Comments (2)
Hi Gabriel,
Please apologise the late reply. This is a very interesting question and not easy to answer. In GeometricIntegrators, we can in principle support time-adaptive methods, but we haven't implemented any, yet.
The canonical reference (Hairer, Lubich, Wanner: Geometric Numerical Integration) touches upon this in Section VIII.2.1. But there are not many details. On the front of variational integrators, there is some discussion in Marsden, West (2001): Discrete mechanics and variational integrators, Section 4.9.
Other than that, a quick Google search leads you to recent work in this area. Some references I am familiar with are
https://doi.org/10.1088/0741-3335/54/1/014004
https://doi.org/10.1007/s10569-012-9441-z
https://doi.org/10.1007/s11075-018-0636-6
https://doi.org/10.3934/jgm.2023010
from geometricintegrators.jl.
Thanks Michael for your answer.
Indeed, I'm familiar with the Hairer Lublich Wanner, but (unless I misunderstood) they do not present an adaptive timestepping method that conserves both sympecticity and the partitioned structure. I'll definitely have a look at the references you provided.
Cheers
Edit : I'm closing the issue for now, although if I find something interesting enough, I'll let you know
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Related Issues (20)
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