Jed, I guess you can stick to Z as eigenvectors or you can allow Z to be
anything a user defines.
Jie
- Original Message -
From: "Jed Brown"
To: "For users of the development version of PETSc"
Sent: Sunday, March 3, 2013 4:15:05 PM
Subject: Re: [petsc-dev] Deflated Krylov solvers for
Barry, Jed pointed out the paper by Tang et al. That paper (Table 1 in page
348) contains a very comprehensive view of different ways to compose
preconditioners with deflation. Even though the paper talks about only CG, but
I guess the methods in general apply to various Krylov methods (I haven'
one and the
same?
I don't know the answer but if we knew the answer it would help us understand
how/where deflation might belong in PETSc (or maybe multiple places).
Barry
On Mar 2, 2013, at 9:43 PM, Jie Chen wrote:
> Mark, Barry, Jed,
>
> You guys raised quite a few
Mark, Barry, Jed,
You guys raised quite a few questions, meanwhile I found a mistake in my note.
I think I should rewrite the note to incorporate a more comprehensive view.
Hopefully the new note will answer you questions (at least to a certain
degree). I have something very important to finish
For the former case, you are not trying to squeeze one subdomain to one compute
node, are you? Why is it memory limited?
- Original Message -
From: "Jed Brown"
To: "For users of the development version of PETSc"
Sent: Friday, March 1, 2013 11:53:35 PM
Subject: Re: [petsc-dev] Deflated K
I second this. How many subdomains for a 1 billion unknown problem?
Jie
- Original Message -
From: "Jed Brown"
To: "For users of the development version of PETSc"
Sent: Friday, March 1, 2013 11:43:35 PM
Subject: Re: [petsc-dev] Deflated Krylov solvers for PETSc
An alternative descrip
Sometimes the convergence rate that is calculated based on the ratio between
lambda_max and lambda_min is rather pessimistic. The distribution of
eigenvalues plays a critical role in convergence. The common argument for the
effectiveness of eigenvector deflation is that "a few extreme eigenvalue
I think the number of deflation vectors should not be large. So the K_c here is
a small matrix, and whether Y is dense or sparse does not make a big
difference. In this regard, deflation is not exactly the same as one V-cycle.
For multigrid, you coarsen a grid of size 1,000,000 to 500,000. But f
Barry
On Feb 26, 2013, at 10:58 PM, Jie Chen wrote:
> To whomever is interested in deflated Krylov solvers:
>
> Deflation is very useful technique for accelerating the convergence of Krylov
> iterations. It seems to me that deflation is not supported in PETSc, except
> for the
My personal experience is to use approximate eigenvectors to deflate conjugate
gradient. In that regard, it is kinda like DGMRES, except that the iterative
method is different. A lot of situations I have seen use eigenvectors, but just
as what Vuik does, you never know when someone will propose
AMG in that low-energy
eigenvectors are processed incrementally and used to define the new coarse
grid.
On Tue, Feb 26, 2013 at 11:58 PM, Jie Chen < jiechen at mcs.anl.gov > wrote:
To whomever is interested in deflated Krylov solvers:
Deflation is very useful technique for accelerating th
ion myself for the moment.
Jie
--
Jie Chen
Mathematics and Computer Science Division
Argonne National Laboratory
Address: 9700 S Cass Ave, Bldg 240, Lemont, IL 60439
Phone: (630) 252-3313
Email: jiechen at mcs.anl.gov
Homepage: http://www.mcs.anl.gov/~jiechen
Oh, in KSPSetTolerances(), the outer_rtol should be the inner_rtol instead...
Could you push a fix for me please?
Jie
- Original Message -
From: "Jed Brown"
To: "Jie Chen"
Cc: "For users of the development version of PETSc" ,
"Hong Zhang"
Se
I am in fact somewhat reluctant to push out everything before it is formally
published and fully tested. The patch consists of more than one algorithmic
developments that may be far away from maturity (but they are likely to work),
though the authors might be the only ones who care about the new
Then do you know who wrote the code? Hong said it was you.
Hong is trying to modify the code but there is something wrong. I am helping to
see what is the problem. The code itself is fine.
Jie
- Original Message -
From: "Jed Brown"
To: "Jie Chen" , "For
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