Cjc/vp demo

[colinjcotter]

Description

A 1D Vlasov Poisson demo

[JHopeCollins]

Looks good, most of the comments are just extra detail where the explanations are brief, and a couple of small code changes to avoid warnings.

The only major suggestion is to reorder/reword the explanation of how the null space is dealt with.

[JHopeCollins]

In the future, it could be nice to have a subsequent demo showing how to do this with a single solver, possibly with Irksome too.

The whole thing is linear, and if you have a mixed space with (phi, f) then the matrix is lower triangular so you can do exactly the method you have here with a multiplicative fieldsplit to first solve for phi at the current stage, then calculate the stage increment df using the latest potential velocity.
If you write this as a single system you can also pass it to Irksome to do the RK scheme.

[colinjcotter]

Josh, the whole thing isn't linear, because of the a*f appearing in the conservation law.

[JHopeCollins]

Josh, the whole thing isn't linear, because of the a*f appearing in the conservation law.

Ah yes, of course. I got fooled because each field is linear in itself so you need two linear solves, but the Jacobian of the second solve depends on the solution of the first so just doing forward substitution won't update the lower blocks.

[connorjward]

This file shouldn't have been added here.

[connorjward]

This file shouldn't have been added here.

[connorjward]

This is now only failing the annoying SLATE wrong option check which is known to fail randomly. I am confident that there is nothing wrong with your code.