This paper introduces a novel matrix-free approach leveraging optimized tensor contractions to accelerate finite-element fluid dynamics simulations, targeting superior performance on modern GPU architectures and exascale computing platforms.
Key findings
The proposed matrix-free approach is expected to achieve 3–5 × speedup over conventional matrix-based methods.
The method reduces memory footprint by orders of magnitude, addressing memory bandwidth limitations.
Sum-factorization techniques combined with cache-optimized data layouts and hardware-specific optimizations are used to enhance performance.
Limitations & open questions
The research is still in the proposal stage and requires validation and risk assessment.
The effectiveness of the approach on actual exascale platforms remains to be demonstrated.