On Tue, Aug 20, 2024 at 1:10 PM neil liu <liufi...@gmail.com> wrote:
> Thanks a lot for your explanation, Stefano. Very helpful.
> Yes. I am using dmplex to read a tetrahdra mesh from gmsh. With parmetis,
> the scaling performance is improved a lot.
> I will read your paper about how to change the basis for Nedelec elements.
>
> cpu # time for 500 ksp steps (s) parallel efficiency
> 2 546
> 4 224 120%
> 8 170 80%
> This results are much better than previous attempt. Then I checked the
> time spent by several Petsc built-in functions for the ksp solver.
>
> Functions time(2 cpus) time(4 cpus) time(8 cpus)
> VecMDot 78.32 43.28 30.47
> VecMAXPY 92.95 48.37 30.798
> MatMult 246.08 126.63 82.94
>
> It seems from cpu 4 to cpu 8, the scaling is not as good as from cpu 2 to
> cpu 4.
> Am I missing something?
>
Did you normalize by the number of calls?
Thanks,
Matt
> Thanks a lot,
>
> Xiaodong
>
>
> On Mon, Aug 19, 2024 at 4:15 AM Stefano Zampini <stefano.zamp...@gmail.com>
> wrote:
>
>> It seems you are using DMPLEX to handle the mesh, correct?
>> If so, you should configure using --download-parmetis to have a better
>> domain decomposition since the default one just splits the cells in chunks
>> as they are ordered.
>> This results in a large number of primal dofs on average (191, from the
>> output of ksp_view)
>> ...
>> Primal dofs : 176 204 191
>> ...
>> that slows down the solver setup.
>>
>> Again, you should not use approximate local solvers with BDDC unless you
>> know what you are doing.
>> The theory for approximate solvers for BDDC is small and only for SPD
>> problems.
>> Looking at the output of log_view, coarse problem setup (PCBDDCCSet), and
>> primal functions setup (PCBDDCCorr) costs 35 + 63 seconds, respectively.
>> Also, the 500 application of the GAMG preconditioner for the Neumann
>> solver (PCBDDCNeuS) takes 129 seconds out of the 400 seconds of the total
>> solve time.
>>
>> PCBDDCTopo 1 1.0 3.1563e-01 1.0 1.11e+06 3.4 1.6e+03 3.9e+04
>> 3.8e+01 0 0 1 0 2 0 0 1 0 2 19
>> PCBDDCLKSP 2 1.0 2.0423e+00 1.7 9.31e+08 1.2 0.0e+00 0.0e+00
>> 2.0e+00 0 0 0 0 0 0 0 0 0 0 3378
>> PCBDDCLWor 1 1.0 3.9178e-02 13.4 0.00e+00 0.0 0.0e+00 0.0e+00
>> 1.0e+00 0 0 0 0 0 0 0 0 0 0 0
>> PCBDDCCorr 1 1.0 6.3981e+01 2.2 8.16e+10 1.6 0.0e+00 0.0e+00
>> 0.0e+00 11 11 0 0 0 11 11 0 0 0 8900
>> PCBDDCCSet 1 1.0 3.5453e+01 4564.9 1.06e+05 1.7 1.2e+03
>> 5.3e+03 5.0e+01 2 0 1 0 3 2 0 1 0 3 0
>> PCBDDCCKSP 1 1.0 6.3266e-01 1.3 0.00e+00 0.0 3.3e+02 1.1e+02
>> 2.2e+01 0 0 0 0 1 0 0 0 0 1 0
>> PCBDDCScal 1 1.0 6.8274e-03 1.3 1.11e+06 3.4 5.6e+01 3.2e+05
>> 0.0e+00 0 0 0 0 0 0 0 0 0 0 894
>> PCBDDCDirS 1000 1.0 6.0420e+00 3.5 6.64e+09 5.4 0.0e+00 0.0e+00
>> 0.0e+00 1 0 0 0 0 1 0 0 0 0 2995
>> PCBDDCNeuS 500 1.0 1.2901e+02 2.1 8.28e+10 1.2 0.0e+00 0.0e+00
>> 0.0e+00 22 12 0 0 0 22 12 0 0 0 4828
>> PCBDDCCoaS 500 1.0 5.8757e-01 1.8 1.09e+09 1.0 2.8e+04 7.4e+02
>> 5.0e+02 0 0 17 0 28 0 0 17 0 31 14901
>>
>> Finally, if I look at the residual history, I see a sharp decrease and a
>> very long plateau. This indicates a bad coarse space; as I said before,
>> there's no hope of finding a suitable coarse space without first changing
>> the basis of the Nedelec elements, which is done automatically if you
>> prescribe the discrete gradient operator (see the paper I have linked to in
>> my previous communication).
>>
>>
>>
>> Il giorno dom 18 ago 2024 alle ore 00:37 neil liu <liufi...@gmail.com>
>> ha scritto:
>>
>>> Hi, Stefano,
>>> Please see the attached for the information with 4 and 8 CPUs for the
>>> complex matrix.
