[petsc-users] Slepc JD and GD converge to wrong eigenpair

[Jose E. Roman]

In order to answer about GD I would need to know all the settings you are using. Also if you could send me the matrix I could do some tests.
GD and JD are preconditioned eigensolvers, which need a reasonably good preconditioner. But MUMPS is a direct solver, not a preconditioner, and that is often counterproductive in this kind of methods.
Jose


> El 31 mar 2017, a las 16:45, Toon Weyens <toon.weyens at gmail.com> escribió:
> 
> Dear both,
> 
> I have recompiled slepc and petsc without debugging, as well as with the recommended --with-fortran-kernels=1. In the attachment I show the scaling for a typical "large" simulation with about 120 000 unkowns, using Krylov-Schur.
> 
> There are two sets of datapoints there, as I do two EPS solves in one simulations. The second solve is faster as it results from a grid refinement of the first solve, and takes the solution of the first solve as a first, good guess. Note that there are two pages in the PDF and in the second page I show the time · n_procs.
> 
> As you can see, the scaling is better than before, especially up to 8 processes (which means about 15,000 unknowns per process, which is, as I recall, cited as a good minimum on the website.
> 
> I am currently trying to run  make streams NPMAX=8, but the cluster is extraordinarily crowded today and it does not like my interactive jobs. I will try to run them asap.
> 
> The main issue now, however, is again the first issue: the Generalizeid Davidson method does not converge to the physically correct negative eigenvalue (it should be about -0.05 as Krylov-Schur gives me). In stead it stays stuck at some small positive eigenvalue of about +0.0002. It looks as if the solver really does not like passing the eigenvalue = 0 barrier, a behavior I also see in smaller simulations, where the convergence is greatly slowed down when crossing this.
> 
> However, this time, for this big simulation, just increasing NCV does not do the trick, at least not until NCV=2048.
> 
> Also, I tried to use target magnitude without success either.
> 
> I started implementing the capability to start with Krylov-Schur and then switch to GD with EPSSetInitialSpace when a certain precision has been reached, but then realized it might be a bit of overkill as the SLEPC solution phase in my code is generally not more than 15% of the time. There are probably other places where I can gain more than a few percents.
> 
> However, if there is another trick that can make GD to work, it would certainly be appreciated, as in my experience it is really about 5 times faster than Krylov-Schur!
> 
> Thanks!
> 
> Toon