On Tue, Sep 11, 2018 at 11:53 AM Jed Brown <j...@jedbrown.org> wrote:
> Matthew Knepley <knep...@gmail.com> writes: > > > On Tue, Sep 11, 2018 at 10:32 AM Zhang, Hong <hongzh...@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/>