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:

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

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:
• src/Domain/Tags/SurfaceJacobian.hpp