Enhancing data locality of the conjugate gradient method for high-order matrix-free finite-element implementations
نویسندگان
چکیده
This work investigates a variant of the conjugate gradient (CG) method and embeds it into context high-order finite-element schemes with fast matrix-free operator evaluation cheap preconditioners like matrix diagonal. Relying on data-dependency analysis appropriate enumeration degrees freedom, we interleave vector updates inner products in CG iteration matrix-vector product only minor organizational overhead. As result, around 90% entries three active vectors are transferred from slow RAM memory exactly once per iteration, all additional access hitting cache memory. Node-level performance analyses scaling studies up to 147k cores show that proposed optimizations is two times faster than standard solver as well optimized pipelined s-step methods for large sizes exceed processor caches, provides similar near strong limit.
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ژورنال
عنوان ژورنال: International Journal of High Performance Computing Applications
سال: 2022
ISSN: ['1741-2846', '1094-3420']
DOI: https://doi.org/10.1177/10943420221107880