Enhancing data locality of the conjugate gradient method for high-order matrix-free finite-element implementations

@article{Kronbichler2022EnhancingDL,
  title={Enhancing data locality of the conjugate gradient method for high-order matrix-free finite-element implementations},
  author={Martin Kronbichler and Dmytro Sashko and Peter Munch},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.08909}
}
This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying on a data-dependency analysis and appropriate enumeration of degrees of freedom, we interleave the vector updates and inner products in a CG iteration with the matrix-vector product with only minor organizational overhead. As a result, around 90% of the… 

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