| ... | ... | @@ -965,15 +965,11 @@ integration over cell faces turns out to be too complicated. |
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The face-averaged magnetic field components are then obtained from the
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integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
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`g->bx[iz][iy][ix]` = \[*h*<sub>*y*</sub>*Δ*<sub>`iy`</sub>(*h*<sub>*zy*</sub>*Â*<sub>*z*</sub>)−*h*<sub>*y*</sub>*Δ*<sub>`iz`</sub>*Â*<sub>*y*</sub>\]/*δ*𝒜<sub>*x*</sub>
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`g->bx[iz][iy][ix]` = \[*h*<sub>*y*</sub>*Δ*<sub>iy</sub>(*h*<sub>*zy*</sub>*Â*<sub>*z*</sub>)−*h*<sub>*y*</sub>*Δ*<sub>iz</sub>*Â*<sub>*y*</sub>\]/*δ*𝒜<sub>*x*</sub>
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`g->by[iz][iy][ix]` = \[*Δ*<sub>`iz`</sub>*Â*<sub>*x*</sub>−*h*<sub>*zy*</sub>*Δ*<sub>`ix`</sub>(*h*<sub>*y*</sub>*Â*<sub>*z*</sub>)\]/*δ*𝒜<sub>*y*</sub>
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`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>
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where (*Â*<sub>*x*</sub>, *Â*<sub>*y*</sub>, *Â*<sub>*z*</sub>) denote
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the path integrals
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`g->by[iz][iy][ix]` = \[*Δ*<sub>iz</sub>*Â*<sub>*x*</sub>−*h*<sub>*zy*</sub>*Δ*<sub>ix</sub>(*h*<sub>*y*</sub>*Â*<sub>*z*</sub>)\]/*δ*𝒜<sub>*y*</sub>
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`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>
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`g->bx[iz][iy][ix]`$=\left[h_y\Delta_{iy} (h_{zy}\hat{A}_z)
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-h_y\Delta_{iz} \hat{A}_y\right]/\delta \mathcal{A}_x$
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| ... | ... | @@ -994,6 +990,8 @@ $\Delta_{iy}X=X(\mathtt{iz,iy+1,ix})-X(\mathtt{iz,iy,ix})$, |
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$\Delta_{iz}X=X(\mathtt{iz,iy,ix+1})-X(\mathtt{iz,iy,ix})$
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and $(\hat{A}_x,\hat{A}_y,\hat{A}_z)$ are the cell-edge integrals
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and (*Â*<sub>*x*</sub>, *Â*<sub>*y*</sub>, *Â*<sub>*z*</sub>)
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are the cell-edge integrals
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| ... | ... | |
