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 <[email protected]>: > 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 > > > > > > > > > > > On Sep 11, 2018, at 3:51 PM, Josh L <[email protected]> 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 > > > >
