called beyond r_max.
If interior is false and if the operator() or gradient() is called with a point within r_min, an error will occur and original_radius_over_radius will return std::nullopt.
This is a special, simplified, case of the domain::CoordinateMaps::ShapeMapTransitionFunctions::Wedge class where both the inner and outer surface are spheres centered on the same center.
Member Function Documentation
◆ get_clone()
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inlineoverridevirtual |
◆ gradient() [1/2]
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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]
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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!=()
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overridevirtual |
◆ operator()() [1/2]
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overridevirtual |
Evaluate the transition function \(G(r,\theta,\phi)\) at the Cartesian coordinates source_coords and possibly divide by the radius \(r\).
Details
If one_over_radius_power has a value, then divide \(G\) by \(r\) to that power. This is done here because the transition function knows how to handle points in various regions of the map.
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
◆ operator()() [2/2]
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overridevirtual |
Evaluate the transition function \(G(r,\theta,\phi)\) at the Cartesian coordinates source_coords and possibly divide by the radius \(r\).
Details
If one_over_radius_power has a value, then divide \(G\) by \(r\) to that power. This is done here because the transition function knows how to handle points in various regions of the map.
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
◆ operator==()
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overridevirtual |
◆ original_radius_over_radius()
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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 \(\Sigma(t, \theta, \phi) = \sum_{lm} \lambda_{lm}(t)Y_{lm}(\theta, \phi)\) (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. ( \(\ref{eq:shape_map_radius}\)) for \(r\) after substituting \(G(r,\theta,\phi)\).
- Parameters
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target_coords The mapped Cartesian coordinates \(\tilde{x}^i\). radial_distortion The spherical harmonic expansion \(\Sigma(t, \theta, \phi)\).
Returns: The quantity \(r/\tilde{r}\).
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
The documentation for this class was generated from the following file:
- src/Domain/CoordinateMaps/TimeDependent/ShapeMapTransitionFunctions/SphereTransition.hpp