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 $\mathrm{\Sigma }$ with constant logical coordinate ${\xi }^i$ is:

$$\begin{array}{}\text{(1)}& J^{\mathrm{\Sigma }}=J\sqrt{{\gamma }^{jk}(J^{-1}{)}_j^i(J^{-1}{)}_k^i}\end{array}$$

where $J_j^i=\partial x^i/{\xi }^j$ is the volume Jacobian with determinant $J$ and inverse $(J^{-1}{)}_j^i=\partial {\xi }^i/\partial x^j$. 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.

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

• src/Domain/Tags/SurfaceJacobian.hpp