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Second-order in time #60

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rckirby opened this issue Jan 12, 2023 · 0 comments
Open

Second-order in time #60

rckirby opened this issue Jan 12, 2023 · 0 comments

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@rckirby
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rckirby commented Jan 12, 2023

It should be possible to extend Irksome to do second-order in time problems via Runge-Kutta-Nystrom without forcing a rewrite as a first-order system (which uses more memory to store solutions and requires a larger stiffness matrix per-time-step). Things that have to happen:

  • Extend TimeDerivative to allow higher-order derivatives
  • Allow expanded tableaux for RKN
  • Figure out how to modify the UFL substitutions to DTRT, making sure we can do first and second derivatives in time (e.g. telegraph equation)
  • Engineer the top-level interface. Plausibly we want TimeStepper to uniformly accept second-order equations, just making sure that we have a ButcherTableau suitable for RKN on input.
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