[petsc-users] Direct linear solver in Petsc

[Mark Adams]

On Fri, Jun 12, 2020 at 1:18 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Jun 12, 2020 at 12:49 PM Qin Lu via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
>
>> Hello,
>>
>> I plan to solve a small sparse linear equation system using the direct
>> solver, since the number of unknowns is small (less than 1000). Here I got
>> a few questions:
>>
>> 1. Is there a general guide line on the size of the system that direct
>> solver is more efficient than iterative solver?
>>
>
> I would say at least to 50K unknowns, maybe 100K, depending on sparsity.
>

The dimension of your problem is important here, 1D is perfect in serial,
2D 100K at reachable, 100K in 3D is painful. And multiple dofs per vertex
don't hurt much so you could think of these numbers as vertices.


>
>
>> 2. Is the native Petsc direct solver (using KSPPREONLY and PCLU) designed
>> to solve dense system or sparse system?
>>
>
> Sparse. We use LAPACK for dense.
>
>
>> 3. Is the native Petsc direct solver comparable to SuperLU and MUMPS in
>> performance? Do they use different algorithms?
>>
>
> It is likely slower than SuperLU and not as robust as MUMPS, but there is
> no substitute for just running and comparing.
>
>   Thanks,
>
>     Matt
>
>
>> Thanks in advance for your help.
>>
>> Best Regards,
>> Qin
>>
>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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