>>> I am solving Maxwell equations (Attahced) using 2nd-order Nedelec
>>> elements (two dofs each edge, and two dofs each face).
>>> The computational domain consists of different mediums, e.g., vacuum and
>>> substrate (different permitivity).
>>> The PML is used to truncate the computational domain, absorbing the
>>> outgoing wave and introducing complex numbers for the matrix.
>>>
>>> Thanks a lot for your suggestions. I will try MUMPS.
>>> For now, I just want to fiddle with Petsc's built-in features to know
>>> more about it.
>>> Yes. 5000 is larger. Smaller value. e.g., 30, converges very slowly.
>>>
>>> Thanks a lot.
>>>
>>> Have a good weekend.
>>>
>>>
>>> On Sat, Aug 17, 2024 at 9:23 AM Stefano Zampini <
>>> stefano.zamp...@gmail.com> wrote:
>>>
>>>> Please include the output of -log_view -ksp_view -ksp_monitor to
>>>> understand what's happening.
>>>>
>>>> Can you please share the equations you are solving so we can provide
>>>> suggestions on the solver configuration?
>>>> As I said, solving for Nedelec-type discretizations is challenging, and
>>>> not for off-the-shelf, black box solvers
>>>>
>>>> Below are some comments:
>>>>
>>>>
>>>> - You use a redundant SVD approach for the coarse solve, which can
>>>> be inefficient if your coarse space grows. You can use a parallel direct
>>>> solver like MUMPS (reconfigure with --download-mumps and use
>>>> -pc_bddc_coarse_pc_type lu -pc_bddc_coarse_pc_factor_mat_solver_type
>>>> mumps)
>>>> - Why use ILU for the Dirichlet problem and GAMG for the Neumann
>>>> problem? With 8 processes and 300K total dofs, you will have around 40K
>>>> dofs per process, which is ok for a direct solver like MUMPS
>>>> (-pc_bddc_dirichlet_pc_factor_mat_solver_type mumps, same for Neumann).
>>>> With Nedelec dofs and the sparsity pattern they induce, I believe you
>>>> can
>>>> push to 80K dofs per process with good performance.
>>>> - Why 5000 of restart for GMRES? It is highly inefficient to
>>>> re-orthogonalize such a large set of vectors.
>>>>
>>>>
>>>> Il giorno ven 16 ago 2024 alle ore 00:04 neil liu <liufi...@gmail.com>
>>>> ha scritto:
>>>>
>>>>> Dear Petsc developers,
>>>>>
>>>>> Thanks for your previous help. Now, the PCBDDC can converge to 1e-8
>>>>> with,
>>>>>
>>>>> petsc-3.21.1/petsc/arch-linux-c-opt/bin/mpirun -n 8 ./app -pc_type
>>>>> bddc -pc_bddc_coarse_redundant_pc_type svd -ksp_error_if_not_converged
>>>>> -mat_type is -ksp_monitor -ksp_rtol 1e-8 -ksp_gmres_restart 5000 -ksp_view
>>>>> -pc_bddc_use_local_mat_graph 0 -pc_bddc_dirichlet_pc_type ilu
>>>>> -pc_bddc_neumann_pc_type gamg -pc_bddc_neumann_pc_gamg_esteig_ksp_max_it
>>>>> 10
>>>>> -ksp_converged_reason -pc_bddc_neumann_approximate -ksp_max_it 500
>>>>> -log_view
>>>>>
>>>>> Then I used 2 cases for strong scaling test. One case only involves
>>>>> real numbers (tetra #: 49,152; dof #: 324, 224 ) for matrix and rhs. The
>>>>> 2nd case involves complex numbers (tetra #: 95,336; dof #: 611,432) due
>>>>> to PML.
>>>>>
>>>>> Case 1:
>>>>> cpu # Time for 500 ksp steps (s) Parallel
>>>>> efficiency PCsetup time(s)
>>>>> 2 234.7
>>>>> 3.12
>>>>> 4 126.6
>>>>> 0.92 1.62
>>>>> 8 84.97
>>>>> 0.69 1.26
>>>>> However for Case 2,
>>>>> cpu # Time for 500 ksp steps (s) Parallel
>>>>> efficiency PCsetup time(s)
>>>>> 2 584.5
>>>>> 8.61
>>>>> 4 376.8
>>>>> 0.77 6.56
>>>>> 8 459.6
>>>>> 0.31 66.47
>>>>> For these 2 cases, I checked the time for PCsetup as an example. It
>>>>> seems 8 cpus for case 2 used too much time on PCsetup.
>>>>> Do you have any ideas about what is going on here?
>>>>>
>>>>> Thanks,
>>>>> Xiaodong
>>>>>
>>>>>
>>>>>
>>>>
>>>> --
>>>> Stefano
>>>>
>>>
>>
>> --
>> Stefano
>>
>
--
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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