[Trilinos-Users] [EXTERNAL] Recycling Conjugate Gradient (RCG) for poisson problem

Parks, Michael L mlparks at sandia.gov
Mon Nov 26 15:26:05 MST 2012


   If you have all the RHS vectors available simultaneously (I'm assuming you do not), using block CG might be most efficient. If the RHS vectors change slowly from one to the next, you can use the solution to the previous solve as the initial guess for the next solve. If neither of these are the case, Recycling CG is a good choice. I've used RCG preconditioned with ML before with no issues. RCG is meant to solve sequential linear systems. In particular, for the first system in the sequence, RCG should give exactly the same convergence behavior as CG. If you're not getting that behavior, there is an error somewhere. 

   If you want, please e-mail me the source code segment where you called RCG and I'll have a look over it. 


- Mike

Mike Parks
Sandia National Laboratories

> -----Original Message-----
> From: trilinos-users-bounces at software.sandia.gov [mailto:trilinos-users-
> bounces at software.sandia.gov] On Behalf Of Bart Janssens
> Sent: Monday, November 26, 2012 2:24 PM
> To: trilinos-users at software.sandia.gov
> Subject: [EXTERNAL] [Trilinos-Users] Recycling Conjugate Gradient (RCG) for
> poisson problem
> Hello,
> I need to solve a series of Poisson problems, where the matrix stays exactly the
> same every timestep but the RHS changes. I'm not sure what the best approach
> is, I've tried pre-factoring the matrix using MUMPS, but this consumes way too
> much memory so it won't scale beyond 1.5M mesh nodes on our cluster.
> I thought maybe the recycling methods might help, but I'm not sure how well
> these are supposed to work on a problem like this. In Trilinos
> 11.0.3 (and 10.12 before), the RCG method seems to give strange
> results: a Belos BlockCG solve preconditioned with ML runs in about 90 CG
> iterations, but when keeping all settings the same except for changing to RCG,
> it won't converge anymore (stops at 1000 iterations, even on the first solve).
> Does anyone have any pointers for using the RCG method, or other ideas of
> how I could accelerate the convergence for this problem, possibly exploiting
> the fact that the matrix stays the same for the entire simulation? The poisson
> problem is for a scalar on a 3D hexahedral finite element mesh.
> Kind regards,
> --
> Bart
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