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SpECTRE
v2024.04.12
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The determinant of the induced Jacobian on a surface. More...
#include <SurfaceJacobian.hpp>
Public Types | |
| using | type = Scalar< DataVector > |
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.