Hardware for physics simulations?

Just wondering what physics simulations in blender need most to speed up and stabilize them.

I find myself using alot of cloth and hair sims these days, often fluids and others too - but the simulating time can be a huge pain - and that’s assuming blender doesn’t just crash immediately…
So i’m wondering if I can upgrade part of my computer to help with it specifically.

I’m sure the CPU has an effect, but i’m not sure what characteristics are best - more cores? Higher clock speeds? etc.
Also, does the GPU have any effect? Is CUDA purely for rendering visuals or does it help with this also? I’ve been needing a GPU upgrade for ages anyway, so really hoping that has some effect.

I currently have an Intel i7 4770k CPU and an aging Nvidia GTX 570 GPU, for the sake of reference.

Thanks~

About the processor. Since the processor is needed for the final rendering, on the one hand, the more productive the processor then better (at least 4 cores). But this is a matter of price. Given my own experience, I can say that it’s better to choose Intel than AMD. It also happens that the six cores of AMD will work just like Intel’s four.
About the GPU. Better nVidia is based on CUDA with as much memory as possible on board, as CUDA technology is required for visualization by the GPU.