Fair enough. I wiped out all references to petsc in my code and started from
scratch and used just the options you mentioned.. and I get good convergence as
first reported in the PCMG reference! I have attached the output. Now that it
is behaving, could you recommend some options to exercise the multigrid?
Thanks a lot for your time (and patience!)
----------------------
KSP Object: 8 MPI processes
type: gmres
GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
Orthogonalization with no iterative refinement
GMRES: happy breakdown tolerance 1e-30
maximum iterations=1, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=1e+10
left preconditioning
using PRECONDITIONED norm type for convergence test
PC Object: 8 MPI processes
type: bjacobi
block Jacobi: number of blocks = 8
Local solve is same for all blocks, in the following KSP and PC objects:
KSP Object: (sub_) 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000
left preconditioning
using NONE norm type for convergence test
PC Object: (sub_) 1 MPI processes
type: ilu
ILU: out-of-place factorization
0 levels of fill
tolerance for zero pivot 1e-12
using diagonal shift to prevent zero pivot
matrix ordering: natural
factor fill ratio given 1, needed 1
Factored matrix follows:
Matrix Object: 1 MPI processes
type: seqaij
rows=9015, cols=9015
package used to perform factorization: petsc
total: nonzeros=517777, allocated nonzeros=517777
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 3476 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object: 1 MPI processes
type: seqaij
rows=9015, cols=9015
total: nonzeros=517777, allocated nonzeros=517777
total number of mallocs used during MatSetValues calls =0
using I-node routines: found 3476 nodes, limit used is 5
linear system matrix = precond matrix:
Matrix Object: 8 MPI processes
type: mpiaij
rows=75000, cols=75000
total: nonzeros=4427800, allocated nonzeros=4427800
total number of mallocs used during MatSetValues calls =0
using I-node (on process 0) routines: found 3476 nodes, limit used is 5
----- Original Message -----
From: "Barry Smith" <[email protected]>
To: "PETSc users list" <petsc-users at mcs.anl.gov>
Sent: Wednesday, May 2, 2012 10:34:17 AM
Subject: Re: [petsc-users] Multigrid
Run with -pc_type ml -ksp_type fgmres -ksp_max_it 100 -ksp_view and
NOTHING else. Don'ts set any KSP or PC options in the code! Then send us ALL
the output.
Barry
I am getting all confused with "I ran with these options and this happened, I
ran with these options and this happened, I ran with these options and this
happened". I am getting information overload with too much information and yet
not enough information.
On May 2, 2012, at 12:27 PM, Karthik Duraisamy wrote:
> Hello,
>
> With PCML, I tried
>
> -mg_coarse_pc_type redundant ; -mg_coarse_ksp_type preonly ;
> KSPSetType(ksp, KSPGMRES);
>
> and the residual still diverges after a while. Strangely, if I use PCMG (with
> 0 levels), it works OK, but not with PCML.
>
> This is definitely strange. Here is the entire piece of relevant code.
>
> When initializing Petsc, I do the following: (let's call this the first bit
> and I do this only once)
>
> KSPSetOperators(ksp, A_, A_, SAME_NONZERO_PATTERN);
> KSPSetInitialGuessKnoll(ksp, PETSC_TRUE);
> KSPSetType(ksp, KSPFGMRES);
> KSPGMRESSetRestart(ksp, 100);
> KSPSetFromOptions(ksp);
>
>
> Then for each outer solver iteration: (let's call this the second bit and I
> do this every outer iteration)
>
> PC pc;
> KSPGetPC(ksp,&pc);
> PCSetType(pc, PCMG);
> KSPSetOperators(ksp, A_, A_, SAME_NONZERO_PATTERN);
> PetscOptionsSetValue("-ksp_initial_guess_nonzero", "true");
> KSPSetType(ksp, KSPGMRES);
> KSPGMRESSetRestart(ksp, 100);
> KSPSetFromOptions(ksp);
>
>
> I have tried various combinations of preconditioners and smoothers (including
> fgmres, bcgsl, etc) but the only combination that works is the above. Any of
> the PCML options that I have tried failed.
