[petsc-dev] TSBASICSYMPLECTIC

[Constantinescu, Emil M.]

On 9/11/18 10:53 AM, Jed Brown 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.

I agree, symplectic is a bad name for these integrators - this is 
because of historical reasons. Actually these integrators only work for 
separable Hamiltonians. The class of symplectic integrators is much 
larger and overlaps with other "classes" like Jed pointed out.

In the end I think users will accept this imperfect nomenclature b/c 
it's widely accepted by physicists - but then you need to consider a 
two-partitioned system only... which is a Hamiltonian.