Fix #2546: Implemented ADT-based probe search and batched AllReduce

[guptapratykshh]

Proposed Changes

This PR addresses the performance bottleneck experienced when using a large number of probes (e.g., >100) in parallel simulations. The previous implementation used a brute-force O(N) linear search per probe to find the nearest grid point, resulting in O(N_probes * N_points) complexity which caused significant slowdowns.

The changes include:

1. ADT-Based Nearest Neighbor Search: Implemented an Alternating Digital Tree (ADT) strategy for probe location. This reduces search complexity to O(log(N_points)) per probe. A heuristic is used to switch to ADT only when the number of probes exceeds a threshold (default: 10).
2. Batched Communication: Consolidated the AllReduce operations for probe values. Instead of performing one MPI reduction per probe, all probe values are now collected and reduced in a single batched operation at the end of the output routine, significantly reducing MPI overhead.
3. Regression Testing: Added a new regression test case (test_11_probes.cfg) to parallel_regression.py that specifically exercises the ADT path (11 probes) and verifies the correctness of the probe output against known values.

Related Work

Fixes issue #2546 (Probe performance bottleneck).

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

[guptapratykshh]

Please look into this PR , while removing the formatting all the changes of the file (CFlowOutput.cpp) were removed by mistake in the last PR. @pcarruscag

[pcarruscag]

Thanks, looks good now.

[bigfooted]

@guptapratykshh can you update the regression values in parallel_regression.py (after you've checked that everything works as intended)?

[pcarruscag]

Are you using AI to review PRs @bigfooted?
Why would this PR change the probe value @guptapratykshh?!

[pcarruscag]

Unexplained regressions

[guptapratykshh]

The values I initially committed for this new test case (probe_performance_11) were incorrect: the probe values were accidentally taken from Iteration 0 (initialization), while the RMS density was from the last iteration.

I updated parallel_regression.py to consistently check the values at the final iteration (Iter 3), ensuring the test actually validates the simulation result.

[pcarruscag]

The regression values for test flatplate_udobj changed, this case only uses one probe, hence its results should not be affected by the ADT change. I suspect some kind of memory error or undefined behavior.
Please determine what is introducing the discrepancy.