>
> Notes:
> - If I keep both of the above bits, it converges very well
>
> - If I keep both of the above bits, but replace PCMG with PCML, it diverges
> quickly
>
> - If I removed the first bit and kept the second bit, the residuals diverge
> even with PCMG
>
> - If I keep the first bit and remove the second bit, the residuals diverge
> eventually, but at a slow rate
>
>
> I am very confident with the rest of the code as I've been using PETSc (with
> just the first bit) for 3 years on 100s of problems.
>
> Regards,
> Karthik
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> ----- Original Message -----
> From: "Barry Smith" <bsmith at mcs.anl.gov>
> To: "PETSc users list" <petsc-users at mcs.anl.gov>
> Sent: Wednesday, May 2, 2012 6:02:06 AM
> Subject: Re: [petsc-users] Multigrid
>
>
> This is likely helping a great deal:
>
> KSPGMRESSetRestart(ksp, 100);
>
> You can try this with ml also
>
> On May 2, 2012, at 1:33 AM, Karthik Duraisamy wrote:
>
>> Hello again,
>>
>> I played with BoomerAMG and ML (for the 2D problem with a reasonable
>> condition number), and so far, they haven't worked (the residual eventually
>> diverges). The options that I am using are (for instance)
>>
>> PC pc;
>> KSPGetPC(ksp,&pc);
>> PetscOptionsSetValue("-ksp_type", "gmres");
>
> Here you NEED fgmres since the smoother is gmres by default. You can see
> this with -ksp_view
>
>> KSPSetOperators(ksp, A_, A_, SAME_NONZERO_PATTERN);
>> PetscOptionsSetValue("-ksp_initial_guess_nonzero", "true");
>> PCSetType(pc, PCML);
>> PetscOptionsSetValue("-pc_ml_maxNlevels", "3");
>> PetscOptionsSetValue("-mg_coarse_ksp_type","richardson");
>> PetscOptionsSetValue("-mg_coarse_pc_type","sor");
>> PetscOptionsSetValue("-mg_coarse_pc_sor_its","8");
>
> Just use -mg_coarse_pc_type redundant -mg_coarse_ksp_type preonly instead of
> the above.
>
>
> Barry
>
>> PetscOptionsSetValue("-ksp_monitor","1");
>> KSPSetFromOptions(ksp);
>
>
>>
>> I have replaced KSP with bcgsl, fgmres, etc.
>>
>> As I mentioned earlier, the following works like a charm:
>>
>> PC pc;
>> KSPGetPC(ksp,&pc);
>> PCSetType(pc, PCMG);
>> KSPSetOperators(ksp, A_, A_, SAME_NONZERO_PATTERN);
>> PetscOptionsSetValue("-ksp_initial_guess_nonzero", "true");
>> KSPSetType(ksp, KSPGMRES);
>> KSPGMRESSetRestart(ksp, 100);
>> KSPSetFromOptions(ksp);
>>
>>
>> Regards,
>> Karthik.
>>
>>
>>
>> ----- Original Message -----
>> From: "Barry Smith" <bsmith at mcs.anl.gov>
>> To: "PETSc users list" <petsc-users at mcs.anl.gov>
>> Sent: Tuesday, May 1, 2012 9:14:05 PM
>> Subject: Re: [petsc-users] Multigrid
>>
>>
>> On May 1, 2012, at 6:00 PM, Karthik Duraisamy wrote:
>>
>>> So as I understand it, GMRES is used as a preconditioner and as a solver
>>> when I use PCMG with defaults. If this is the case, I should be able to
>>> recreate this set up without the PCMG. Any pointers as to how this can be
>>> done?
>>>
>>> Also, yes indeed, my mesh is completely unstructured, so I will have to use
>>> ml or boomeramg.
>>>
>>> The problems that I am attempting involve RANS of compressible turbulent
>>> combustion (finite volume, steady). The high condition numbers are because
>>> of the extreme grid stretching and stiff source terms (in the turbulence
>>> and combustion model).
>>
>> With a condition number like that I wouldn't even consider using double
>> precision, I think you would just be computing meaningless noise. With
>> petsc-dev you can use quad precision ./configure --with-precision=__float128
>> using recent GNU compilers
>> (no we haven't tested the gfortran sides of things).
