[petsc-users] Performance of PETSc TS solver

[Jin, Shuangshuang]

Hello, Jed and Barry, thanks for your reply.

We are solving a power system dynamic simulation problem. We set up the DAE equations and its Jacobian matrix, and would like to use the Trapezoid method to solve it. 

That's also the reason why we chose TSTHETA. From the PETSc manual, we read that:

"-ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN). This method can be applied to DAE.
For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN)."

I haven't heard of ARKIMEX or ROSW before. Are they some external packages or DAE solvers that implement the Trapezoid method?

I have also tried the -ksp_type preonly -pc_type lu option you indicated but failed. The PETSC ERROR messages are: No support for this operation for this object type! Matrix format mpiaij does not have a built-in PETSc LU!

Attached please see the log_summary for running the TSTHETA with -ts_theta_theta 0.5 and its default ksp solver. Please help me to evaluate the performance and see what's the bottleneck of the slow computation speed.

Thanks a lot!

Shuangshuang


 



-----Original Message-----
From: Barry Smith [mailto:bsmith at mcs.anl.gov] 
Sent: Monday, August 12, 2013 6:39 PM
To: Jed Brown
Cc: Jin, Shuangshuang; petsc-users at mcs.anl.gov
Subject: Re: [petsc-users] Performance of PETSc TS solver


   Also always send the output from running with -log_summary whenever you ask performance questions so we know what kind of performance it is getting.

   Barry

On Aug 12, 2013, at 8:14 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> "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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