[petsc-users] TAO with time dependent problem

[Josh L]

Hi Alp,

Yes, my minimal energy problem reduces to the solution of (1).

Is there any reference on the problem you mention in the last paragraph?

Thanks,
Josh




2018-09-12 9:26 GMT-05:00 Dener, Alp <adener at anl.gov>:

> Hi Josh,
>
> In the FormFunctionAndGradient() function, the gradient you compute and
> provide TAO must be the gradient of the objective function with respect to
> the optimization variables. If your optimization variables are u, and your
> objective function is J(u), then FormFunctionGradient would need to compute
> J(u) and dJ/du.
>
> I’m not entirely sure if I understand your problem correctly, but it seems
> that your minimal energy problem reduces to the solution of equation (1).
> Is this correct?
>
> TAO is not the right package to solve time-dependent PDEs like (1)
> directly. You would want to use TS for that. However, TAO can be used to
> solve the original energy minimization problem. A good example of this is
> the canonical obstacle problem that aims to minimize the Dirichlet energy
> function subject to a constraint that represents the obstacle. That problem
> reduces to the solution of the Laplace equation with the appropriate
> boundary conditions matching the obstacle, which would be discretized and
> solved as a stand-alone PDE. However, the same problem can also be solved
> as an optimization problem where the objective function is the Dirichlet
> energy function, and the associated gradient is related to the stiffness
> matrix associated with the Laplace equation. The two formulations are
> mathematically equivalent. If I’m interpreting your problem correctly, you
> should be able to take a similar approach, but you would need to derive the
> gradient of your energy function and see how you can construct it in
> relation to equation (1).
>
> ——
> *Alp Dener*
> Argonne National Laboratory
> http://www.mcs.anl.gov/person/alp-dener
>
>
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> On Sep 11, 2018, at 3:51 PM, Josh L <ysjosh.lo at gmail.com> wrote:
>
> Hi,
>
> I am using PETSc TAO to solve the following equation obtained from
> minimizing certain energy and constitutive model:
>
> u_xx - u - u_t =0    (1)
>
> For simplicity, the coefficients are neglected.
> In the routine to form function value and gradient, I use (1) to form my
> gradient vector, and my energy definition to calculate function value.Is it
> correct?
>
> I only found one tao example that solves time dependent problem, but it is
> using TS which I am not using.
>
>
> Thanks,
> Josh
>
>
>
>
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