>>
>> Barry
>>
>>
>>> I have been trying a reduced problem in these 2D test cases, in which the
>>> condition number is only 1e7.
>>>
>>> Thanks,
>>> Karthik.
>>>
>>>
>>> ----- Original Message -----
>>> From: "Mark F. Adams" <mark.adams at columbia.edu>
>>> To: "PETSc users list" <petsc-users at mcs.anl.gov>
>>> Sent: Tuesday, May 1, 2012 3:50:31 PM
>>> Subject: Re: [petsc-users] Multigrid
>>>
>>>
>>> Also, note that PCMG can not create coarse grid spaces for an (MPI)AIJ
>>> matrix. If you use regular grids (DA?) then PETSc can construct geometric
>>> multigrid coarse grid spaces, although I don't know if PCMG will construct
>>> these for you (I don't think it will and I can see from your output that
>>> PCMG just used one grid). 'ml', hypre' and 'gamg' (a native AMG solver)
>>> will do real AMG solvers for you. All three can work on a similar class of
>>> problems.
>>>
>>>
>>> Also, you mention that you have a condition number of 1.e20. That is
>>> astronomical for such a small problem. How did you compute that number? Do
>>> you know where the ill-conditioning comes from? Is this an elliptic
>>> operator?
>>>
>>>
>>> Mark
>>>
>>>
>>>
>>>
>>> On May 1, 2012, at 6:31 PM, Matthew Knepley wrote:
>>>
>>>
>>>
>>> On Tue, May 1, 2012 at 6:27 PM, Karthik Duraisamy < dkarthik at
>>> stanford.edu > wrote:
>>>
>>>
>>>
>>> The following was output for the very first iteration whereas what I had
>>> attached earlier was output every iteration. I am still a bit perplexed
>>> because PCMG drops the residual like a rock (after the first few iterations
>>> whereas with no PCMG, it is very slow)
>>>
>>>
>>>
>>> Because the smoother IS the solver you were using before. Just like I said
>>> last time, what you are doing is
>>> wrapping up the same solver you used before, sticking it in another GMRES
>>> loop, and only looking at the
>>> outer loop. This has nothing to do with MG.
>>>
>>>
>>> Matt
>>>
>>>
>>> KSP Object: 8 MPI processes
>>> type: gmres
>>> GMRES: restart=100, using Classical (unmodified) Gram-Schmidt
>>> Orthogonalization with no iterative refinement
>>> GMRES: happy breakdown tolerance 1e-30
>>> maximum iterations=1, initial guess is zero
>>> using preconditioner applied to right hand side for initial guess
>>> tolerances: relative=0.01, absolute=1e-08, divergence=1e+10
>>> left preconditioning
>>> using DEFAULT norm type for convergence test
>>> PC Object: 8 MPI processes
>>> type: mg
>>> MG: type is MULTIPLICATIVE, levels=1 cycles=v
>>> Cycles per PCApply=1
>>> Not using Galerkin computed coarse grid matrices
>>> Coarse grid solver -- level -------------------------------
>>> KSP Object: (mg_levels_0_) 8 MPI processes
>>> type not yet set
>>> maximum iterations=1, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> left preconditioning
>>> using DEFAULT norm type for convergence test
>>> PC Object: (mg_levels_0_) 8 MPI processes
>>> type not yet set
>>> linear system matrix = precond matrix:
>>> Matrix Object: 8 MPI processes
>>> type: mpiaij
>>> rows=75000, cols=75000
>>> total: nonzeros=4427800, allocated nonzeros=4427800
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node (on process 0) routines: found 3476 nodes, limit used is 5
>>>
>>>
>>> ----- Original Message -----
>>> From: "Matthew Knepley" < knepley at gmail.com >
>>> To: "PETSc users list" < petsc-users at mcs.anl.gov >
>>> Sent: Tuesday, May 1, 2012 3:22:56 PM
>>> Subject: Re: [petsc-users] Multigrid
>>>
>>>
>>> On Tue, May 1, 2012 at 6:18 PM, Karthik Duraisamy < dkarthik at
>>> stanford.edu > wrote:
>>>
>>>
>>>
>>> Hello,
>>>
>>> Sorry (and thanks for the reply). I've attached the no multigrid case. I
>>> didn't include it because (at least to the untrained eye, everything looks
>>> the same).
