[petsc-users] large number of iteration.

[Smith, Barry F.]

    Ok, I think you want to use PCFIELDSPLIT with two fields u and c. Start by using PC_COMPOSITE_MULTIPLICATIVE with direct solvers (LU) for each field. Then try replacing the direct solvers LU with hypre BoomerAMG first one at a time. 

    Let us know how it goes and we'll make additional suggestions,

    Barry


> On Aug 6, 2018, at 12:58 PM, Josh L <ysjosh.lo at gmail.com> wrote:
> 
> 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
> > 
> 
>