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version 4.2
authored
Oct 29, 2025
by
Udo Ziegler
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3-NIRVANA-user-guide/3.2-User-interfaces.md
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@@ -971,25 +971,15 @@ integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
`g->bz[iz][iy][ix]`
=
\[
*Δ*
<sub>
ix
</sub>
(
*h*
<sub>
*y*
</sub>
*Â*
<sub>
*y*
</sub>
)−
*Δ*
<sub>
iy
</sub>
*Â*
<sub>
*x*
</sub>
\]
/
*δ*
𝒜
<sub>
*z*
</sub>
`g->bx[iz][iy][ix]`
$=
\l
eft[h_y
\D
elta_{iy} (h_{zy}
\h
at{A}_z)
-h_y
\D
elta_{iz}
\h
at{A}_y
\r
ight]/
\d
elta
\m
athcal{A}_x$
where the difference operators
*Δ*
<sub>
ix
</sub>
,
*Δ*
<sub>
iy
</sub>
and
*Δ*
<sub>
iz
</sub>
are given by
`g->by[iz][iy][ix]`
$=
\l
eft[
\D
elta_{iz}
\h
at{A}_x
-h_{zy}
\D
elta_{ix} (h_y
\h
at{A}_z)
\r
ight]/
\d
elta
\m
athcal{A}_y$
*Δ*
<sub>
ix
</sub>
X=X(iz,iy,ix+1)-X(iz,iy,ix)
`g->bz[iz][iy][ix]`
$=
\l
eft[
\D
elta_{ix} (h_y
\h
at{A}_y)
-
\D
elta_{iy}
\h
at{A}_x
\r
ight]/
\d
elta
\m
athcal{A}_z$
*Δ*
<sub>
iy
</sub>
X=X(iz,iy+1,ix)-X(iz,iy,ix)
where the difference operators $
\D
elta_{ix}$, $
\D
elta_{iy}$ and
$
\D
elta_{iz}$ are given by
*Δ*
<sub>
iz
</sub>
X=X(iz,iy,ix+1)-X(iz,iy,ix)
$
\D
elta_{ix}X=X(
\m
athtt{iz,iy,ix+1})-X(
\m
athtt{iz,iy,ix})$,
$
\D
elta_{iy}X=X(
\m
athtt{iz,iy+1,ix})-X(
\m
athtt{iz,iy,ix})$,
$
\D
elta_{iz}X=X(
\m
athtt{iz,iy,ix+1})-X(
\m
athtt{iz,iy,ix})$
and $(
\h
at{A}_x,
\h
at{A}_y,
\h
at{A}_z)$ are the cell-edge integrals
and (
*Â*
<sub>
*x*
</sub>
,
*Â*
<sub>
*y*
</sub>
,
*Â*
<sub>
*z*
</sub>
)
are the cell-edge integrals
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