[petsc-users] large number of iteration.

[Josh L]

Hi Barry,

(1)
I am basically solving the equilibrium coupled with phase field equation:

1-D example
u is displacement and c is phase-field parameter.

equilibrium: (c^2)*E* (\Delta u) = 0

phase-field equation:  2*G_c*L*(\Delta c)-E*(\epsilon)^2*c+G_c/2L(1-c)=0

I solve the above 2 equations coupled.
it is the formulation for quasi-static fracture problem, where G_c is the
critical energy release rate and L is the length scale in phase-field
method (both constant).

The free energy I am using now is
1-D:

\psi=c^2*0.5*E*\epsilon^2+G_c/4L*(1-c)^2+G_c*L*grad c * grad c


it is not convex w.r.t u and c simultaneously.

(2)

with an appropriate step size. Newton's method usually converges with 5
iteration, and I can see the quadratic convergence of Newton's method.




Thanks,
Josh



2018-08-05 22:23 GMT-05:00 Smith, Barry F. <bsmith at mcs.anl.gov>:

>
>
> > On Aug 5, 2018, at 9:38 PM, Josh L <ysjosh.lo at gmail.com> wrote:
> >
> > Hi,
> >
> > I am using GRMES to solve the linear systems within Newton Raphson.
> > I am using finite element method to solve fracture problem with phase
> field method.(the formulation gives symmetric but indefinite hessian so
> can't use CG)
>
>     What exact equations are you using for the phase field method?
>
>      With the direct LU solver roughly how many iterations does your
> Newton's method take?
>
>
>    Barry
>
> >
> > The total iteration number to solve one linear system is often very
> large( > 2000) even for a small sized problem(120K degree of freedom). I've
> tried different preconditioner, but it doesn't help a lot.  I have checked
> my hessian and right hand side, and sure they are correct.
> >
> > I think it might stem from the great difference in element
> size(max/min=100) and damage stiffness around crack.
> >
> > Anyone has idea to reduce the number of iteration?
> >
> > Now, I get away with it by using LU, which is not ideal for large size
> problem (I will have to run it in the future)
> >
> >
> > Thanks,
> > Josh
> >
>
>
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