[petsc-dev] TSBASICSYMPLECTIC

[Matthew Knepley]

On Tue, Sep 11, 2018 at 11:53 AM Jed Brown <jed at jedbrown.org> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
>
> > On Tue, Sep 11, 2018 at 10:32 AM Zhang, Hong <hongzhang at anl.gov> wrote:
> >
> >> A few related discussions can be found at
> >>
> https://bitbucket.org/petsc/petsc/pull-requests/1108/rename-bsi-to-symplectic/diff
> >>
> >> In addition, what we have in PETSc now is "Basic Symplectic Integrators"
> >> as introduced in Ernst Hairer's article
> >> https://www.unige.ch/~hairer/poly_geoint/week2.pdf .
> >>
> >> Other types of symplectic methods such as symplectic Runge-Kutta use
> >> different tableaus and cannot be implemented in the same framework as
> the
> >> basic one. So when naming this particular type of symplectic methods, we
> >> think it is better to be specific than general.
> >>
> >
> > All symplectic integrators need the support for splitting into two
> fields,
> > and they all (I think) offer similar guarantees.
>
> Gauss Runge-Kutta (including implicit midpoint) is symplectic and does
> not require any splitting.
>

How do you talk about conservation of the symplectic form? The default
model is on R^{2n} and
you get 1 on one half and -1 on the other half. What do you mean no
splitting?

  Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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