change V-cycle tolerance criterion

[marinlauber]

Solve the pressure oscillation from #96

The fix is to implement a variable depth V-cycle. The criterion to pop! or push! a new level to the multigrid depends on the previous number of v-cycles necessary to reach convergence.

The convergence is measured with a L_\infty norm.

This also implements a basic logging capability to track the convergence of the multigrid solver (to be improved)

TO DO:

• Find the best value for the new tolerance criterion
• Check dependence on Float64/Float32
• Run the benchmark on CPU/GPU
• Clean logging of MultiGrid
• Better test for MultiGrid solver?

[weymouth]

Do we really need to do a V-cycle every time? If there is nothing going on, shouldn't it skip the loop like in the master?

[marinlauber]

I still need to benchmark and correct the tests before it's finalized.

[b-fg]

How's this? You still need to include the latest changes @marinlauber ?

[marinlauber]

Yes, this is not up to date, the latest change from master needs to be included, as well as the latest (my local change) change to the pressure solver. I will try and do this this afternoon.

[marinlauber]

I have just removed the debug flags. I will correct the test and run the TGV on GPU for benchmark.

[b-fg]

Can you please post here the benchmark results? Just to document it in this issue too.

[b-fg]

Also tests are not passing, please have a look at that too :)

[marinlauber]

Results of running ./benchmark.sh

Benchmark environment: jelly sim_step! (max_steps=100)
▶ log2p = 5
┌─────────┬───────────┬────────┬───────────┬─────────────┬────────┬──────────┬──────────┐
│ Backend │ WaterLily │ Julia  │ Precision │ Allocations │ GC [%] │ Time [s] │ Speed-up │
├─────────┼───────────┼────────┼───────────┼─────────────┼────────┼──────────┼──────────┤
│   CPUx1 │   5dea927 │ 1.10.0 │   Float32 │     2262206 │   0.15 │     8.82 │     1.00 │
│   CPUx6 │   5dea927 │ 1.10.0 │   Float32 │     8314557 │   1.16 │     2.23 │     3.95 │
│     GPU │   5dea927 │ 1.10.0 │   Float32 │     4204607 │   1.23 │     0.79 │    11.10 │
│   CPUx1 │   f73b0f8 │ 1.10.0 │   Float32 │     2701319 │   0.17 │     9.66 │     0.91 │
│   CPUx6 │   f73b0f8 │ 1.10.0 │   Float32 │     9932893 │   1.27 │     2.62 │     3.36 │
│     GPU │   f73b0f8 │ 1.10.0 │   Float32 │     5081400 │   1.34 │     0.94 │     9.36 │
└─────────┴───────────┴────────┴───────────┴─────────────┴────────┴──────────┴──────────┘
▶ log2p = 6
┌─────────┬───────────┬────────┬───────────┬─────────────┬────────┬──────────┬──────────┐
│ Backend │ WaterLily │ Julia  │ Precision │ Allocations │ GC [%] │ Time [s] │ Speed-up │
├─────────┼───────────┼────────┼───────────┼─────────────┼────────┼──────────┼──────────┤
│   CPUx1 │   5dea927 │ 1.10.0 │   Float32 │     3193860 │   0.19 │    44.65 │     1.00 │
│   CPUx6 │   5dea927 │ 1.10.0 │   Float32 │    11733545 │   1.08 │    11.57 │     3.86 │
│     GPU │   5dea927 │ 1.10.0 │   Float32 │     5957765 │   0.71 │     2.02 │    22.06 │
│   CPUx1 │   f73b0f8 │ 1.10.0 │   Float32 │     4208427 │   0.22 │    48.49 │     0.92 │
│   CPUx6 │   f73b0f8 │ 1.10.0 │   Float32 │    15447345 │   1.18 │    13.85 │     3.23 │
│     GPU │   f73b0f8 │ 1.10.0 │   Float32 │     7946898 │   0.80 │     2.55 │    17.51 │
└─────────┴───────────┴────────┴───────────┴─────────────┴────────┴──────────┴──────────┘

Benchmark environment: tgv sim_step! (max_steps=100)
▶ log2p = 6
┌─────────┬───────────┬────────┬───────────┬─────────────┬────────┬──────────┬──────────┐
│ Backend │ WaterLily │ Julia  │ Precision │ Allocations │ GC [%] │ Time [s] │ Speed-up │
├─────────┼───────────┼────────┼───────────┼─────────────┼────────┼──────────┼──────────┤
│   CPUx1 │   5dea927 │ 1.10.0 │   Float32 │     1271364 │   0.17 │     8.11 │     1.00 │
│   CPUx6 │   5dea927 │ 1.10.0 │   Float32 │     4677263 │   0.93 │     2.05 │     3.95 │
│     GPU │   5dea927 │ 1.10.0 │   Float32 │     2304513 │   1.67 │     0.50 │    16.25 │
│   CPUx1 │   f73b0f8 │ 1.10.0 │   Float32 │     1357166 │   0.19 │     8.27 │     0.98 │
│   CPUx6 │   f73b0f8 │ 1.10.0 │   Float32 │     4999132 │   1.12 │     2.11 │     3.85 │
│     GPU │   f73b0f8 │ 1.10.0 │   Float32 │     2469674 │   1.42 │     0.55 │    14.74 │
└─────────┴───────────┴────────┴───────────┴─────────────┴────────┴──────────┴──────────┘
▶ log2p = 7
┌─────────┬───────────┬────────┬───────────┬─────────────┬────────┬──────────┬──────────┐
│ Backend │ WaterLily │ Julia  │ Precision │ Allocations │ GC [%] │ Time [s] │ Speed-up │
├─────────┼───────────┼────────┼───────────┼─────────────┼────────┼──────────┼──────────┤
│   CPUx1 │   5dea927 │ 1.10.0 │   Float32 │     1146285 │   0.09 │    49.56 │     1.00 │
│   CPUx6 │   5dea927 │ 1.10.0 │   Float32 │     4007692 │   0.63 │    12.00 │     4.13 │
│     GPU │   5dea927 │ 1.10.0 │   Float32 │     1915606 │   0.31 │     1.26 │    39.48 │
│   CPUx1 │   f73b0f8 │ 1.10.0 │   Float32 │     1326286 │   0.15 │    51.17 │     0.97 │
│   CPUx6 │   f73b0f8 │ 1.10.0 │   Float32 │     4688832 │   1.02 │    12.39 │     4.00 │
│     GPU │   f73b0f8 │ 1.10.0 │   Float32 │     2264255 │   0.61 │     1.36 │    36.51 │
└─────────┴───────────┴────────┴───────────┴─────────────┴────────┴──────────┴──────────┘

[marinlauber]

I fixed the tests. It should be fine now.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (5dea927) 96.44% compared to head (577b12e) 96.45%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master      #97   +/-   ##
=======================================
  Coverage   96.44%   96.45%           
=======================================
  Files          12       12           
  Lines         450      451    +1     
=======================================
+ Hits          434      435    +1     
  Misses         16       16           

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[weymouth]

Speed-up, passing tests, and closes a issue. Merging!

[weymouth]

@marinlauber Why are there three computed residuals? It looks like only r₂ is used.