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danfortunato / ultraSEM

The ultraspherical spectral element method
MIT License
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A class for timestepping #14

Open danfortunato opened 5 years ago

danfortunato commented 5 years ago

Since we store the solution operator, we can do implicit or semi-implicit time-stepping without having to recompute the operator at each time step. Martinsson has a paper on this for HPS here. It would be great to have an abstract class to represent different time-steppers and the ability to specify a time-dependent PDE. Having a time-dependent PDE example in the paper would be nice.

@nickhale, do you have an idea on the best way to structure such a class? I know there is spin2/spinop2 in chebfun, which has you specify the linear and nonlinear parts of the PDE independently.

nickhale commented 5 years ago

We could certainly do something like this, although I think it would be more for marketing rather than there being much mathematically interesting going on (other than the fact that, once we've built, we can solve quickly.)

Chebfun has similar functionality in pde15s (and related methods). I think that's all that's needed here, rather than complicating things with another class. Or at least that's where we could start.