I am trying to numerically solve $u_{xx} + u_{yy} + u_{zz} = 0$ using a 27-point stencil, meaning each node in my finite difference domain interacts with every node in a $3 \times 3 \times 3$ cube centered around itself. I have found the coefficients for the two-dimensional 9-point stencil, but I do not know how to generate the coefficients for the 27-point stencil, nor can I find them readily available online. Could someone provide a reference to a paper which uses or derives them, or could someone show me how I might start the derivation process myself?
2026-03-26 16:23:08.1774542188
Coefficients for the three-dimensional discrete Laplacian
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