On Thu, Apr 23, 2009 at 11:07 AM, Nguyen, Hung V ERDC-ITL-MS <span dir="ltr"><<a href="mailto:Hung.V.Nguyen@usace.army.mil">Hung.V.Nguyen@usace.army.mil</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Hello,<br>
<br>
I tried to solver the SPD linear system with using cg/asm preconditioner and<br>
found that it doesn't scale well, see table below. Note: it does scale well<br>
with cg/jacobi preconditioner.<br>
<br>
Do you know why it doesn't scale?</blockquote><div><br>ILU is incredibly unpredictable. You have not provided the Jacobi numbers, but<br>the particular nonzero pattern of the non-overlapping matrix must be much more<br>
amenable. Also, this is a really really bad preconditioner for your system. I would<br>put my time into figuring out why my system is so ill-conditioned and try to<br>formulate a good preconditioner, like an approximate system, etc.<br>
<br> Matt<br> </div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"><br>
Thanks,<br>
<br>
-hung<br>
<br>
Number Pes Solver Time (secs) #it<br>
1 31.317345 544<br>
2 263.172225 6959<br>
4 734.828840 23233<br>
8 805.217591 41250<br>
16 611.813716 49262<br>
32 345.331928 49792<br>
64 212.084555 53771<br>
<br>
<br>
---<br>
1 : aprun -n 1 ./test_matrix_read -ksp_type cg -pc_type asm -pc_asm_type<br>
basic -sub_pc_type ilu -sub_ksp_type preonly -ksp_rtol 1.0e-12 -ksp_max_it<br>
100000<br>
Time in PETSc solver: 31.317345 seconds<br>
The number of iteration = 544<br>
The solution residual error = 1.658653e-08<br>
2 norm 7.885361e-07<br>
infinity norm 6.738382e-09<br>
1 norm 2.124207e-04<br>
<br>
Application 679466 resources: utime 0, stime 0<br>
************************ Beginning new run ************************<br>
<br>
2 : aprun -n 2 ./test_matrix_read -ksp_type cg -pc_type asm -pc_asm_type<br>
basic -sub_pc_type ilu -sub_ksp_type preonly -ksp_rtol 1.0e-12 -ksp_max_it<br>
100000<br>
Time in PETSc solver: 263.172225 seconds<br>
The number of iteration = 6959<br>
The solution residual error = 1.794494e-08<br>
2 norm 6.579571e-07<br>
infinity norm 8.745052e-09<br>
1 norm 1.907733e-04<br>
<br>
-- Here is info about matrix A:<br>
<br>
Computed <structure:nrows> as <178353><br>
Computed <structure:symmetry> as <0><br>
Computed <structure:nnzeros> as <3578321><br>
Computed <structure:max-nnzeros-per-row> as <27><br>
Computed <structure:min-nnzeros-per-row> as <6><br>
Computed <structure:left-bandwidth> as <76553><br>
Computed <structure:right-bandwidth> as <76553><br>
<br>
<br>
<br>
</blockquote></div><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<br>