Document performance expectations

[jedbrown]

What are good problem sizes AmgX? This is arguably the job of AmgX itself, but it would be useful for the wrapper documentation to say something about problem sizes or time to solution. For example, I added these options to the GAMG configuration and find that on a 2-socket E5-2687W (ca. 2012 8-core Sandy Bridge Xeon CPUs), it outperforms a P100 running AmgX AGG for all problem sizes.

-mg_levels_ksp_max_it 1 -mg_levels_ksp_type richardson

Meanwhile, AmgX Classical (clearly the variant that has been optimized) outperforms this CPU GAMG configurations for solve times longer than about 15ms (a 50x50x50 problem size).

This isn't a comparison of contemporary hardware (the P100 is more expensive, uses more power, and is several years more recent), but gives a rough picture of what someone could expect.

[jedbrown]

I guess this is the point of the notebook on figshare, but a link or reproduced figure from the repository would still be useful to anyone that finds your software first.

[piyueh]

We hope visitors to this repo think we are merely sharing a tool we used in our research, instead of promoting something or comparing different libraries. Also, we don't know how AmgX performs beyond our CFD codes. After all, different types of linear equations, solver configurations, and hardware can yield different performance results. So we leave out performance results to prevent the visitors from getting a biased impression.

But I do agree that it's helpful to provide some performance expectations with the poisson example. Given that the matrix & RHS are hard coded in this example, users can expect to have similar performances using provided solver configurations and similar hardware. Thus, users can check if there is any problem when getting obviously different performances.