StrahlkorperTags Namespace Reference

Holds tags and ComputeItems associated with a Strahlkorper. More...

## 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...

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...

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...

$\nabla^2 r_{\rm surf}$, 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...

(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 > >

## Detailed Description

Holds tags and ComputeItems associated with a Strahlkorper.