Matrix Free Differentiation

[stevengj]

@stillyslalom

Your computational kernel should specialize on the dimensionality and order of your operators, and that specialization will be made easier if you use static arrays for your operators, and pass those in as arguments as well.

Alternatively, see this post for an example of a fast dimension-agnostic matrix-free finite-difference stencil: Seemingly unnecessary allocation within for loop - #8 by stevengj

Note that, as mentioned in this post, you are typically better off using ghost cells / padding to implement your boundary conditions than putting if statements inside critical inner loops. And for something performance-critical like the difference operation, you really benefit from hard-coding/unrolling it.

See also some related discussions:

• Automatic function generation for finite-difference stencils using metaprogramming
• [ANN] Stencils.jl for fast small/direct stencils on CPU/GPU
• Generating finite-difference stencils
• Code Optimization for Differential Equations · DifferentialEquations.jl