[petsc-users] Performance of PETSc TS solver

[Jed Brown]

"Jin, Shuangshuang" <Shuangshuang.Jin at pnnl.gov> writes:

> Hello, PETSc developers,
>         I have a question regarding the performance of PETSc TS solver
>         expecially the TSTHETA. I used it to solve my DAE equations. 

TSTHETA is not L-stable and not stiffly accurate, so it's not normally
something that you'd want to use for a DAE.  Make sure you're getting
meaningful results and try switching to something like an ARKIMEX or
ROSW since those are likely better for your problem.

>   I have recorded the solution times when different numbers of processors are used:
>
> 2 processors: 1021 seconds,
> 4 processors: 587.244 seconds,
> 8 processors: 421.565 seconds,
> 16 processors: 355.594 seconds,
> 32 processors: 322.28 seconds,
> 64 processors: 382.967 seconds.
>
> It seems like with 32 processors, it reaches the best
> performance. However, 322.28 seconds to solve such DAE equations is
> too slow than I expected.

The number of equations (1152) is quite small, so I'm not surprised
there is no further speedup.  Can you explain more about your equations?

>
> I have the following questions based on the above results:
> 1.      Is this the usual DAE solving time in PETSc to for the problem with this dimension?

That depends what your function is.

> 2.      I was told that in TS, by default, ksp uses GMRES, and the
> preconditioner is ILU(0), is there any other alterative ksp solver or
> options I should use in the command line to solve the problem much
> faster?

I would use -ksp_type preonly -pc_type lu for such small problems.  Is
the system dense?

> 3.      Do you have any other suggestion for me to speed up the DAE computation in PETSc?

Can you describe what sort of problem you're dealing with, what causes
the stiffness in your equations, what accuracy you want, etc.
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