[petsc-users] Direct linear solver in Petsc

[Mark Adams]

On Fri, Jun 12, 2020 at 12:56 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?
>

No. Direct solvers are about O(N^2) complexity and iteratives solvers can
be O(N) - O(N^inf)


> 2. Is the native Petsc direct solver (using KSPPREONLY and PCLU) designed
> to solve dense system or sparse system?
>

sparse.


> 3. Is the native Petsc direct solver comparable to SuperLU and MUMPS in
> performance? Do they use different algorithms?
>

PETSc's is only in serial and CPU. MUMPS and SuperLU are MPI parallel.
SuperLU runs on GPUs.

SuperLU and MUMPS have more optimizations, such that there is probably a
significant difference on some problems but it's hard to say in general.


>
> Thanks in advance for your help.
>
> Best Regards,
> Qin
>
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