[petsc-users] Time integrated adjoints

[Emil Constantinescu]

On 4/15/15 12:37 PM, Barry Smith wrote:
>
>    Hong and Emil,
>
>      You will need to answer this.
>
>
>> On Apr 15, 2015, at 6:24 AM, Dave Makhija <makhijad at colorado.edu> wrote:
>>
>> Barry,
>>
>> Is the method exact if I have a time dependent mass matrix (dF/dU_t changes each time step)? I'm not sure it's possible if TSSetIJacobian expects a function which computes the combination of dF/dU and a*dF/dU_t. But, perhaps there is something I'm missing.

In the adjoint derivation, we assumed that we have F = M U_t - f(t,U); 
so a*dF/dU_t is a*M, which holds if M=M(t). So in principle it should 
work. However, because M(t_n) and M(t_{n+1}) are different, the adjoint 
implementation might be slightly inconsistent -- and I'm saying this out 
of caution. We did not test it on problems with M=M(t). Do you have such 
an example interfaced with PETSc we can try?

Emil


>> Otherwise, it looks very comprehensive. I like how you added the "cost integrand". If I recall correctly, the Trilinos package Rythmos is missing this.
>>
>> Thanks!
>>
>> Dave
>>
>> On Tue, Apr 14, 2015 at 8:30 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>
>>> On Apr 14, 2015, at 1:06 AM, Dave Makhija <makhijad at colorado.edu> wrote:
>>>
>>> Hello,
>>>
>>> I'm evaluating my options for computing time dependent adjoints. I did not think PETSc supported this, but I see "TSAdjointSolve" in the development branch. That would be fantastic news if you plan to support time integrated adjoints!
>>>
>>> What features are envisioned and when is the targeted release date?
>>
>>    Dave,
>>
>>     We currently have discrete adjoint computations for explicit RK methods and for implicit theta methods (backward Euler and Crank-Nicholson). The development copy of the users manual has some discussion (http://www.mcs.anl.gov/petsc/petsc-master/docs/manual.pdf page 135) and there are several examples.   I urge you to try them out now in master and stay in contact with us to insure we provide what you need as we are actively developing them.
>> We plan a release for early June.
>>
>>    Barry
>>
>>>
>>> Thanks!
>>>
>>> Dave
>>
>>
>