Recently I have stumbled upon this video of M. J. Gander https://www.youtube.com/watch?v=dn5vqN8ezuE and the coresponding notes that he wrote on Time Parallel Time Integration and I find it a quite interesting topic.
I would like to ask about the possible gain of applying the parareal algorithm to particle simulations (e.g. the SPH method used in fluid dynamics).
I have a specific code on which I would like to try it but I would like to know first if it will even work.
The framework in which I would like to apply it is as follows: Say that the problem is governed by an advection-diffusion equation. For reasons that are a bit involved, this equation is solved by splitting the problem into two sub-problems: an advection and a diffusion problem. These are solved sequentially. Suppose that both sub-problems can be solved using particles (i.e. no finite differences, finite volumes etc discretization).
Could parareal be applied to this problem given the fact that I use the splitting? Is it possible to apply parareal only to one of the sub-problems (possibly only the advection part)?
Any feedback is welcome! Feel free to ask for any other clarification.