» Symbolically generated GPU-based LBM
Experimental generation of OpenCL kernels using SymPy, Mako and PyOpenCL.
- Implements a straight forward AB pattern
- All memory offsets are statically resolved
- Underlying symbolic formulation is optimized using CSE
- Characteristic constants of D2Q9 and D3Q27 are transparently recovered using only discrete velocities
This code was originally written for a seminar report on the advantages of symbolic generation of LBM implementations.
The source is available on Github and cgit alongside detailed benchmarks on both a older Nvidia K2200 and a more recent Nvidia Tesla P100. All in all the results of the CSE-optimized versions are surprisingly good, reaching up to 99.8% of the theoretical upper performance limit.
Performance
Theoretical maximum performance on tested hardware:
| GPU | Bandwidth | D2Q9 | D3Q19 | D3Q27 | |||
|---|---|---|---|---|---|---|---|
| single | double | single | double | single | double | ||
| K2200 | 63.2 GiB/s | 893 | 459 | 435 | 220 | 308 | 156 |
| P100 | 512.6 GiB/s | 7242 | 3719 | 3528 | 1787 | 2502 | 1262 |
Maximum measured performance…
| GPU | D2Q9 | D3Q19 | D3Q27 | |||
|---|---|---|---|---|---|---|
| single | double | single | double | single | double | |
| K2200 | 843.4 | 326.4 | 423.2 | 163.8 | 303.0 | 116.0 |
| P100 | 6957.4 | 3585.0 | 3420.2 | 1763.8 | 2374.6 | 1259.6 |
…relative to theoretical maximum
| GPU | D2Q9 | D3Q19 | D3Q27 | |||
|---|---|---|---|---|---|---|
| single | double | single | double | single | double | |
| K2200 | 94.4% | 71.1% | 97.3% | 74.5% | 98.4% | 74.4% |
| P100 | 96.1% | 96.4% | 96.9% | 98.7% | 94.9% | 99.8% |
For more details see the result/ and notebook/ directories.