Parallelize Biot-Savart kernels

[camUrban]

Problem Statement

The Biot-Savart kernels in _aerodynamics_functions.py use nested loops over vortices and evaluation points. While they are JIT-compiled with Numba, they are not parallelized.

Proposed Solution

Investigate parallelizing the Biot-Savart kernel loops using Numba's prange or similar mechanisms to take advantage of multiple cores.

[IlyasFardaouix]

I think the root cause might be related to the fact that the prange function in Numba only works with arrays, but the Biot-Savart kernel loops are using indices directly. Have you tried using Numba's jit decorator with the nopython flag to ensure that the loops are compiled to machine code, which might provide a performance boost?

[camUrban]

Hi @IlyasFardaouix. The Biot-Savart kernels are actually already decorated with @njit (which is equivalent to @jit(nopython=True)). Also, based on Numba's documentation for prange, indices look like they should work fine.

[haotianh9]

I think the problem is here:

PteraSoftware/pterasoftware/_aerodynamics_functions.py

Lines 539 to 541 in 68aa6c4

	if r0 < _eps:
	singularity_counts[0] += 1
	continue

this code block and several other simillar ones are creating race conditions, preventing parallel from actually happening.

the fixed version get speedup starting from 200 points × 100 vortices system, where it gets 3.07x speedup on my own machine . Thus, you probably need a switch between whether parallel or not based on current problem size (even better if this can be automatically tested and selected on initial run for each machine).

btw, it seems to me that these race conditions created by singularity_counts are diagnotstic only, probably you can have a compile time" option to make it not appear at production run, only at debugging process

I have created pull request #162 for this, and will continue working on using GPU to accelerate this further

[camUrban]

@haotianh9 That's a good point about using some form of size-based switch that diverts to parallel or serial implementations of the kernels. Let's discuss further in #161.