Namespaces | Classes | Typedefs
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...
 
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 > >
 

Detailed Description

Holds tags and ComputeItems associated with a Strahlkorper.