Pushing Memory Bandwidth Limitations Through Efficient Implementations of Block-Krylov Space Solvers on GPUs

Understand

Lattice quantum chromodynamics simulations in nuclear physics have benefited from a tremendous number of algorithmic advances such as multigrid and eigenvector deflation.

• These improve the time to solution but do not alleviate the intrinsic memory-bandwidth constraints of the matrix-vector operation dominating iterative solvers.
• Batching this operation for multiple vectors and exploiting cache and register blocking can yield a super-linear speed up.
• Block-Krylov solvers can naturally take advantage of such batched matrix-vector operations, further reducing the iterations to solution by sharing the Krylov space between solves.