ParMETIS on simple domains correction

[oanaoana]

This PR closes #25691.

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[roystgnr]

I know it's hard to come up with a good answer to "at what point should we overrule the user and stop trusting Parmetis", but the answer in the docs is 28, the answer in the comment is 32, and the answer in the code is 20? :-D

I don't see any other problems here, but I'll wait until after your planned squash/rebase/etc before submitting an official review.

[oanaoana]

Good catch! With the going back and forth on the figs and doc I didn't get to make sure it's consistent everywhere. I would have noticed after civet runs and I give it another look. Annoying one can't run all the civet tests before pushing, the local tests aren't always enough.

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[lindsayad]

So it sounded like you guys were able to reproduce the poor performance of parmetis with small local element counts without PetscExternalPartitioner?

[oanaoana]

@lindsayad yeah, using the libmesh one for example. The behaviour is not identical and depends on how the partitioner is initialized. There is certainly a difference between Libmesh and Petsc but the partitioning becomes poor at low elements per process in either case and almost for any initialization. So it made most sense to do a switch for the edge cases.

[NamjaeChoi]

@YaqiWang @jthano

[roystgnr]

partitioning becomes poor at low elements per process in either case

Well, the trick was that in the libMesh case the partitioning becomes better at very low elements per process ... because it turns out that we specifically test for that and switch from Parmetis to serialization+Metis. We don't test robustly enough, so the problem is still reproduceable in some cases, but according to the git logs I hit even worse cases (crashes, not just bad partitioning) back in 2012 and added this same sort of workaround then.

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Job Coverage on 1a91538 wanted to post the following:

Framework coverage

	843ddc	#27691 1a9153
	Total	Total	+/-	New
Rate	85.09%	85.09%	+0.00%	100.00%
Hits	104028	104032	+4	4
Misses	18226	18226	-	0

Diff coverage report

Full coverage report

Modules coverage

Coverage did not change

Full coverage reports

Reports

• framework
• chemical_reactions
• combined
• contact
• electromagnetics
• external_petsc_solver
• fluid_properties
• fsi
• functional_expansion_tools (FAILED)
• geochemistry
• heat_transfer
• level_set
• misc
• navier_stokes
• optimization
• peridynamics
• phase_field
• porous_flow
• ray_tracing
• rdg
• reactor
• richards
• scalar_transport
• solid_mechanics
• solid_properties
• stochastic_tools
• thermal_hydraulics
• xfem

This comment will be updated on new commits.

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Job Coverage on 1a91538 wanted to post the following:

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