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Consider a regular rectangular 2D $r$-$z$ mesh with constant spacing $\Delta r$ along the $r$-axis with $n$ points and spacing $\Delta z$ along the $z$-axis with $m$ points. I thought it would be a straightforward formula for node connectivity/node numbering. But searching the internet is finding complicated ideas for general situations.

What is the formula for the node number of the point $(i, j)$ in a regular rectangular 2D $r$-$z$ mesh with constant spacing?

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Supposing that you enumerate first in $r$ and then in $z$, you have the following enumeration

$$n_\text{node} = j n + i\, ,$$

assuming zero-indexing.

It is a good exercise for you to deduce this result. I think it is correct, but it does not hurt to double-check.

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  • $\begingroup$ Also, it is interesting to think about how different choices for 1D enumeration can make the numerical solution easier or harder. $\endgroup$
    – Maxim Umansky
    Aug 9, 2022 at 18:45
  • $\begingroup$ what are j, n and i? $\endgroup$
    – wander95
    Aug 9, 2022 at 19:49
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    $\begingroup$ $i$, $j$ and $n$ are defined in your original question. $\endgroup$
    – nicoguaro ♦
    Aug 10, 2022 at 2:34

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