[petsc-users] Doubt about BT and BASIC NEWTONLS

[Francesc Levrero-Florencio]

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.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20211116/4585c3b0/attachment.html>