>>>
>>>
>>>
>>> Did you send all the output from the MG case? There must be a PC around it.
>>> By default its GMRES, so there would be
>>> an extra GMRES loop compared to the case without MG.
>>>
>>>
>>> Matt
>>>
>>>
>>> Regards,
>>> Karthik
>>>
>>> KSP Object: 8 MPI processes
>>> type: gmres
>>> GMRES: restart=100, using Classical (unmodified) Gram-Schmidt
>>> Orthogonalization with no iterative refinement
>>> GMRES: happy breakdown tolerance 1e-30
>>> maximum iterations=1
>>> using preconditioner applied to right hand side for initial guess
>>> tolerances: relative=1e-05, absolute=1e-50, divergence=1e+10
>>> left preconditioning
>>> using nonzero initial guess
>>> using PRECONDITIONED norm type for convergence test
>>> PC Object: 8 MPI processes
>>> type: bjacobi
>>> block Jacobi: number of blocks = 8
>>> Local solve is same for all blocks, in the following KSP and PC objects:
>>> KSP Object: (sub_) 1 MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (sub_) 1 MPI processes
>>> type: ilu
>>> ILU: out-of-place factorization
>>> 0 levels of fill
>>> tolerance for zero pivot 1e-12
>>> using diagonal shift to prevent zero pivot
>>> matrix ordering: natural
>>> factor fill ratio given 1, needed 1
>>> Factored matrix follows:
>>> Matrix Object: 1 MPI processes
>>> type: seqaij
>>> rows=9015, cols=9015
>>> package used to perform factorization: petsc
>>> total: nonzeros=517777, allocated nonzeros=517777
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node routines: found 3476 nodes, limit used is 5
>>> linear system matrix = precond matrix:
>>> Matrix Object: 1 MPI processes
>>> type: seqaij
>>> rows=9015, cols=9015
>>> total: nonzeros=517777, allocated nonzeros=517777
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node routines: found 3476 nodes, limit used is 5
>>> linear system matrix = precond matrix:
>>> Matrix Object: 8 MPI processes
>>> type: mpiaij
>>> rows=75000, cols=75000
>>> total: nonzeros=4427800, allocated nonzeros=4427800
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node (on process 0) routines: found 3476 nodes, limit used is 5
>>>
>>>
>>> ----- Original Message -----
>>> From: "Matthew Knepley" < knepley at gmail.com >
>>> To: "PETSc users list" < petsc-users at mcs.anl.gov >
>>> Sent: Tuesday, May 1, 2012 3:15:14 PM
>>> Subject: Re: [petsc-users] Multigrid
>>>
>>>
>>> On Tue, May 1, 2012 at 6:12 PM, Karthik Duraisamy < dkarthik at
>>> stanford.edu > wrote:
>>>
>>>
>>>
>>> Hello Barry,
>>>
>>> Thank you for your super quick response. I have attached the output of
>>> ksp_view and it is practically the same as that when I don't use PCMG. The
>>> part I don't understand is how PCMG able to function at the zero grid level
>>> and still produce a much better convergence than when using the default PC.
>>> Is there any additional smoothing or interpolation going on?
>>>
>>>
>>>
>>> You only included one output, so I have no way of knowing what you used
>>> before. However, this is running GMRES/ILU.
>>>
>>>
>>> Also, for Algebraic Multigrid, would you recommend BoomerAMG or ML ?
>>>
>>>
>>>
>>> They are different algorithms. Its not possible to say generally that one
>>> is better. Try them both.
>>>
>>>
>>> Matt
>>>
>>>
>>> Best regards,
>>> Karthik.
