SpECTRE  v2022.06.14
domain::Tags::DetSurfaceJacobian< SourceFrame, TargetFrame > Struct Template Reference

The determinant of the induced Jacobian on a surface. More...

#include <SurfaceJacobian.hpp>

Public Types

using type = Scalar< DataVector >
 

Detailed Description

template<typename SourceFrame, typename TargetFrame>
struct domain::Tags::DetSurfaceJacobian< SourceFrame, TargetFrame >

The determinant of the induced Jacobian on a surface.

The surface Jacobian determinant on a surface \(\Sigma\) with constant logical coordinate \(\xi^i\) is:

\begin{equation} J^\Sigma = J \sqrt{\gamma^{jk} (J^{-1})^i_j (J^{-1})^i_k} \end{equation}

where \(J^i_j = \partial x^i / \xi^j\) is the volume Jacobian with determinant \(J\) and inverse \((J^{-1})^i_j = \partial \xi^i / \partial x^j\). Note that the square root in the expression above is the magnitude of the unnormalized face normal, where \(\gamma^{jk}\) is the inverse spatial metric.


The documentation for this struct was generated from the following file: