[petsc-users] Doubt about BT and BASIC NEWTONLS

Tue Nov 16 12:37:32 CST 2021

Hi Barry,

Thanks for the quick reply. I am not sure what you meant by "scaling". In
our code, every time our residual is called we do the following in this
order:
- Apply updated Dirichlet BCs in order to assemble the internal forces, and
add them to the residual.
- Assemble the external forces, and subtract them from the residual.
- Update the residual to take into account Dirichet BCs, so we set the
corresponding indices of the residual to - (dirichlet_bc_value -
solution_value), the latter obtained directly from the solution vector of
PETSc. However, note that in this case all Dirichlet BCs are homogeneous,
so this value would be just "solution_value", or 0 throughout the
simulation. This ensures that the solution vector coming from PETSc has the
Dirichlet BCs applied.

This is basically what we do in the residual. If I am not mistaken, the
lambda scaling factor from the line-search would scale the factor
"jacobian^{-1} * residual", so it would scale equally both internal and
external forces.

Regards,
Francesc.

On Tue, Nov 16, 2021 at 5:38 PM Barry Smith <bsmith at petsc.dev> wrote:

>
>   Perhaps this behavior is the result of a "scaling" issue in how various
> terms affect the residual? In particular perhaps the terms for enforcing
> boundary conditions are scaled differently than terms for the PDE
> enforcement?
>
>
>
> > On Nov 16, 2021, at 11:19 AM, Francesc Levrero-Florencio <
> f.levrero-florencio at onscale.com> wrote:
> >
> > Dear PETSc team and users,
> >
> > We are running a simple cantilever beam bending, where the profile of
> the beam is I-shaped, where we apply a bending force on one end and fully
> constrained displacements on the other end. The formulation is a large
> strain formulation in Total Lagrangian form, where the material of the beam
> is a Saint Venant-Kirchhoff hyperelastic material that uses the same
> constants as steel (200E9 GPa Young’s modulus and 0.3 Poisson’s ratio).
> >
> > The simulation finishes in the requested number of time steps by using
> the “basic” type of line-search in the SNES (i.e. traditional Newton method
> without line-search) in a reasonable number of Newton iterations per time
> step (3 or 4 iterations). However, when using the “bt” (or “l2”, and in
> fact no type of line-search ends up yielding convergence) line-search type,
> the convergence never happens within the SNES default maximum number of
> iterations of 50.
> >
> > During solving with traditional Newton, the general behaviour of each
> time step is that the norm of the residual increases on the second call to
> the residual function, but then hugely decreases in the following one or
> two, up to the point where convergence is achieved. Using “bt” line-search,
> the line-search discards the step at lambda=1 immediately because the norm
> of the residual is higher than that produced in the first call to the
> residual function, cutting down the value of lambda to a value
> significantly lower than 1. The simulation then progresses in following
> Newton iterations in a similar fashion, the line-search step at lambda=1 is
> always discarded, and then smaller steps are taken but convergence never
> occurs, for even the first time step.
> >
> > Here are a few values of the relevant norms (using traditional Newton)
> in the first time step:
> >
> > BASIC NEWTON LS
> > Norm of the internal forces is 0
> > Norm of the external forces is 1374.49
> > Norm of the residual is 1374.49
> > Norm of the solution with Dirichlet BCs is 0
> > Number of SNES iteration is 0
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 113498
> > Norm of the external forces is 1374.49
> > Norm of the residual is 105053
> > Norm of the solution with Dirichlet BCs is 0.441466
> > Number of SNES iteration is 0
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 42953.5
> > Norm of the external forces is 1374.49
> > Norm of the residual is 11.3734
> > Norm of the solution with Dirichlet BCs is 0.441438
> > Number of SNES iteration is 1
> >
> > Here are a few values of the relevant norms (using “bt” line-search) in
> the first time step:
> >
> > BT NEWTONLS
> > Norm of the internal forces is 0
> > Norm of the external forces is 1374.49
> > Norm of the residual is 1374.49
> > Norm of the solution with Dirichlet BCs is 0
> > Number of SNES iteration is 0
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 113498
> > Norm of the external forces is 1374.49
> > Norm of the residual is 105053
> > Norm of the solution with Dirichlet BCs is 0.441466
> > Number of SNES iteration is 0
> > (I assume this is the first try at lambda=1)
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 4422.12
> > Norm of the external forces is 1374.49
> > Norm of the residual is 1622.74
> > Norm of the solution with Dirichlet BCs is 0.0441466
> > Number of SNES iteration is 0
> > Line search: gnorm after quadratic fit 1.622742343614e+03
> > (I assume that in this line-search iteration 0.05 < lambda < 1, but the
> corresponding residual is not smaller than the one in the first call, 1622
> > 1374)
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 2163.76
> > Norm of the external forces is 1374.49
> > Norm of the residual is 1331.88
> > Norm of the solution with Dirichlet BCs is 0.0220733
> > Number of SNES iteration is 0
> > Line search: Cubically determined step, current gnorm 1.331884625811e+03
> lambda=5.0000000000000003e-02
> > (This is the accepted lambda for the current Newton iteration)
> > ---------------------------------------------------------------------
> > Norm of the internal forces is 104020
> > Norm of the external forces is 1374.49
> > Norm of the residual is 94739
> > Norm of the solution with Dirichlet BCs is 0.441323
> > Number of SNES iteration is 1
> >
> > My question would be, any idea on how to deal with this situation? I
> would imagine a “hack” would be to bypass the first residual norm, and have
> the line-search use the following one as the “base norm” to check its
> reduction in further iterations, but we are open to any ideas.
> >
> > Thanks for your help in advance and please keep up the good work!
> >
> > Regards,
> > Francesc.
>
>
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