scimloperators with multiple input/outputs

[vpuri3]

I am defining the gradient operator as follows:

Dx = F \ Dxh * F
Dy = F \ Dyh * F

grad = [Dx, Dy]

where F is the Fourier transform wrapped in a FunctionOperator, and Dx, Dy are DiagonalOperators. I want to effectively share the work of applying the Fourier transform. The order of operations should be:

function grad(u)
mul!(uh, F, u)

mul!(uxh, Dxh, uh)
mul!(uxh, Dxh, uh)

ldiv!(ux, F, uxh)
ldiv!(uy, F, uyh)

ux, uy
end

So effectively, I want a SciMLOperators that accepts/returns arrays of inputs like F*u, F*u = FF(u). This would be useful for working with coupled equations like the Navier Stokes where you would want to define operators on (component) vectors like (vx, vy, vz, p).

[vpuri3]

more about sharing work here: SciML/SciMLOperators.jl#86