DAE solver for non-smooth currents

[valentinsulzer]

Fix (at least one of the) DAE solvers to work when the input current is not smooth.

Hacky approach is to do step-by-step and match up discontinuities with steps, or try stepping the differential and algebraic equations separately

[martinjrobins]

could we augment model.events to take 2 types of events: "termination" and "discontinuity". The solver would then make sure to integrate up to just before a discontinuity, and restart integration just after the discontinuity.

[valentinsulzer]

Good idea, so would the discontinuities be a list of variables for which to look out for discontinuities? Or do we analyse the input current (a parameter) before solving to identify discontinuities and then tell the model/solver about them before solving?

[martinjrobins]

I'm thinking that the user would manually specify where the discontinuities occur in time, based on the parameters of the model. Therefore discontinuities would be an expression that evaluates to the time when the discontinuity takes place.

So, given a model that has parameter a and which exhibits a discontinuity at 2*a, the user would set model.events = [(pybamm.DISCONTINUITY, 2*a)]

Then it would be easy for the solver to get the list of where discontinuities occur in time, and make sure that the integration is restarted at each discontinuous time-point

[martinjrobins]

Each event now needs 3 pieces of info, its name, expression and type (DISCONTINUITY or TERMINATION). I think this needs a separate class to encapsulate this (and provide some documentation). Implemented this as Event, so that to create some events you might do something like this:

        model.events = [
            pybamm.Event("var1 = 1.5", pybamm.min(var1 - 1.5)),
            pybamm.Event("var2 = 2.5", pybamm.min(var2 - 2.5)),
            pybamm.Event("nonsmooth rate",
                         pybamm.Scalar(2.5),
                         pybamm.EventType.DISCONTINUITY
                         )
        ]