I do not know if the scaling of the BC equations could affect the norms of the nonlinear residual in your situation. I suggest you look at which coefficients of the residual are blowing up in the first step to see if you can understand why they get increased.
Barry > On Nov 17, 2021, at 12:15 PM, Francesc Levrero-Florencio > <f.levrero-floren...@onscale.com> wrote: > > Hi Barry, > > I believe that what you are referring to is what Jed is referring to in this > thread, am I right? > https://scicomp.stackexchange.com/questions/3298/appropriate-space-for-weak-solutions-to-an-elliptical-pde-with-mixed-inhomogeneo/3300#3300 > > <https://scicomp.stackexchange.com/questions/3298/appropriate-space-for-weak-solutions-to-an-elliptical-pde-with-mixed-inhomogeneo/3300#3300> > > We do set the rows/cols of the Jacobian to zero except the diagonal component > which is set to one, as you mention. I understand that in the case of only > homogeneous Dirichlet BCs it is generally a good idea to scale that diagonal > component so that the condition number of the Jacobian improves. I assume > that what Jed mentions is the inhomogeneous Dirichlet BC version of this > scaling, which also acts on the corresponding indices of the residual, not > just the Jacobian. My question is the following, since the case we are > encountering problems with is a system with only homogeneous Dirichlet BCs, > how does it apply? Also, would this scaling affect the convergence of the > NEWTONLS with "bt" line-search? Without any scaling we can solve this example > with "basic" (with a very reasonable convergence rate), but not with "bt" > line-search. > > Regards, > Francesc. > > On Tue, Nov 16, 2021 at 6:55 PM Barry Smith <bsm...@petsc.dev > <mailto:bsm...@petsc.dev>> wrote: > > By "scaling" I mean you may need to rescale the residual terms from the > Dirichlet boundary conditions to be the same order (in terms of the > characteristic size of the elements) as they are for the other residuals. > > It seems in your formulation the Jacobian entries of the residual for > Dirichlet boundary conditions are 1 on the diagonal while the Jacobian > entries of the residual for the PDE entries will have a scaling related to > the finite element method you are using, for example in 3d with an operator > grad dot grad the Jacobian entry will be order dx = (dx)^3 * (1/dx)^2. Thus > you should scale the Dirichlet boundary condition residuals by dx to get the > same scaling. > > Barry > > >> On Nov 16, 2021, at 1:37 PM, Francesc Levrero-Florencio >> <f.levrero-floren...@onscale.com <mailto:f.levrero-floren...@onscale.com>> >> wrote: >> >> 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 <bsm...@petsc.dev >> <mailto:bsm...@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-floren...@onscale.com <mailto:f.levrero-floren...@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. >> >
