StrahlkorperTags Namespace Reference

Holds tags and ComputeItems associated with a `Strahlkorper`

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## Namespaces | |

aliases | |

Defines type aliases used in Strahlkorper-related Tags. | |

## Classes | |

struct | CartesianCoords |

`CartesianCoords(i)` is \(x_{\rm surf}^i\), the vector of \((x,y,z)\) coordinates of each point on the surface. More... | |

struct | D2xRadius |

`D2xRadius(i,j)` is \(\partial^2 r_{\rm surf}/\partial x^i\partial x^j\). Here \(r_{\rm surf}=r_{\rm surf}(\theta,\phi)\) is the function describing the surface, which is considered a function of Cartesian coordinates \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\) for this operation. More... | |

struct | DxRadius |

`DxRadius(i)` is \(\partial r_{\rm surf}/\partial x^i\). Here \(r_{\rm surf}=r_{\rm surf}(\theta,\phi)\) is the function describing the surface, which is considered a function of Cartesian coordinates \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\) for this operation. More... | |

struct | InvHessian |

`InvHessian(k,i,j)` is \(\partial (J^{-1}){}^k_j/\partial x^i\), where \((J^{-1}){}^k_j\) is the inverse Jacobian. `InvHessian` is not symmetric because the Jacobians are Pfaffian. `InvHessian` doesn't depend on the shape of the surface. More... | |

struct | InvJacobian |

`InvJacobian(0,i)` is \(r\partial\theta/\partial x^i\), and `InvJacobian(1,i)` is \(r\sin\theta\partial\phi/\partial x^i\). Here \(r\) means \(\sqrt{x^2+y^2+z^2}\). `InvJacobian` doesn't depend on the shape of the surface. More... | |

struct | Jacobian |

`Jacobian(i,0)` is \(\frac{1}{r}\partial x^i/\partial\theta\), and `Jacobian(i,1)` is \(\frac{1}{r\sin\theta}\partial x^i/\partial\phi\). Here \(r\) means \(\sqrt{x^2+y^2+z^2}\). `Jacobian` doesn't depend on the shape of the surface. More... | |

struct | LaplacianRadius |

\(\nabla^2 r_{\rm surf}\), the flat Laplacian of the surface. This is \(\eta^{ij}\partial^2 r_{\rm surf}/\partial x^i\partial x^j\), where \(r_{\rm surf}=r_{\rm surf}(\theta(x,y,z),\phi(x,y,z))\). More... | |

struct | NormalOneForm |

`NormalOneForm(i)` is \(s_i\), the (unnormalized) normal one-form to the surface, expressed in Cartesian components. This is computed by \(x_i/r-\partial r_{\rm surf}/\partial x^i\), where \(x_i/r\) is `Rhat` and \(\partial r_{\rm surf}/\partial x^i\) is `DxRadius` . See Eq. (8) of [2]. Note on the word "normal": \(s_i\) points in the correct direction (it is "normal" to the surface), but it does not have unit length (it is not "normalized"; normalization requires a metric). More... | |

struct | Radius |

(Euclidean) distance \(r_{\rm surf}(\theta,\phi)\) from the center to each point of the surface. More... | |

struct | Rhat |

`Rhat(i)` is \(\hat{r}^i = x_i/\sqrt{x^2+y^2+z^2}\) on the grid. Doesn't depend on the shape of the surface. More... | |

struct | Strahlkorper |

Tag referring to a `Strahlkorper` More... | |

struct | Tangents |

`Tangents(i,j)` is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. `CartesianCoords` ) and are considered functions of \((\theta,\phi)\). More... | |

struct | ThetaPhi |

\((\theta,\phi)\) on the grid. Doesn't depend on the shape of the surface. More... | |

## Typedefs | |

template<typename Frame > | |

using | items_tags = tmpl::list< Strahlkorper< Frame > > |

template<typename Frame > | |

using | compute_items_tags = tmpl::list< ThetaPhi< Frame >, Rhat< Frame >, Jacobian< Frame >, InvJacobian< Frame >, InvHessian< Frame >, Radius< Frame >, CartesianCoords< Frame >, DxRadius< Frame >, D2xRadius< Frame >, LaplacianRadius< Frame >, NormalOneForm< Frame >, Tangents< Frame > > |

Holds tags and ComputeItems associated with a `Strahlkorper`

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