[petsc-users] Pre-check before each line search function evaluation

[Alexander Lindsay]

I can do exactly what I want using SNESLineSearchPrecheck and
-snes_linesearch_type basic ... I just can't use any more exotic line
searches

On Thu, Nov 30, 2023 at 1:22 PM Alexander Lindsay <alexlindsay239 at gmail.com>
wrote:

> If someone passes me just L, where L represents the "global" degrees of
> freedom, in this case they represent unknowns on the trace of the mesh,
> this is insufficient information for me to evaluate my function. Because in
> truth my degrees of freedom are the sum of the trace unknowns (the unknowns
> in the global solution vector) and the eliminated unknowns which are
> entirely local to each element. So I will say my dofs are L + U.
>
> I start with some initial guess L0 and U0. I perform a finite element
> assembly procedure on each element which gives me things like K_LL, K_UL,
> K_LU, K_UU, F_U, and F_L. I can do some math:
>
> K_LL = -K_LU * K_UU^-1 * K_UL + K_LL
> F_L = -K_LU * K_UU^-1 * F_U + F_L
>
> And then I feed K_LL and F_L into the global system matrix and vector
> respectively. I do something (like a linear solve) which gives me an
> increment to L, I'll call it dL. I loop back through and do a finite
> element assembly again using **L0 and U0** (or one could in theory save off
> the previous assemblies) to once again obtain the same K_LL, K_UL, K_LU,
> K_UU, F_U, F_L. And now I can compute the increment for U, dU, according to
>
> dU = K_UU^-1 * (-F_U - K_UL * dL)
>
> Armed now with both dL and dU, I am ready to perform a new residual
> evaluation with (L0 + dL, U0 + dU) = (L1, U1).
>
> The key part is that I cannot get U1 (or more generally an arbitrary U)
> just given L1 (or more generally an arbitrary L). In order to get U1, I
> must know both L0 and dL (and U0 of course). This is because at its core U
> is not some auxiliary vector; it represents true degrees of freedom.
>
> On Thu, Nov 30, 2023 at 12:32 PM Barry Smith <bsmith at petsc.dev> wrote:
>
>>
>>   Why is this all not part of the function evaluation?
>>
>>
>> > On Nov 30, 2023, at 3:25 PM, Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>> >
>> > Hi I'm looking at the sources, and I believe the answer is no, but is
>> there a dedicated callback that is akin to SNESLineSearchPrecheck but is
>> called before *each* function evaluation in a line search method? I am
>> using a Hybridized Discontinuous Galerkin method in which most of the
>> degrees of freedom are eliminated from the global system. However, an
>> accurate function evaluation requires that an update to the "global" dofs
>> also trigger an update to the eliminated dofs.
>> >
>> > I can almost certainly do this manually but I believe it would be more
>> prone to error than a dedicated callback.
>>
>>
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