Solving DWF Dirac Equation Using Multi-splitting Preconditioned Conjugate Gradient with Tensor Cores on NVIDIA GPUs

Understand

We show that using the multi-splitting algorithm as a preconditioner for the domain wall Dirac linear operator, arising in lattice QCD, effectively reduces the inter-node communication cost, at the expense of performing more on-node floating point and memory operations.

• Correctly including the boundary \textit{snake} terms, the preconditioner is implemented in the QUDA framework, where it is found that utilizing kernel fusion and the tensor cores on NVIDIA GPUs is necessary to achieve a sufficiently performant preconditioner.
• A reduced-dimension (reduced-$L_s$) strategy is also proposed and tested for the preconditioner.
• We find the method achieves lower time to solution than regular CG at high node count despite the additional local computational requirements from the preconditioner.