>>>
>>> type: mg
>>> MG: type is MULTIPLICATIVE, levels=1 cycles=v
>>> Cycles per PCApply=1
>>> Not using Galerkin computed coarse grid matrices
>>> Coarse grid solver -- level -------------------------------
>>> KSP Object: (mg_levels_0_) 8 MPI processes
>>> type: gmres
>>> GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
>>> Orthogonalization with no iterative refinement
>>> GMRES: happy breakdown tolerance 1e-30
>>> maximum iterations=1, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> left preconditioning
>>> using PRECONDITIONED norm type for convergence test
>>> PC Object: (mg_levels_0_) 8 MPI processes
>>> type: bjacobi
>>> block Jacobi: number of blocks = 8
>>> Local solve is same for all blocks, in the following KSP and PC objects:
>>> KSP Object: (mg_levels_0_sub_) 1 MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (mg_levels_0_sub_) 1 MPI processes
>>> type: ilu
>>> ILU: out-of-place factorization
>>> 0 levels of fill
>>> tolerance for zero pivot 1e-12
>>> using diagonal shift to prevent zero pivot
>>> matrix ordering: natural
>>> factor fill ratio given 1, needed 1
>>> Factored matrix follows:
>>> Matrix Object: 1 MPI processes
>>> type: seqaij
>>> rows=9015, cols=9015
>>> package used to perform factorization: petsc
>>> total: nonzeros=517777, allocated nonzeros=517777
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node routines: found 3476 nodes, limit used is 5
>>> linear system matrix = precond matrix:
>>> Matrix Object: 1 MPI processes
>>> type: seqaij
>>> rows=9015, cols=9015
>>> total: nonzeros=517777, allocated nonzeros=517777
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node routines: found 3476 nodes, limit used is 5
>>> linear system matrix = precond matrix:
>>> Matrix Object: 8 MPI processes
>>> type: mpiaij
>>> rows=75000, cols=75000
>>> total: nonzeros=4427800, allocated nonzeros=4427800
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node (on process 0) routines: found 3476 nodes, limit used is 5
>>> linear system matrix = precond matrix:
>>> Matrix Object: 8 MPI processes
>>> type: mpiaij
>>> rows=75000, cols=75000
>>> total: nonzeros=4427800, allocated nonzeros=4427800
>>> total number of mallocs used during MatSetValues calls =0
>>> using I-node (on process 0) routines: found 3476 nodes, limit used is 5
>>>
>>>
>>>
>>> ----- Original Message -----
>>> From: "Barry Smith" < bsmith at mcs.anl.gov >
>>> To: "PETSc users list" < petsc-users at mcs.anl.gov >
>>> Sent: Tuesday, May 1, 2012 1:39:26 PM
>>> Subject: Re: [petsc-users] Multigrid
>>>
>>>
>>> On May 1, 2012, at 3:37 PM, Karthik Duraisamy wrote:
>>>
>>>> Hello,
>>>>
>>>> I have been using PETSc for a couple of years with good success, but
>>>> lately as my linear problems have become stiffer (condition numbers of the
>>>> order of 1.e20), I am looking to use better preconditioners. I tried using
>>>> PCMG with all the default options (i.e., I just specified my
>>>> preconditioner as PCMG and did not add any options to it) and I am
>>>> immediately seeing better convergence.
>>>>
>>>> What I am not sure of is why? I would like to know more about the default
>>>> parameters (the manual is not very explicit) and more importantly, want to
>>>> know why it is working even when I haven't specified any grid levels and
>>>> coarse grid operators. Any
>>>> help in this regard will be appreciated.
>>>
>>> First run with -ksp_view to see what solver it is actually using.
>>>
>>> Barry
>>>
>>>>
>>>> Also, ultimately I want to use algebraic multigrid so is PCML a better
>>>> option than BoomerAMG? I tried BoomerAMG with mixed results.
>>>>
>>>> Thanks,
>>>> Karthik
>>>>
>>>>
>>>>
>>>> --
>>>>
>>>> =======================================
>>>> Karthik Duraisamy
>>>> Assistant Professor (Consulting)
>>>> Durand Building Rm 357
>>>> Dept of Aeronautics and Astronautics
>>>> Stanford University
>>>> Stanford CA 94305
>>>>
>>>> Phone: 650-721-2835
>>>> Web: www.stanford.edu/~dkarthik
>>>> =======================================
>>>
>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>
>
