Cg/asm doesn't scale

[Matthew Knepley]

On Thu, Apr 23, 2009 at 11:07 AM, Nguyen, Hung V ERDC-ITL-MS <
Hung.V.Nguyen at usace.army.mil> wrote:

> Hello,
>
> I tried to solver the SPD linear system with using cg/asm preconditioner
> and
> found that it doesn't scale well, see table below. Note: it does scale well
> with cg/jacobi preconditioner.
>
> Do you know why it doesn't scale?


ILU is incredibly unpredictable. You have not provided the Jacobi numbers,
but
the particular nonzero pattern of the non-overlapping matrix must be much
more
amenable. Also, this is a really really bad preconditioner for your system.
I would
put my time into figuring out why my system is so ill-conditioned and try to
formulate a good preconditioner, like an approximate system, etc.

  Matt


>
> Thanks,
>
> -hung
>
> Number Pes   Solver Time (secs)  #it
> 1                31.317345         544
> 2               263.172225        6959
> 4             734.828840        23233
> 8             805.217591        41250
> 16            611.813716        49262
> 32            345.331928        49792
> 64            212.084555        53771
>
>
> ---
> 1 :  aprun -n 1  ./test_matrix_read  -ksp_type cg -pc_type asm -pc_asm_type
> basic   -sub_pc_type ilu -sub_ksp_type preonly -ksp_rtol 1.0e-12
> -ksp_max_it
> 100000
> Time in PETSc solver: 31.317345 seconds
> The number of iteration       = 544
> The solution residual error = 1.658653e-08
> 2 norm 7.885361e-07
>  infinity norm 6.738382e-09
>  1 norm 2.124207e-04
>
> Application 679466 resources: utime 0, stime 0
> ************************ Beginning new run ************************
>
> 2 :  aprun -n 2  ./test_matrix_read  -ksp_type cg -pc_type asm -pc_asm_type
> basic   -sub_pc_type ilu -sub_ksp_type preonly -ksp_rtol 1.0e-12
> -ksp_max_it
> 100000
> Time in PETSc solver: 263.172225 seconds
> The number of iteration       = 6959
> The solution residual error = 1.794494e-08
> 2 norm 6.579571e-07
>  infinity norm 8.745052e-09
>  1 norm 1.907733e-04
>
> -- Here is info about matrix A:
>
> Computed <structure:nrows> as <178353>
> Computed <structure:symmetry> as <0>
> Computed <structure:nnzeros> as <3578321>
> Computed <structure:max-nnzeros-per-row> as <27>
> Computed <structure:min-nnzeros-per-row> as <6>
> Computed <structure:left-bandwidth> as <76553>
> Computed <structure:right-bandwidth> as <76553>
>
>
>
>


-- 
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
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