Welcome to parallel-gpu-workshop-JuliaCon21 Discussions!

[luraess]

👋 Welcome!

We’re using Discussions as a place to exchange about topics related to this short course. We hope that you:

• Ask questions you’re wondering about.
• Share ideas.
• Welcome others, stay open-minded and respectful.

[chris-revell]

Hello. Thank you for presenting this workshop at JuliaCon; it has been very helpful. I wonder if you could explain or provide a reference for how the dtau time step is set within the psuedotime iteration for the implicit methods? I can see that is is calculated in the following line: dtau .= (1.0./(min(dx, dy)^2 ./inn(H).^npow./4.1) .+ 1.0/dt).^-1. However, it is not immediately obvious to me how this expression was derived from the basic CFL condition, or how it should be adapted for other PDEs. Thanks very much.

[chris-revell]

Ah, so is the pseudo-transient iterative approach a requirement to best leverage the GPU? I was looking at the split scheme described here https://www.sciencedirect.com/science/article/pii/S0021999116001947, which, to my current poor understanding, involves an approximation to linearise one component, which can be solved implicitly, leaving another component to be solved explicitly.

[luraess]

pseudo-transient iterative approach a requirement to best leverage the GPU

No, don't get me wrong - sorry if I was unclear. I was just pointing out that if you use an (partly) implicit scheme, then you are likely to need the solution of a linear system of equation (in your ref a pseudo-spectral approach seems to be used). This may be the performance bottleneck of your application as approximating the inverse of (large) sparse arrays may become costly in terms of memory pressure.

[chris-revell]

That makes sense. Would you say that the GPU is less effective for schemes that require matrix inversion?

[luraess]

the GPU is less effective for schemes that require matrix inversion

Not exactly. There may be a trade-off. The GPU can certainly handle "matrix inversions" well, but the implementation may not scale; the larger the problem size, the nonlinearly more memory transfers may be needed which may turn out to be the bottleneck at some point.

[chris-revell]

Thanks for the input. Seems like I've got a lot to look into!