Table B.1: Divergence in the three different geometries handled by HERACLES.
Cartesian Cylindrical Spherical

$\nabla\cdot\vec{ P}_{x}$ $\partial_{\rm r} P_{rr} + \nabla_{\theta,z}\cdot\vec{ P}_{r}$ $+ \frac{P_{rr}-P_{\theta\theta}}{r}$ $\partial_{\rm r} P_{rr} + \nabla_{\theta,\phi}\cdot\vec{ P}_{r}$ $+ \frac{2 P_{rr}-P_{\theta\theta}-P_{\phi\phi}}{r}$

$\nabla \cdot {\mathbb P}=$ $\nabla\cdot\vec{ P}_{y}$ $\frac{1}{r}\nabla\cdot(r \vec{ P_{\theta}})$ $\frac{1}{r}\partial_\theta P_{\theta\theta} + \frac{1}{r}\nabla_{r,\phi}\cdot(r \vec{ P_{\theta}})$ $+ \cot \theta \frac{P_{\theta\theta}-P_{\phi\phi}}{r}$

$\nabla\cdot\vec{ P}_{z}$ $\nabla\cdot\vec{ P}_{z}$ $\frac{1}{r \sin \theta}\nabla\cdot(r \sin \theta \vec{ P_{\phi}})$

**Table B.1:** Divergence in the three different geometries handled by HERACLES.
	Cartesian	Cylindrical		Spherical
	$\nabla\cdot\vec{ P}_{x}$	$\partial_{\rm r} P_{rr} + \nabla_{\theta,z}\cdot\vec{ P}_{r}$	$+ \frac{P_{rr}-P_{\theta\theta}}{r}$	$\partial_{\rm r} P_{rr} + \nabla_{\theta,\phi}\cdot\vec{ P}_{r}$	$+ \frac{2 P_{rr}-P_{\theta\theta}-P_{\phi\phi}}{r}$
$\nabla \cdot {\mathbb P}=$	$\nabla\cdot\vec{ P}_{y}$	$\frac{1}{r}\nabla\cdot(r \vec{ P_{\theta}})$		$\frac{1}{r}\partial_\theta P_{\theta\theta} + \frac{1}{r}\nabla_{r,\phi}\cdot(r \vec{ P_{\theta}})$	$+ \cot \theta \frac{P_{\theta\theta}-P_{\phi\phi}}{r}$
	$\nabla\cdot\vec{ P}_{z}$	$\nabla\cdot\vec{ P}_{z}$		$\frac{1}{r \sin \theta}\nabla\cdot(r \sin \theta \vec{ P_{\phi}})$

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