A transition function that falls off as \(f(r) = g(r) / r\) where \(g(r) = ar + b\). More...
#include <SphereTransition.hpp>
Public Member Functions | |
| SphereTransition (double r_min, double r_max) | |
| 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 distorted_radius) const override |
| 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 distorted_radius) 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 \(f(r) = g(r) / r\) where \(g(r) = ar + b\).
Details
The coefficients \(a\) and \(b\) are chosen so that the function \(g(r) = ar + b\) falls off linearly from 1 at r_min to 0 at r_max. This means that \(f(r)\) falls off from \(1/r_{\text{min}}\) at r_min to 0 at r_max. The coefficients are
\begin{align} 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}
Member Function Documentation
◆ get_clone()
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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]
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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 at the Cartesian coordinates source_coords.
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
◆ operator()() [2/2]
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overridevirtual |
Evaluate the transition function at the Cartesian coordinates source_coords.
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
◆ operator==()
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overridevirtual |
◆ original_radius_over_radius()
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overridevirtual |
Given the mapped coordinates target_coords and the corresponding spherical harmonic expansion \(\sum_{lm} \lambda_{lm}(t)Y_{lm}\), distorted_radius, this method evaluates the original radius from the mapped radius by inverting the domain::CoordinateMaps::TimeDependent::Shape map. It also divides by the mapped radius to simplify calculations in the shape map.
Implements domain::CoordinateMaps::ShapeMapTransitionFunctions::ShapeMapTransitionFunction.
The documentation for this class was generated from the following file:
- src/Domain/CoordinateMaps/TimeDependent/ShapeMapTransitionFunctions/SphereTransition.hpp