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Vlasov equation is pretty straightforward

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It would be easy to solve with Fem packages like firedrake, but in my case I have 6d distribution function: it depends on 3d vector of spatial coordinates and 3d vector of impulses.

In plasma physics particle in cells is the method of choice for such problem, but I'd like to leverage modern computational techinques. The question is, what kind of packages are availble? Doing 6d mesh and finite elements manually is too tiresome.

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    $\begingroup$ Is that for charged particles? Are you going to couple it with the Poisson equation to solve for the electric field? $\endgroup$ Nov 9 '21 at 19:13
  • $\begingroup$ Yes, I'm going to solve with coupled with Maxwell's equations. $\endgroup$
    – Moonwalker
    Nov 10 '21 at 14:28
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    $\begingroup$ I know at least one project where for solving the kinetic equation in 6D people use the package Chombo commons.lbl.gov/display/chombo/… $\endgroup$ Nov 10 '21 at 22:18
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Take a look at hyper.deal, which was written for this kind of thing. In general, you may want to look at the literature on the "radiative transfer problem" (say, the papers by Marv Adams and colleagues) on how to solve these kinds of problems.

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There's nothing wrong with PIC (to my eye), though you could experiment with other methods. For example, your problem has features similar to those of the lattice Boltzmann method. Another possibility is tensor trains.

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  • $\begingroup$ I'm familiar with tt methods, but my question is more about existing frameworks for the discretization of multidimensional problems, I'd like to use something like firedrake. $\endgroup$
    – Moonwalker
    Nov 9 '21 at 15:08
  • $\begingroup$ Maybe something like this: arxiv.org/pdf/1912.13282.pdf $\endgroup$ Nov 9 '21 at 16:22

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