A study of optimization levers in a GPU pseudospectral Taylor–Green vortex solver

Preprint, not peer reviewed. The Taylor–Green vortex at Re = 1600 is the standard verification benchmarkfor incompressible turbulence solvers and is also useful for studyingGPU FFT performance. We port a Fourier pseudospectral solver to NVIDIA’snvmath-python and CuPy and, on a single A100, measure three transformleveloptimizations one at a time with the hardware/algorithm confoundingremoved: single- versus double-precision arithmetic, real-to-complex (R2C)versus complex-to-complex transforms, and cuFFT LTO-IR callback fusion.Three results follow. First, the single-precision speedup is ≈ 2× on a datacenterGPU with 1:2 FP64 throughput, not the ≈ 3× obtained on workstationclassparts that throttle FP64. As precision moves arithmetic intensity andmachine balance in opposite directions, the value of reduced precision ishardware-class-dependent rather than a fixed constant. Second, single precisioncosts no measurable accuracy. At matched resolution fp32 and fp64agree to five significant figures, and an error budget over precision, timestep, and grid places the converged peak dissipation at εmax ≈ 1.285 × 10^−2.Third, callback fusion is an amortizing optimization — a net loss at 128^3 anda 1.17–1.18× gain at 256^3 — with a structural ceiling set by the projectionand time-integration passes that have no transform to fuse into. It tradesmemory for speed whereas R2C does the reverse. Hardware profiling identifiesthe unifying cause as the mempry-boundedness of every kernel so eachlever turns out to be a byte reduction. Expressing any of them requires aplan-object FFT interface rather than a stateless one.