# Implementing Laplacian operator acting on a 2D array

**URL:** https://discourse.julialang.org/t/implementing-laplacian-operator-acting-on-a-2d-array/111615
**Category:** Modelling & Simulations
**Tags:** finite-element, finitediff, operator
**Created:** [March 14, 2024, 1:21pm UTC](https://discourse.julialang.org/t/implementing-laplacian-operator-acting-on-a-2d-array/111615 "2024-03-14T13:21:06Z")
**Posts on this page:** 1
**Showing post:** 3

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### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 14, 2024, 6:54pm UTC](https://discourse.julialang.org/t/implementing-laplacian-operator-acting-on-a-2d-array/111615/3 "2024-03-14T18:54:16Z")

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You can always just write a loop in Julia. Loops are fast. For example, this post give example code for \nabla^2 in N dimensions with a loop: [Seemingly unnecessary allocation within for loop - #8 by stevengj](https://discourse.julialang.org/t/seemingly-unnecessary-allocation-within-for-loop/72556/8) … writing code that only works in 2d is even easier.

For periodic boundary conditions, the naive approach is to compute i\pm 1 modulo the size in the loop body, but this will slow things down a lot. A very flexible approach is to use “ghost cells” (padding) as in the code linked above, which lets the loop body not care about the boundary conditions, which are updated in a separate (cheap) loop over the boundaries.

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